Module 1

Risk is defined as an uncertainty concerning the occurrence of a loss .ex: the loss of being killed by a speeding vehicle. Under risk mgmt risk is identified with life or property being insured. So we hear such statements as the building is unacceptable risk or the driver is poor risk.

Objective risk :-( degree of risk) is defined as the relative VARiation of actual loss from the expected loss. This decreases as the number of exposures increase. It VARies inversely with the square root of the number of cases under observation. Suppose 10,000 houses are built and 1% of these are to burn per year. That means 100 are to burn. That does not mean that 100 houses will exactly be burnt. It may VARy plus or minus. Objective risk may be calculated by using some statistical measure like sd/cv. because obj -risk can be measured it is an extremely useful concept for an insurer as the number of exposures increases an insurer can predict its future loss more accurately

The law of large numbers state that as the number of exposures unit increases the more closely the actual loss experience will approach the expected loss experience.2. Subjective risk:- this is the uncertainty based on a mental condition or state of mind of a person. Ex:- a person in a drunken state might drive home. He is uncertain whether he will reach home safely or would be caught by the police. The mental uncertainty is called as subjective risk. Two different may alter their course of action like taking an auto home instead of driving.

Chance of loss is closely related to the concept of risk. It is defined as the probability that an event will occur. like risk probability has both objective and subjective aspects.Objective probability:- it refers to the long run relative frequency of an event based on the assumption of an infinite number of observations and of no change in the underlying conditions

Objective probability can be determined in two ways:-1. They can be determined by deductive reasoning. These are also

call-ed as priori probabilities. (toss of a coin where the answer is ½. Also in case of a dice where the probability is 1/6.

2. Objective probabilities can be determined by inductive reasoning rather than by deductive reasoning. Ex:- probability that a person will die before 25 when his age is 21 years cannot be logically deduced. But if current mortality rates are seen then an insurance policy can be sold for people aged 21 years.

Chance of loss.

Subjective probability

It is the individual personal estimate of the chance of loss. This need not coincide with objective probability. Ex:- people buying lottery tickets on their birthday expecting luck. Factors affecting subjective probabilities are age, gender, intelligence, education, beliefs, use of alcohol etc.

Chance of loss distinguished from risk.Chance of loss is the probability that an event that causes a loss will occur. objective risk is the relative VARiation of actual loss from expected loss. the chance of loss may be identical for two different groups but objective risk may be quite different. ex:- chances of accidents in 2 towns.

Perils and hazardsPerils are the cause of loss. ex:- fire, lightening, floods, earthquake etcHazards are conditions that creates or increases the chance of loss. There are 4 types of hazards:-

1. Physical. 2. Moral 3. Morale. 4. Legal hazards.

Hazards.1. Physical hazards:- these are the physical conditions that

increases the chance of loss (bad roads)2. Moral hazards:- dishonesty or character defects in an individual

like faking injury or making fraudulent claims.3. Morale hazards:- these are carelessness because of the existence of insurance. These increase the chances of loss.4. Legal hazards:-these are the characteristics of the legal system or the regulatory environment. Ex:- adverse jury verdict, Govt. schemes of insurance giving undue benefits

Categories of risk.

1. Pure and speculative risk.2. Fundamental and particular risk.

3. Enterprise risk.Pure risk is defined as situation in which there are only the possibilities of loss or no loss. The only possible outcomes are adverse or neutral (no loss)Speculative risk is a situation in which either profit or loss is possible. Differences:-1. Private insurers underwrite only pure risk.2. The law of large numbers applies to pure risk only.3. Society may benefit from speculative risk even though loss occurs. Example new technology used benefits some. ISRO rockets Programme helps some. Fundamental risk affects the whole economy like famine, natural disasters, terrorist attacks etc.Particular risk affects only the individuals like theft, robberies.Enterprise risk is the major risk faced by a business firm like pure risk, financial risk, speculative etc.

Types of pure risk

Causing financial insecurity1. Personal risk:- premature death, insufficient income during

retirement, poor health, unemployment.2. Property losses like direct loss, indirect losses, (loss of

customers).3. Liability risk:- (bodily injury because of accidents).

Insurance.

The American risk and insurance association has defined insurance as follows:- it is the pooling of fortuitous losses by transfer of such risks to insurers who agree indemnify insured for such losses to provide other pecuniary benefits on their occurrence or to render services connected with the risk.Insurance:-basic characteristics

1. Pooling of losses.2. Payments of fortuitous losses.3. Risk transfer.4. Indemnification of losses.

Pooling of losses:-this is the spreading of losses incurred by the few over the entire group so that in the process average loss is substituted for actual loss.

It involves grouping of a large number of exposure units so that the law of large numbers can operate to provide a substantially accurate

prediction of future losses. Ideally there should be a large number of similar but not necessarily identical exposure units that are subject to the same peril.

2. Payment of fortuitous lossA fortuitous loss is one that is unforeseen and unexpected and occurs as a result of chance. That means the loss must be accidental and occur randomly. Insurance policies cover only accidental losses and not intentional losses.

3.risk transferRisk transfer means that a pure risk is transferred from the insured to the insurer who typically is in a stronger financial position to pay the loss than insured. From the point of an individual pure risk are premature deaths, poor health, destruction of property personal lawsuits etc.4. IndemnificationIndemnification means that the insured is restored to his or her approximate financial position prior to the occurrence of loss. This is feasible only in case of non life insurance like fire, marine and other non life policies.

Meaning of Risk MgmtIt is a process that identifies loss exposures faced by an organization and selects the most appropriate techniques for treating such exposures. Risk as a term is very ambiguous so using the term loss exposure is considered more appropriate. Loss exposure is any situation or circumstance in which a loss is possible, regardless of whether a loss occurs. here risk managers consider only pure risk exposures faced by the firm .of late even speculative loss exposures are being considered.

Risk management-objectives1. Pre loss objectives.2. Post loss objectives.Pre loss objectives:- the important objectives before a loss occurs include economy, reduction of anxiety and meeting legal obligations.Pre loss objectives

1. The firm should be prepared for potential losses in the most economical way. this preparation involves an analysis of the cost of safety programs, premiums paid and the cost handling losses.

2. Reduction of the anxiety of the risk manager and the key executives.(catastrophic law suit

3. To meet any legal obligations:-

This may be asking the firm to install safety devices, pollution controlling devices, waste disposal etc. The insurance manager must try to ensure that these are provided.

Post loss objectivesRisk management also has certain objectives after a loss occurs:-

1. Survival of the firm. (resume operations in a short time)2. Continue to operate.(competitors would take up the business)3. Stability of earnings.4. Growth of the firm.5. Minimize the effects of loss to the others/society.

Risk management process1. Identify the loss exposures:-

Here we identify all major and minor loss exposures. This involves analysis of all potential losses. A) Property loss exposureB) Liability loss exposures.C) Business income losses.D) Crime loss. E) Foreign loss exposures f) reputation loss2. Analyze the loss exposures:-

a) Loss frequency (probable no. Of losses in a time period)b) Loss severity (size of the loss)

These are done for each type of exposure. when done it helps in finding out the techniques for handling the exposures/estimating the max possible losses.3. Selecting the appropriate technique for treating the loss exposure

a) Risk control b) risk financing.Risk control:-this is a technique for controlling the severity of loss.

1. Avoidance:- (dangerous drugs)2. Loss prevention.( using measures)

3. Loss reduction:- these are the measures to avoid the severity of a loss after it occurs. (Future) uses the sprinklers for fire prevention, having decentralized stores, limiting of the amount of cash so that the chances of theft are avoided, safety programs being implemented in the premises.Risk financing:-this is the funding the losses after the loss have occurred.1. Retention: this is retaining the part or all of the losses that can result from a given loss. this may be active/passive. Active is the retention when the firm is aware of its acts and passive when the firm neglects its acts like forgetting to act , failure to act, failure to identify the loss exposure. Risk retention level:- a firm has to determine its risk retention level. A strong firm can retain a higher amount of risk than a weaker firm. Here

a firm can estimate the maxi-mum level of risk it can absorb without insuring like % of annual earnings or % of working capital. If the risk is retained then the firm should think of how it would finance the risk:-

a) Current net income.b) Funded reserve.c) Unfunded reserve (book entries)d) Credit line with bankers using borrowed funds.

2.non insurance transfers:- these are methods used in which the pure risk and its financial consequences are transferred to some other firm like leased transfers, contracts, agreements, annual maintenance contracts etc.3. Commercial insurance contracts on yearly basis.

Module 2

Risk management Futures and forwardsa derivative instrument is a financial contract whose payoff structure is determined by the value of an under-lying commodity, security, interest rate, share price index exchange, oil price and like. so a

derivative instrument derives its value from some underlying VARiable. a derivative instrument promises to convey ownership.DerivativesAll derivatives are based on some cash products. it includes commodities, metals, foreign exchange, bonds, short term debt securities such as t- bills, over the counter money market products like loan or deposits. the purposes for which derivatives are used are:-

1. Reduction of funding costs.2. Enhancing the yield on assets.3. Modifying the payments structure of assets to correspond to the

investors market view. but the most important use of derivatives is in transferring market risk called as hedging which is protection of losses .

Hedging is protection against losses resulting from unforeseen price or volatility changes. So hedging is a very important tool of risk management.there are many kinds of derivatives: futures, options, interest rate swaps and mortgage derivatives.Forward contractsa deal for the purchase or sale of a commodity security or other asset can be in the spot or forward markets. a spot or cash market is most commonly used for trading. in a forward contract the buyer agrees to pay cash at a later date when the seller delivers goods. Usually no money changes hands when forward contracts are made. Normally one of the parties may ask for some initial good faith deposit to ensure that the contract is honored. Here the price at which the contract is entered is decided at the time of entering into the contract.

The essential idea of entering into a forward contract is to peg the price and thereby avoid the price risk. So one is assured of the price at which one can buy/sell goods or other assets. so the risk of price moving adversely is avoided. At the maturity of a contract if the market price is greater than the agreed price the buyer gains.

Forward contracts have been in existence for some time. The formal start to it happened in 1848 when the Chicago board of trade was established as a commodities exchange. A forward contract is a good means of avoiding price risk. Each party faces the risk of default.

Once a position of buy/sell is taken an investor cannot retreat with-out the consent of the other party or by taking a reverse posit-ion of the earlier contract. These are contracts entered on a one to one basis and with no standardization. The problems of credit risk and no liquidity led to the formation of futures contracts.

futures contracts.a futures contract represents an improvement over the forward contracts in terms of 1. Standardization, 2. performance and 3. Liquidity.a futures contract is a standardized contract between two parties where one of the parties commits to sell and the other to buy .

This is done for a stipulated quantity, quality of a commodity, currency, security, index or some other specified item at an agreed price on a given date in the future. the future contracts are standardized ones so that :-1. The quantity of the commodity could be transferred or would form a basis of gain/loss on maturity of contract.2. The quality of a commodity, and the place of its delivery would be made.3. The date and month of delivery.4. The units of price quotation.5. The minimum amount by which the price would change and the price limits for days operations are specified.Futures contracts are traded on commodity or other future exchanges. People buy and sell futures as like other commodities.when an investor buys a futures contract ( he takes a long position) on an organized exchange he is in fact assuming the right and obligation of taking the delivery of the item on the specified date. When an investor takes a short position one assumes the right and obligation to make delivery of the underlying asset. There is no risk of non performance in the case of trading in futures contract. This is because of the clearing house which plays a pivotal role in the clearing.A clearing house takes the opposite position in each trade, so that it becomes a buyer to a seller and a seller to a buyer. When a party takes a short position it is obliged to sell the commodity at the stipulated price to the clearing house on the maturity of the contract.the clearing house guarantees the performance of the futures contracts, the parties in the contracts are required to keep margins with it. The margins are taken to ensure that each party to a contract performs it. The margins are adjusted on a daily basis to account for gains and losses.this depends on the price at which the futures contracts are being traded in the market. This is known as marking to the market and involves giving a credit to the buyer of the contract if the price of the contract rises and debiting the seller’s account by an equal amount.Similarly the buyers balance is reduced when the contract price declines and the sellers account is accordingly updated. in effect the profit/loss on a futures contract is settled daily and not on maturity of the contract as for a forward contract.

it is not necessary to hold on to a futures contract until maturity and one can easily close out a position. Either of the parties may reverse their position by initiating a reverse trade so that the original buyer of a contract can sell an identical contract at a later date canceling the earlier.the fact that the buyer as well the seller of a futures contract are free to transfer their interest in the contract to another party makes such contracts essentially marketable instruments. Futures contracts are highly liquid in nature. here a small number of contracts are held for deliveryDifferences forwards and futures contracts:

1. standardization:- a forward contract is made by the seller and the buyer where the terms are settled mutually. in a futures contract the transaction as regards quantity / quality / place etc are standardized. Only the price is negotiated.

2. Liquidity:- There are no secondary markets for forward contracts while the futures are traded on organized exchanges. so futures contracts are more liquid than the forward contracts.

3. Conclusion of contract:-a forward contract is generally concluded with a delivery of the asset in question whereas a futures contract is concluded either with delivery of goods or by paying up of price differences. This has to be done before the conclusion of the maturity of the first contract and is called as offsetting a trade.

4. Margins:-a forward contract has zero value for both the parties as no collateral is required. But in a futures contract a third party called clearing corp. is also involved with which margin is required to be kept by both parties. 5. profit/loss settlement:-The settlement of a forward contract takes place on the date of maturity so that profit/loss is booked on maturity. Futures contracts are marked to daily so that the profits or losses are settled daily.

Classification of derivatives based on features1. nature of contracts:-

a) Forward rate contracts and futures. b) Options. c) Swaps.The nature of the contract sets upon the rights and obligations of both the position to the contract.

2. Underlying asset:- there can be a contract which is similar in all aspects except for the underlying asset. a) Foreign exchange. b) Equities.c) Interest bearing financial assets.d) Commodities. Ex:- options in currency/stock.3. Market mechanism:- a) OTC products. b) Exchange traded products.role of a clearing house:- it performs two critical functions.1. Offsetting customer’s dealings.2. Assuring the financial integrity of the transactions in exchange. Important features of derivatives.

Derivatives became very popular because of their unique nature. They offer a combination of characteristics which are not found in other assets. There are four important features that distinguish derivatives from the underlying assets and make them useful for a VARiety of purposes.1. Relation between the values of derivatives and their underlying assets:-When the value of underlying assets change so do the value of derivatives based on them. Ex:- if the product price changes the instrument price also changes. in a currency future contract price to be paid is fixed by the future contract. This is done by depending on the movement of the underlying currency. the relation between values of the underlying assets and options are more complicated but the values of the option and the underlying assets are still to be related so derivatives appear similar to real commodities.2. It is easier to take short position in derivatives than in other assets: - as all transactions in derivatives take place in future specific date it is easy for the investor to sell the underlying assets. He can take view of the market /product which is not possible in any other assets. 3. exchange traded derivatives are liquid and have low transaction cost: - this is because of standardized terms and low credit risk. Transaction cost is low because of high volume of trade and due to high competition. Also margin requirements in exchange traded derivatives are very low so risk associated is very low. 4. it is possible to construct a portfolio which is exactly needed without having the underlying assets:- ex:- a person with a floating rate of interest can limit his exposure by buying interest rate cap. This derivative pays the firm the difference between the floating rate and predetermined max cap rate whenever the rate increases exceeding the cap.

participants in derivatives market.the participants can be banks, FI’s, brokers, corporate, individuals etc. the participants are:-

1. hedgers:-a transaction in which an investor seeks to protect a position in the spot market by using an opposite position in the derivatives is known as hedge. These are people who want to reduce risk or eliminate risk. These are people exposed to risk in normal business operations and try to eliminate risk. 2. Speculators: - a person who trades expecting to make profit out of price changes. These are people who voluntarily accept what hedgers want to avoid. He has a view on the market and based on the forecast he takes a long /short position in the derivatives.3. Arbitrageurs:- arbitrage means obtaining risk free profits by simultaneously buying and selling identical instruments in different markets. They consistently keep track of the different markets. Whenever there is any chance of getting profit without any risk they will take the position and make risk less profits.

Participants in derivatives market.They perform a very valuable economic function by keeping the derivatives prices and current underlying assets price closely consistent. Arbitrageurs are in the same class as that of speculators to the extent that they have no risk to hedge. They make money out of changes in price in different markets.

Derivative market in Indiain December the securities contract regulation act was amended to include derivatives within the sphere of securities and the regulatory framework was developed for governing derivatives trading. The act also specified that derivatives shall be legal and valid only when traded on recognized stock exchanges.Derivatives trading commenced in India in June 2000 after the grant of final approval by SEBI to this effect in may 2000. SEBI permitted the derivatives segments of two stock exchanges: - NSE and BSE and their clearing houses to commence trading and settlement in approved derivatives contracts. Initially SEBI approved trading in index futures contracts based on S&P CNX NIFTY and BSE-30(SENSEX) index. This was followed by approval for trading in options based on these two indexes and options on individual securities. the trading in SENSEX options and trading in options on individual securities started June 2001.Derivatives trading on NSE started with S&P CNX NIFTY index futures in June 2000.futures contracts on individual stocks were launched in

November 2001 while the trading in index options commenced in June 2001 and trading in options on individual securities began in July 2001.Types of derivative instruments available in India:-

1. forwards.- a forward contract is a contract between two parties to buy or sell an underlying asset at today’s pre-agreed price on a specified date in the future.Derivative market instrument in IndiaForward contracts in India can be booked by companies, firms and any person having authentic foreign exchange exposures only to the extent and in the manner allowed by RBI. Foreign exchange brokers are not allowed to book the contract.2. Futures. 3. Options.4. Swaps:-These are derivative products which are traded between two parties as a private agreement and not on exchanges. These are traded between dealers. The swaps normally dealt are currency swaps and interest rate swaps.

Mechanism of futures marketsFutures contracts are traded in auction markets where the prices are order driven. In these markets each broker and trader can buy at the lowest offered price and sell at the highest bid price and the liquidity is maintained by the participation of these buyers and sellers.Some of these buyers and sellers are hedgers seeking to protect their investments, some are speculators who are risk-takers seeking to trade in pursuit of profit incidentally keep bid and ask prices close together and to provide efficient trading in the system.Futures contracts are designed in such a way so that their prices should always reflect the prices of the underlying cash market. The activities of speculators and arbitrageurs also bring in price alignment. In “calendar spreading” traders sell the current delivery month contract and buy a later delivery month contract.This reduces the price VARiance between the futures contracts. Arbitrage also helps keep the cash and futures prices aligned. Ex: - futures contracts seem to be overpriced in relation to the underlying commodity, arbitrageurs will sell the futures contract and simultaneously buy the commodity making profit.

History of futures marketsThis was originally established to meet the needs of the farmers and merchants. Farmers have to face risk of prices and this depends on the vagaries of VARious kinds. The companies who buy grain also face the uncertainty and price risk. This is on account of over supply and scarcity in the market.

It makes sense to make some sort of futures contracts. The contracts provide a way for each side to eliminate the risk it faces because of the uncertain future price of grain. in 1848 the Chicago board of trade was established to bring farmers and merchants together. This was done to standardize the quantity and quality of trade.

Chicago board of tradeWithin a few years the first futures type contract was established and called as “to arrive” contract. Speculators became interested in contract and found trading the contract to be a better alternative than trading in the grains. The Chicago board of trade now offers futures contracts on other underlying assets including Soya products and treasury bonds and notes. The Chicago mercantile exchange:In 1874 the Chicago produce exchange was established providing a market for butter, egg, poultry, and other perishable agricultural product. In 1919 it was renamed as the Chicago mercantile exchange and was reorganized for futures trading. Since then it has taken care of VARious products and in 1982 it introduced futures on S&P 500 STOCK index.

Traditionally futures have been traded by “open outcry” system. This involves using a complicated system of hand symbols for physical trading on the floor. In 1981 CME introduced Eurodollar future which gave way to futures on stock indexes and option products. in 1992 it went electronic.

Other exchangesMany other exchanges throughout the world trade futures contracts. Among them the popular exchanges are 1. London International Financial Futures Exchanges (LIFFE) TOKYO International Financial Futures Exchange (TIFFE), Singapore International Monetary Exchange (SIMEX), Sydney Futures Exchange (SFE).

Clearing house.A clearing house is an institution that clears all the transaction undertaken by a futures exchange. It could be part of the same exchange or a separate entity. It computes the daily settlement amount due to or from each of the members and from other clearing houses and match the same.Members who execute trade on the exchange floor are of two types.

1. Floor brokers: - these brokers will execute the orders on others account. These people are normal-ly self employed individual member of the exchange.

2. Floor traders: - these traders execute trades on their own account. Some also execute the orders for the account of others.

Floor tradersThis mechanism is known as dual trading and such traders are known as dual traders. Some of the floor traders are classified as ‘scalpers’. A scalper is a person who stands ready either to buy or sell. They add to the liquidity to the market as they are market makers. They are also called as ‘position traders’ they tend to carry the positions for longer period of time thereby adding liquidity to the market.

Contract specification for the futures.A futures contract between the two parties should specify in some detail the exact nature of the asset, price, contract size, delivery arrangements, delivery months, tick size, limits on daily price fluctuation and the trading unit.1. The asset:-the delivery of the asset needs to be specified at the time of entering into a contract. If the underlying asset is a commodity there may be VARiations in the quality and grade.

2. Price:- The price agreeable to the buyer and seller at the time of delivery of the contract is specified at the time of agreement. The futures prices if quoted are convenient and easy to understand3. The contract size:-It specifies the amount of asset to be delivered under one contract. If the size is too large many investors cannot use it for hedging/ speculation as the risk involved is too large. If it is too small then the coat of trading is too much.4. Delivery arrangements:-The place of delivery is very import-ant when transport cost is significant.5. Delivery months:-A futures contract is referred to by its delivery month. the period VARies from item to item.For example July corn, means that the contract is for delivery in July. For certain contracts the delivery period runs throughout the month. The date on which the contract ceases to trade is specified by the exchange. 6. Tick size:- the contract also specifies the minimum price fluctuation or tick size. For example in soybean con-tract, one tick is ¼ cent per bushel as the minimum size of contract for soybean is 5000 bushel. 7. Limits on daily price movements:-The daily price movements’ limits are specified by the exchange. If the price moves up by a limit it is referred to as limit up and vice versa.

The prime purpose of the daily price limit is to prevent large price fluctuations and to safeguard the interest of genuine traders.

Basis:The basis is the relationship between the cash price of a good and the futures price of that good. It represents the difference between the cash price and future price of a single commodity.Basis=current price-futures price. The futures market can portray a pattern of either normal/inverted.If the prices for more distant futures are higher than the nearby futures it is referred to as ‘normal’ market condition.In an ‘inverted market’ the distant futures are lower than the prices that are near to expiration. When the future contract is at expiration the futures price and spot price of a commodity is the same. So the basis must be zeroThis behavior pattern of the basis over a period of time is referred to as ‘convergence’. If the current price lies above the futures price and as the time elapses and future contract is nearing maturity, the basis narrows and at the time of maturity the futures price should be equivalent to cash price. Thus basis would be zero leading to no arbitrage situation.

Basis risk:If the hedge can eliminate the full risk it is a situation known as perfect hedging, but as some uncertainty is associated always with the future and the difference between the spot prices and future prices may change, there are chances of basis risk. so basis risk may arise because of imperfect hedging between spot price of the asset and the futures price of the contract used.

Spreads:A spread is the difference between two futures prices. For the same underlying good if there are two different prices on two different expiration dates the underlying spread is known ‘intra commodity’ spread.(or time spread)if the spread is between two different but related products then it is known as inter-commodity spread.

Concept of cost of carry :The extent to which the futures price exceeds the cash price at one point of time is determined by the concept of cost of carry that refers to the carrying charges. The carrying charges can be further classified into storage, insurance, transportation and financing cost. Carrying cost plays a crucial role in determining pricing relationships between spot and futures

Convenience yield, contango and backwardation

The shortage of the physical commodity is probably one of the reason for having additional cost other than cost of carrying. When there is a shortage in a commodity there is an implied yield (return) by holding the commodity. This yield is referred to as convenience yield. If the futures prices obtained by full carry relationship (cost of carry i.e. the estimated cost of futures prices) are accurately projected the basis is negative as the future prices are higher than the cash prices. This condition is referred to as ‘contango’ market (which means the prices of futures market are determined by cost of carry).This sort of market is featured by progressively rising future prices as the time to delivery becomes more distant. if the futures price is less than the cash price the basis is positive. This condition prevails only if the futures prices are determined by some other factors other than cost of carrying. When the future prices are lower than the cash prices it is known as backwardation. It is featured by lower futures prices as delivery becomes more distant

Expectation principleThis theory postulates that the expected basis would be equal to zero. This is based on the argument that futures prices are an unbiased estimate of expected future spot prices as would be expected in an efficient market. Thus there is no room for any excess returns for either the hedgers/speculator

Hedging using futures Hedging is the process of reducing exposure to risk. Hedge is any act that reduces the price risk of a certain position in the cash market. Similarly exports and imports are exposed to currency risk. This exposure can be hedged through derivatives like futures, options etc.

Hedging with currency futuresFutures are one of the derivatives where an exporter and importer can hedge their positions by selling/buying futures. as the futures market does not require upfront premium for entering into contract as in the case of options it provides an a cost effective way for hedging the exchange risk.Currency futures provide a means to hedge the traders’ position who wishes to lock in exchange rates on future currency transactions. By purchasing (long hedge) or selling (short hedge) foreign exchange futures a corporate or individual can fix the incoming and outgoing cash flows in one currency with another.Any one who is dealing with a foreign currency is faced with an exchange risk since the cash flows in terms of domestic currency are known only at the time of conversion. A person who is long or is expected to go long in a foreign currency will have to sell the same on a given day.

A hedge can be obtained now by selling futures in that currency against a domestic currency. Similarly a person who is short or is expected to go short in a foreign currency will have to go long on the same on a given day. A hedge may be obtained by buying futures in that currency against a domes-tic currency instead of buying the currency later in the spot market.

Determining the effective price using futuresLet sp1 be the spot price at time t1.Sp2 be the spot price at time t2.Ft1 be the futures price at time t1.Ft2 be the futures price at time t2.Sp1 – ft1= basis at t1Sp2 – ft2 =basis at t2.Let us assume that a transaction took place at t1 and closed at t2. Profits made in futures market by closing out position at t2= ft1- ft2. Price received for asset while selling in the spot market =sp2.=sp2+(ft1-ft2)=ft1+(sp2-ft2)=ft1+b2….. Where b2 represents basis at t2. As b2 is unknown the futures transaction is exposed to basis risk.If b2=b1 then the effective price at currency sold will be :-Ft1 +sp1 – ft1 =sp1.Hedge ratio:-a hedger has to determine the number of futures contracts that provide best hedge for his risk return profile. It allows the hedger to determine the number of contracts that must be employed to minimize the risk of the combined cash/futures position.That means the hedger has to take a futures position i.e. The number of the futures contracts times the quantity represented by each contract which will result in the maximum reduction in the VARiability of the value of his total hedged position. in simple form the hedge ratio hr is the ratio of size of the position taken in futures contracts to the size of the exposure.

Hedge ratioThe general definition of hedge ratio is:-Hr= futures position = qf cash market position qs where hr is the hedging ratio, qf is quantity (units) of the asset represented by futures position and qs is quantity of spot cash asset that is being hedged.

The basic long and short hedges

Hedging refers to by taking a posit-ion in the futures that is opposite to a position taken in the cash market or to a future cash obligation that one has or will incur. Hedging can be classified into two categories:-

1. Short hedge. 2. Long hedge.

Short and long hedge.Short hedge: - (selling hedge)Is a hedge that involves taking a short position in futures contract. In other words it occurs when a trader plans to purchase or produce a cash commodity sells future to hedge the cash position. It means having a sold position.It is a commitment to deliver. The main objective is to protect the value of the cash position against a decline in cash prices. A short hedge is appropriate when the hedger already owns an asset and expects to sell it at some time in the futures. Once the short futures are established it is expected that a decrease (increase) in the value of the cash position will be fully or partially compensated by a gain (loss) in short futures position.

Long hedge:A long hedge (or a buying hedge) involves taking a long position in the futures contract. The basic objective here is to protect itself against a price increase in the underlying asset prior to purchasing it in either the spot /forward market. A long hedge is appropriate when a firm has to purchase a certain asset in futures and wants to lock in a price now.It is also called as ‘being long’ or having a net bought position or an holding of the asset. It is also known as inventory hedge because the firm already holds the asset in inventory. The terms ‘long’ and ‘short’ apply to both the spot and futures market and are widely used in the futures trading.A person who holds stocks of an asset is obviously regarded as ‘being long’ in the spot market but it is not necessary to actually hold stock. Similarly it is in the case of ‘short’ where one who has made a forward sale regarded as ‘being short’ on the spot market.

Sometimes it is seen that the firms wish to hedge against a particular asset but no futures contract are available. This situation is called as asset mismatch. Further in many cases same futures period on a particular asset is not available, it is called as maturity mismatch.Referring to different situations as could be seen there is still a possibility to hedge against a price risk in related assets (commodities or securities) or by using futures contracts that expire on dates other than those on which hedges are lifted. Such hedges are called as cross hedges.

In actual practice and in real business world it will be rare for all factors to match so well. Thus a cross hedge is a hedge in which the characteristics of the spot and futures positions do not match perfectly, either in quantity, quality, maturity, or physical assets change between spot and futures markets.

Currency futuresIn 1972 Chicago mercantile exchange was the first exchange to introduce the financial futures contracts. All developed countries start-ed importing a plethora of foreign goods which in turn created a demand for foreign currencies. So huge international transactions led to the development of foreign currency markets and futures. The foreign currency futures contracts need to specify a trading unit (dollar, pound etc), quotation (say, US$ per pound), minimum price change, contract months, us$ value of currency as on a day, and the delivery date. Presently Euro, Yen, Swiss Franc, British Pound Canadian Pound and Australian Dollar Are Traded On CME.Currency futures can be defined as “a binding obligation to buy or sell a particular currency against another at a designated rate of exchange on a specified future date. ”The contract size specifications for the few currencies traded in the CME are as follows:-

1. British pound- 62,500 as minimum trading qty.2. Canadian dollars- 1,00,000 minimum3. Japanese yen-12,500,000 as minimum4. Swiss francs-1, 25,000 as minimum.5. Australian dollar- 1,00,000 as min

Investment and consumption assets:Investment asset is an asset that is held for investment purposes by significant number of investors. Gold, silver, stocks and bonds are examples. A consumption asset is held purely for consumption. Ex:- copper, food articles etc. We can determine forward and futures prices for an investment asset for both spot and other VARiables. Short sellingShort selling or shorting involves selling as asset that is not owned. It is something that is possible for some but not for all investment assets. This is done by borrowing from another or investor. At some stage the investor has to purchase the share to close the deal. This is replaced with borrow-ed shares and profit is made if price falls. Short selling and short squeezedIf at any time while the contract is open the broker runs out of shares to borrow the investor is short squeezed and is forced to close out the position immediately even if not ready to do so. An investor with a short position must pay to the broker any income such as

dividend/interest that would normally be received on the securities that have been shorted. Determination of forward pricesREPO rate: - it refers to the risk free rate of interest for many arbitrageurs operating in the futures market. Repurchase agreement refers to the agreement where the owner of the securities agrees to sell them to a financial institution and buy the same back later. The repurchase price is slightly higher than the Treasury bill rate

Assumptions and notations1. There are no transaction costs.2. Same tax rate for all trading p/l.3. Lending/borrowing at risk free interest rate.4. Traders are ready to take advantage of arbitrage opportunities

as and when arise. These assumptions are equally available for all market participants (large/small.

5. T=time remained up to delivery date in the contract.6. S= spot market/cash market.7. K= delivery price at time t.8. F= forward/future price today.9. F = value of long forward today.10. R = risk free rate of interest.11. T = current or present period.

The forward priceWe consider three situations:-

1. Investment assets providing no income.2. Investment assets providing known income.3. Investment assets providing known yield/income (dividends.)4. Asset that provides no income.

This is the easiest forward contra-ct to value because such assets do not give any income to the holder. These are usually non-dividend paying equity shares and discount bonds. Ex: - consider a long forward contract to purchase a share (non div paying) in three months. Assume that the current stock price is Rs 100.

Forward price – of an asset providing no incomeThe three month risk free rate of interest is 6%p.a. Assume that the three month forward price is Rs 105:- the arbitrageur can borrow Rs 100 @ 6% for 3 months, buy one share at Rs 100 and short a forward contract for Rs 105, the sum of money required to pay off the loan is 100e 0.06*0.25 =101.50This way he will book a profit of Rs 3.50 i.e. 105-101.50.we can generalize as :- F = SERT

Where F= forward price of stock, S= spot price, T= maturity period, and R= risk free rate, e= expiration period.If F > SERT then the arbitrageur can buy the asset and wil go for a short forward contract on the asset.If F < SERT then he can short and go for long forward contract on it.

Forward prices that provides known cash incomeThese are for coupon bearing bonds, treasury securities etc:-Consider a long forward to purchase a coupon bond whose current price is Rs 900 maturing in 5 years. We assume that the forward contract matures in one year so that the forward contract is to purchase a four year bond in one year. Assume that the coupon payments are Rs 40, 6monthly and 12monthly. Also 6monthly and 12 monthly risk free interest is 9% and 10%.We assume that the forward price is high at Rs 930. In this case the arbitrageur can borrow Rs 900 to buy the bond and short a forward contract. Then the first coupon payment has a present value of:-40e-0.09*0.5 = Rs= 38.24. So the balance amount Rs 861.76 (900-38.24) is borrow-ed @ 10% for year. the amount owing at the end of the year is:-861.76e 0.1*1 =952.39. The second coup-on provides Rs 40 towards this amount and Rs 930 is received for the bond under the terms of the forward contract .the arbitrageur will earn (Rs 40 + 930) -952.39 = 17.61So it can be generalized that for such assets where the income is known the forward price would be F = (s – i) ert.If f>(s-i)ert the investor can earn the profit by buying the asset and shorting the asset forward and taking a long position in a forward contract and vice versa.

Forward price where the income is a known dividend yield

A known dividend yield means that when income expressed as a percentage of the asset life is known. Here we assume that dividend yield is paid continuously as a constant annual rate at q then the forward price for a asset would be: - f = se (r- q) tLet us consider a 6-month forward contract on a security where 4% p.a. Continuous div is expected. The risk free return is 10%, the current price is Rs 25. The forward price is f=se(r-q)t f=se (0.1-.04)*0.5 =25.76. If the forward price is > than the spot price then he can buy the asset and enter into a short forward contract to enter a lock in a risk less profit and vice versa.

Valuing forward contractThe value of a forward contract at the time of its writing is zero. However at a later date it may prove to be a +ve / -ve value. It may be determined as follows:- f = (f-k) e-rt where f=value of forward contract. F= forward price and k = delivery price of the asset, t = time to maturity and r= risk free return/risk free rate of interest. We compare a long forward contract that has a delivery price of ‘f’ with an otherwise identical long forward contract with a delivery price of ‘k’. we know that the for-ward price is changing with the passage of time and that is why later on f and k may not be equal which were otherwise equal at the time of entrance of contract. The difference between the two is only in the amount that will be paid for the security at the time ‘t’ under the first contract this amount is ‘f’, and under the second contract it is ‘k’. A cash outflow difference of f-t at the time t translates to a difference of (f-t)e-rt today.Therefore the contract with a delivery price of f is less valuable than the contract with a delivery price of k by an amount of (f-k)e-rt. The value of contract that has a delivery price of f is by definition zero. Similarly the value of a short forward contract with the delivery price k is f=(k-f)e rt.Consider a six month long contract of a non income paying security. The risk free rate of interest is 6% p.a. The stock price is Rs 30 and the delivery price is Rs 28. Compute the value of the forward contract.Forward price f=30e 0.06*.05 =rs30.90Value of forward contract=F= (f-k)e-rt (30.90-28)e -0.06*.5 =2.9-0.09= 2.81 app. Or f=30-28 -0.06*0.5 =2.84 app.We can show the value of long forward contract as:-

1. Asset with no income =f=s-ke-rt2. Asset with known income:-

f=s-i-ke-rt.3. Asset with known dividend yield. at the rate q:- f=se-qt –ke-rt .so in each case the forward price f is the value of k which makes f equal to zero.

Gain on long and short position per contractThe concept of the forward price for a forward contract is just like the future price for a future contract. A contract’s current forward price is the delivery price that would apply if the contract were negotiated today. The forward price is the delivery price which would make that contract to zero value. that means the forward price and the delivery price are equal at the time the contract is written.However in practice as the time passes the forward price is liable to change whereas the delivery price remains same. It means the forward

price and delivery price may not be equal at any time after the start of the contract except by chance. in fact the forward price at any given time VARies with the maturity of the contractThe forward price of a contract usually depends upon the spot and foreign exchange quotations given by VARious banks. As the for-ward rates are normally quoted for a year and available in forward exchange market the trader can easily make the adjustments in their forward rates.

Gains on long and spot positions per contractNotations:-

1. Ft t=forward price at time t of a contract that expires at time t.2. St =spot price at t (enter period).3. St = future spot price at t4. K = delivery price.

The profit and loss on a forward contract is determined by future spot rate st.

Gains on long and short position per contract.Those holding long forward positions, the profit will arise on the futures spot price is higher than the delivery price. (assume that the forward price and delivery price are the same) since the mark-et price of the asset is higher than the price at which the buyers (long) have contracted to buy. Gains on long position per contract =no of units*(future spot price – forward price or delivery price.)= no of units [st-k(or ft t)] Where the no of units is per contract. (Those holding short forward positions the gain will incur to them of the futures spot price falls below the forward price.) Gains on short position per contra-ct:- = no of units*(forward price-futures spot price)=no of units * [ft t(or k) –st] Where the number of units is per contract.

Theories of futures prices There are two important theories which have made efforts to explain the relationship between spot and futures prices. They are:-

1. The cost of carry approach.2. The expectation approach

1. The cost of carry approachTop economists like Keynes and hicks have argued that futures prices essentially reflect the carrying cost of the underlying assets. The interrelationship between the spot and futures prices reflect the

carrying costs i.e. The amount to be paid to store the asset from the present time to the future maturity time/ date.Carrying costs are of several types: 1. Storage costs. 2. Insurance costs. 3. Transportation costs. 4. Financing costs.1. Storage costs:- these are costs of storing and maintaining the asset in safe custody. Rent, pilferage, deterioration in quality etc.2 insurance costs:- amount incurred on safety of assets against fire, damage, accidents etc. the premium paid is called as insurance costs.3. Transportation costs:- when the futures contract matures then the delivery is to be given at a particular place and time at VARious locations.4. Cost of financing the underlying asset:-if gold costs Rs 5,000 per 10 grams and the cost of financing is 1% per month then Rs 50 is the financing charge.Apart from the carrying cost we may also have the possibility of earning a yield on storing the asset called as convenience yield. The marginal cost of carrying of an asset is:- ct = cgt - yt where:-Ct = net cost of carrying the asset.Cgt = gross carrying cost of that quantity.Yt = convenience yield.The cost of carry model in perfect market:-Future price= spot price +carrying cost.

Conditions of a perfect market:-No transaction cost, unlimited capacity to borrow/lend, borrowing rates are same, no credit risk, no margin for trading, no taxes, and goods can be stored without loss in quality.

The expectation approachThe economists argued that the futures prices as the market expectation of the price at the futures date. Traders who use the futures market to hedge would like to study how todays futures prices are related to market expectations about futures prices. Expected futures profit = expected futures price – initial future price any major deviation of the futures prices from the expected prices will be corrected by speculative activity. Profit seeking traders will trade as long as the futures price is sufficiently far away from the expected futures spot price.

Stock index futures A stock index or stock market index is a portfolio consisting of a collection of different stocks. That means a stock index

is just like a portfolio consisting of a collection of different securities proportions traded on a particular stock exchange like NIFTY S&P CNX, traded on NSE, the S&P 500 index is composed of 500 common stocks.

These indices provide summary measure of changes in the value of a particular segments of the stock markets which is covered by the specific index. This means that a change in a particular index reflects the change in the average value of the stocks included in the index.The number of stocks included in a particular index may depend upon its objectives and thus the size VARies index to index. For example the SENSEX has 30 stocks whereas 500 stocks are covered under standards and POOR’S 500.Common features:-1. A stock index covers a specific no of stocks like 30, 50, 100, 500 etc.2. Selection of a base period on which index is based. Starting value of base is 100, 1000 etc.3. The method or rule of selection of a stock for inclusion in the index to determine the value of the index.4. There are VARious methods used to calculate like arithmetic mean etc5. There are three types of index constructions like price weighted, return weighted and market capitalization weighted index.6. A stock index represents the change in the value of a set of stocks which constitute the index. 7. The index should represent the market and be able to represent the returns obtained by a typical portfolio of that market.8. A stock index also acts as the barometer for market behavior, a benchmark for the portfolio performance. It also reflects the changing expectations of the market.9. The index components should be highly liquid, professionally maintained and accurately calculated.A stock index futures contract is a future is a contract to buy/sell the face value of a stock index. The most actively traded index is the American S&P 500 index.

MODULE 3

Risk management using swapsThe term swap means to barter or to give in exchange or to exchange one for another. so swaps are private agreements between the two parties to exchange cash flows in the future according to a

prearranged formula. So swaps are an agreement to exchange payments of two different kinds in the future.

In the context of financial markets the term swap has two meaning:-1. It is a purchase and simultaneous forward sale or vice versa.2. It is defined as the agreed exchange of future cash flows possibly

but not necessarily with a spot exchange of cash flows.The second definition of swap is most commonly used stating as an agreement to the future exchange of cash flows. These can be regard-ed as series or portfolios of forward contract. Such a currency swap is similar to a succession of forward foreign exchange contracts with relatively distant maturity basis. The study of swap is thus a natural extension of forward and future contract. Financial swap is a specific funding technique which permits a borrower to access one market and then exchange the liability for another type of liability. Swaps can be helpful to change the nature of liability accrued on a particular instrument with the others.It means that swaps are not a funding instrument rather just like a device to obtain the desired form of financing indirectly which otherwise might be inaccessible or too expensive. Basically swaps involve the exchange of interest or currency exposures or a combination of both by borrowers.They may not necessarily involve the legal swapping of actual debts but an agreement is executed to meet certain cash flows under the loan or lease agreements.Swap market exist because different companies have specific access to VARious financial markets and they have different needs.Some companies have better access to Japanese markets than others where-as other’s may have good reputation in us markets. Some need floating rate of payments. So swap is a private agreement between the two parties to exchange predetermined amount of cash flows in future as per desired formula along with others terms.

Evolution of swap marketLike most new products/instruments in international finance swaps are not executed in a physical market. Participants and dealers in the swap market are many and VARied in their location, character and motives. Swaps originated in early 1970’s when many countries imposed foreign exchange restrictionsSome are of the opinion that swaps owe their origin to the exchange rate instability that followed the demise of the Bretton Woods system during the mid 1970’s. In 1980 a few countries liberalized their foreign exchange regime as a result some of the treasurers structured their portfolio’s and brought a new product called swaps.They replaced their back to back loans with swap deals which found them more flexible and simpler due to simpler documentation. It also

lowered financing cost and tax differences in comparison to the earlier contracts. Also MNC’s started directly interacting instead of banks.A major dramatic change in the swap market has been the emergence of large banks and performed as aggressive market makers in dollar interest rate swaps. They offered bid /offer quotes for both interest rate and currency swaps. Banks also found a counter party who exactly required the same to hedge the transaction. In 1984 the international swap dealers association was formed to speed up the growth in the swap markets by standardizing the documents. in 1985 the first swap code was devised. In 1987 it formed a standard forms agreement. These contracts are structured as master agreements.

Features of swaps.1. Counter parties:- all swaps involve the exchange of a series of

periodic payments between at least 2 parties.(example :- interest rate fixed/floating)

2. Facilitators: - swap agreements are usually arranged through an intermediary financial institution like a banker. Brokers and swap dealer are two categories of facilitators.

a) Brokers bring parties to a swap deal. Their basic idea is to initiate the Counter parties to finalize a deal.

b) Swap dealers: - they themselves become the counter parties and takeover risk. They have to price the swap, and manage the portfolio.

3. Cash flows:-here we have 2 different cash flows. It is a deal where we exchange two financial obligations in the future. so we examine the present value of future cash streams.4. Documentations:- formalities are lesser as compared to a loan, less time consuming and simpler.5. Transaction costs:-they are very low at almost ½% of the total sum of the contract.6. Benefits to parties:- these deals are needed as long as both parties are happy and find it profitable.7. Termination: both parties need to terminate the contract and not one party.8. Default risk:-as they are bilateral agreements there are possibilities of default risk by both the party.Types of swaps:-the basic purpose of swaps is to hedge the risk as desired by both the parties. The major risks are interest rate, currency, commodity, equity - debt, credit, climate, etc.

Interest rate swaps:-It is a financial agreement between two parties who wish to change the interest payments or receipts in the same currency on assets or

liabilities to a different basis. There is no exchange of the principal amount in this swap.It is an exchange of interest payments for a specific maturity on a agreed upon notional amount. The term notional refers to the theoretical principal underlying the swap. it is used only to calculate the interest to be exchanged under the interest rate swap. The example of exchanging a fixed to floating rate of interest in the same currency is called as the plain vanilla swap. It involves credit differentials between two borrowers which generate sufficient cost savings for both the parties.

Features of interest rate swaps1. Notional principal:- in the interest rate swap agreement the interest amount whether fixed or floating is calculated on a specified amount borrowed or lent. It is the notional because the parties do not exchange this amount at any time. It remains constant at all times. It is used to compute the sequence of payments of cash flow2. Fixed rate:-this is the rate which is used to calculate the size of the fixed payment. Banks or the other financial Institutions who make the market in interest rate swaps quote the fixed rate they are willing to pay if they are fixed rate payers in a swap (bid swap rates), they are willing to receive if they are floating rate payers in a swap(ask swap rate). Ex:- a bank might quote a us $ floating to fixed 5-year swap rate:-Treasuries+20bp/treasuries+40bp vs 6 month LIBOR.The quote indicates the following:-1. The said bank is willing to make fixed payment at a rate equal to the current yield on a 5 year treasury notes +20 basis points (.20%) in return for receiving floating payments at 6 months LIBOR.2. The bank has offered to accept at a rate equal to 5 year treasury notes plus 40 basis points in return for payment of 6 months LIBOR.Floating rate:- it is defined as one in the market index like LIBOR treasury bill rate etc on which basis the floating interest rate is determined in the swap agreement. The maturity of the underlying index equals the interval between payment dates. Trade date, effective date, reset date, and payment date:-All the above mentioned dates are important terms in the swap deal:The fixed rate payments are normally paid semi annually/yearly. The trade date may be defined as such date on which the swap deal is concluded.Effective date is that date from which the first fixed/floating payment starts to accrue. for ex:- a 5 year swap is traded on 30-08-2002 the effective date may be 01-09-2002 and ten payments dates from 1-03-2003 to 01-09-2007.the floating rate payments in swaps are set in advance and paid in arrears.Relevant dates for the floating payment:-

1) D(s) 2.d(1) and 3.d(2).Where d(s) is setting date on which floating rate applicable for the next payment is set.D(1)=that date from which the next floating payment starts to accrue. D(2)= payment is due.

Types of interest rate swaps

1. Plain vanilla swap:- it is also known as fixed for floating swap. Here one party with a floating interest rate liability is exchanged with fixed rate liability. Usually swap period ranges from 2 to 15 years for a predetermined notional principal amount. Most of the deals occur within 4 years period.

2. Zero coupon to floating:-the holders of zero-coupon bonds get the full amount of loan and interest accrued at the maturity of the bond. Hence in this swap the fixed rate player makes a bullet payment at the end and the floating rate player makes the periodic payment throughout the swap period.

3. Alternative floating rate:- in this type of swap the floating reference can be switched to other alter-natives as per the requirement of the counter party. These alternatives include 3 month libor,1 month commercial paper, t-bills rate etc. That means alternative floating interest rates are charged in order to meet the exposure of others.

4. Floating to floating:- in this swap one counter party pays one floating rate say LIBOR while the other counter party pays another say prime for a specified time period. These swap deals are mainly used by non us banks to manage their dollar exposure. 5. Forward swaps:-this swap involves an exchange of interest rate payment that does not begin until a specified future point of time. it is also kind of swap involving fixed for floating interest rate.

6. Equity swap:-the equity swap involves the exchange of interest payments linked to the change of stock index.

7. Swaptions:- these are combination of options and swaps. The buyer of swaption has the right to enter into an interest rate swap agreement by some specified date in the future. the buyer of a swaption will specify whether the buyer will be a fixed rate receiver or a fixed rate payer.

Valuation of interest rate swap

Assuming no default risk an interest rate swap can be valued either as a long position in one bond combined with short in another bond or as a portfolio of forward contracts. In other words interest rate swap (fixed or floating) can be valued by treating the fixed rate payments as being equivalent to a floating rate note (frn).Assuming no default risk an interest rate swap can be valued either as a long position in one bond combined with a short in another bond or as a portfolio of forward contracts. Interest rate swap (fixed or floating) can be valued by treating the fixed rate payments as being equivalent to the cash flows of a conventional bond and the floating rate payments as being equivalent to a floating rate note. (frn) in a interest rate swap the principal amount is not exchanged and further amount is paid in the same currency. Thus the value of swap could be expressed as the value of fixed rate bond and value of floating rate underlying the swap. It may be expressed as:- v = b1- b2 where v=value of swap,b1 = the value of fixed rate bond underlying the swap and b2=value of floating rate bond underlying the swap.

Currency swapsA swap deal can also be arranged across currencies. In this swap the two payment streams being exchanged are denominated in two different currencies. For ex a firm which has borrowed yen at a fixed interest rate can swap away the exchange rate risk by setting up a contract whereby it receives yen at a fixed rate of return for $ at either at fixed /floating int. The currency swap is like interest rate swap, also two party transaction involving two counter parties with different but complimentary needs being bought by a bank. Here three steps are involved:-1. Initial exchange of principal amount.2. Ongoing exchange of interest.3. Re-exchange of principal amount on maturity.The first step is the initial exchange of the principal amount at an agreed rate of exchange. This rate is usually based on the spot rate. This exchange can be on a notional basis i.e. No physical exchange of principal amount. The counter parties simply convert principal amount into the required currency-via the spot market.The second step is related with ongoing exchange of interest. After establishing the principal amount the counter parties exchange interest payment on a agreed date based on the o/s principal amount at the fixed interest rates at the outset of the transaction. The third step is the re-exchange of principal to principal amount. Agreements on this enable the counter parties to re-exchange the principal sums at the maturity date. The structure of a currency swap differs from interest rate swaps in a VARiety of ways.

Types of currency swapsThe major difference is that in a currency swap there is always an exchange of principal amounts at maturity at a predetermined exchange rate. Thus the swap contract behaves like a long dated forward, is forward exchange contract where the forward is the current spot rate.The currency swaps can be of different types based on their structure such as:-1. fixed to fixed currency swap:-Here the currencies are exchanged at fixed rate. One party raises a fixed rate liability in $ and the other a fixed rate funding in pound.The principal amount is equivalent at current market exchange rate. In a swap deal the first party gets pound whereas the second party gets $. Later on the first party gets to make periodic payments in pound to the second in turn gets $ computed at interest at a fixed rate on the respective principal amount of both currencies. at maturity the $ and pound principal are re-exchanged.

2. Floating to floating swap:-here the counter parties will have payments at floating rate in different currencies.

3. Fixed to floating currency swaps: this swap is a combination of a fixed to fixed currency swap and floating swap. here one party makes the payment at a fixed rate in currency say x while the other party makes the payment at a floating rate in currency y.Contracts without the exchange and re-exchange of principals do exist. In most cases a financial intermediary (a swap bank) structures the swap deals and routes the payments from one party to other party. the most important currencies in the currency swaps market are:-

Currency swaps-usesUS$, SWISS FRANC, DEUTSCHE MARK, EURO POUND STERLING, CANADIAN $ & YEN. The currency swap is an important tool to manage currency exposure and cost benefits at the same time. These are often used to provide long term financing in foreign currencies. This is because in many countries fin markets are not well developed.

Valuation of currency swapHere the swaps are valued as the difference between the current values of two conventional bonds. The value of a foreign currency bond and the corresponding value of a domestic currency bond are taken. V=sbf–bd where v=value of swap, s=current exchange rate expressed in no of units of domestic currency, bf=value of a fr Currency bond, and bd =local currency bond

MODULE 4

Risk management using options

An option is a particular type of a contract between two parties where one person gives the other the right to buy or sell a specific price within a specific time period. The option is a specific derivative instrument under which one party gets the right but no obligation to buy /sell a specific quantity of an asset at an agreed price on or before a particular date.The buyer will exercise the option only when he expects to gain. In case of losses he will not exercise the option. nowadays options are traded on a VARiety of instrument like commodities, financial assets, treasury bills, stocks, stock index food grains, petroleum, metals etc.

Options terminologies1. Parties in a option deal:We have two parties the buyer (holder) and seller (writer). The writer grants the buyer the right to buy or sell a particular asset in exchange

for a certain sum of money for the obligation taken by him in the option contract. 2. Exercise price:-The price at which the underlying asset may be sold or purchased by the option buyer from the option writer is called as exercise or strike price. at this price the buyer can exercise his option.

3. Expiration date and exercise date:The date on which an option contract expires is called as expiration date or maturity date. The option holder has the right to exercise his option on any date before the expiration date. Exercise date is date upon which the option is actually exercised.

4. Option premium:- the price at which the option holder buys the right from the option writer is called as option premium /price. This is the consideration paid by the buyer to the seller and it remained with the seller whether the option is exercised or not. this is fixed and paid at the time of writing the option deal.

5. Option ‘in’, ‘out’ and at the money:-When the underlying futures price is greater than the strike price/ exercise price, the option is in the money, and the futures price is lesser than the strike price it will be called as out of money call option, and if the futures price is equal to the strike price it is at the money.

Option terminologiesPay off profile of option

Call opt put optIn the money fut> str fut< strAt the money fut=str fut=strOut of money fut < str fut>str

6. The break even price:-It is that price of the stock where the gain on the option is just equ-al to the option premium. The break even price level is determined by adding the strike price and the premium paid together. Since there is zero sum game the profit from selling a call is the mirror image of the profit from buying the call.

Types of optionsOptions can be classified into:-

1. Call and put options.2. American and European options.3. Exchange traded and OTC traded options.

Call and put options:-

When an option grants the buyer the right to purchase the underlying asset from the writer (seller) a particular quantity at a specified price within a specified expiration date it is called “call option”. The call option holder pays the premium to the writer.A put option is an option where the option buyer has the right to sell the underlying asset to the writer at a specified price at or prior to the option‘s maturity date. It is also called simply as ‘put”. So if we buy a put option to on SBI stock we have gained the right to sell the shares of SBI to the writer at a specified price on or before the expiration date.

Types of options-on the basis of timingA European option can be exercised only at the expiration date where-as the American option can be exercised at any time up to and including the expiration date. Most of the options dealt are American until actually clarified as European. The names are merely conventional not geographic. Ex change traded option contracts are standardized and are traded on the recognized exchanges. OTC options are tailor made agreement sold directly by the dealer. the terms and conditions of these contracts are negotiated by the parties to the contract.

Differences - exchange traded and OTC options 1. Exchange traded are standardized and traded on recognized

stock exchanges. OTC options are written on the counters of commercial & investment bankers.

2. Exchange traded options have certain specified norms relating to quantity, quality, dates etc. Under OTC, norms are negotiated and mutually determined by buyers and sellers

3. Being standardized in nature an option contract traded through the recognized exchange has uniform underlying asset, limited no of strike prices ltd expiration dates etc. but in case of options through OTC the contracts are tailor made as per the requirements of the buyers and sellers. 4. exchange traded options are performed and cleared through a clearing house which acts as a third party. So risk of default is eliminated. But in OTC traded contracts the risk of default is higher as there are only two parties and if the option writer defaults there is no guarantee. 5. On buying a options contract from a exchange the obligation can be fulfilled as follows:

a) The buyer may not exercise the option. he may allow it to expire.

b) In the case of an American option he may exercise his option on or before the expiration date, letting the seller adhere to contract and keep the premium.

C) Either of the parties can execute an offsetting transaction to eliminate the future obligation. But under an OTC option no such facilities exist they are tailor made and un-standardized in nature. so the question of offset-ting does not exist.6. under the writers are expected to deposit margins as they are expos-ed to considerable risk. Under OTC no such margins exist.7. Under the exchange traded options transactions cost are lower but the OTC options depend upon the creditworthiness of the buyer 8. In OTC traded options market, large investment banking firms and commercial banks normally operates as principals as well as brokers. That is why they are less liquid in comparison to the exchange traded options. Further they take them as part of an asset liability management in which they intend to hold them to expiration.

Distinction-options and futures1. Under options one party (buyer) is not obligated to transact the contract at a later date, only the seller is under the obligation to perform the option contract and only if the buyer desires. Under futures both the parties are under the obligation to perform the contract.2. Under the options the buyer of the option has to pay the option premium to the seller and this is forfeited irrespective of completion of the contract. in futures no cash is transferred to either party. 3. Under futures contract the buyer of the contract realizes the gain in cash when the price of the futures contract increases and losses in case of fall in the prices. Under options such symmetric risk/reward relationship does not arise. The most the buyer can loose is the option premium. 4. Options contracts are brought into existence by being traded, if none is traded none exists, also there is no limit on number of option contracts that can be in existence at any time. however in case of future contract there is a process of closing out position which causes contracts to cease.

Options valuation

1. Intrinsic value: - it is the gain to the holder of an option on immediate exercise. Since the investor cannot exercise the option before maturity in European option, so the value is only notional. Under the American option it can be exercised at any time before the expiration date.

That means this value for a call is nothing more than the difference between the market price and strike price of the underlying asset.For a call option:- max {(st –x),0} where st is current stock price, x is strike price of the asset. if st > x it is positive intrinsic value. it cannot be –ve as buyer will not exercise the option. so the value cannot fall below zero. For a put option:-

Intrinsic value is:- Max {(x –st),0} If x>st the value is +ve, x=st the value is zero .

2. Time value of the option:-The value of an American option at any time prior to expiration must be at least to its intrinsic value. In general it will be larger. This is because there is a possibility that the stock price will move further in favor of the option holder.The difference between the value of an option at the particular time t and its intrinsic value at the time is called the time value of an option. This does not hold good to a European option. Major factors that influence the time value are the expected volatility of the stock price, length of the period to expiry, the extent to which the option is in or out of money. It is observed that out of money options have less time value than at the money options since the stock price has further to move before intrinsic value is acquired. Similarly in the money options have less time value than at the money options reason being that their prices contain intrinsic value which is vulnerable to fall in stock price. further the more time remains until expiry the higher the time value tends to be.

Option positionsIn every option contract there are two sides:- 1. The investor who takes the long position ( i.e. He has purchased the option) 2. Opposite to this is the investor who takes the short position (i.e. He has sold or writ-ten the option). So if one takes long position then the other short.There are 4 types of options:- 1.a long position in a call option.2.a long position in a put option.3.a short position in a call option.4.a short position in a put option. Naked (uncovered):- these are options which do not have offsetting positions and are more risky. Where the writer has a corresponding offsetting position in the asset it is a covered option.

Naked and covered optionsWriting a simple uncovered call option indicates toward exposure of the option writer to unlimited potential losses. The aim is to earn premium. in period of stable/falling prices call options writing may result in attractive profits by capturing the time value of an option. Writing an uncovered option shows the investor tolerance for risk.

Covered/uncovered optionsA covered option position involves the purchase or sale of an option in combination with an offsetting (or opposite) position in the asset which underlies the option. the writer of an call option incurs losses when stock prices rise and put writers incur losses when the prices fall.In such a situation the writer can cover the short put with a short position and short call with a long position in the underlying asset. this can be stated as:-Covered call sale=short call +long futures.Covered put sale= short put+ short futures.

Synthetic futures and optionsSynthetic futures positions are created by combining two options positions such that the resulting pay off remains same or nearly same as that of an outright futures position. Synthetic long position is created by combining long call option with short put option having the same strike price. Synthetic short futures are created by combining long put with short call option having the same strike price. Therefore:-Syn long futures=long call +short put.Syn short futures= long put + short call. Similarly we have synthetic options.

The underlying assets in exchange traded optionsVARious assets which are actively traded on the recognized exchanges are stock, stock indices, foreign currencies and futures contracts.1. Stock options:- options on individual shares of common stock have been traded for many years

Stock optionsStock options on a number of over the counter stocks are also available. While the strike prices are not because of cash dividends paid to common stock holders the strike price is adjusted to stock splits, stock dividends, and reorganizations etc, which affect the value of the underlying stock. Stock options are most popular assets traded all over the world.

Foreign currency options

This is another important asset traded on VARious stock exchanges. Major currencies traded are Us$, Aus $,British Pound, Can $,Ger Mark, French Franc, Jap Yen, Swiss Fr. The size of the contract differs from currency to currency. We shall see these under currency options.

Index optionsMany different index options are currently traded on different exchanges. In India trading is undertaken on NSE, and BSE. Like stock option, index option’s strike price is the index value at which the buyer of the option can buy and sell the underlying stock index. The strike index is converted into dollar (rupee) value by multiplying the strike index by the multiple for the contract. if the buyer of the stock index option intends to exercise the option then the stock must be delivered. it would be complicated to settle a stock index option by delivering all stocks that make up the index.So index options are cash settlement contracts. If the option is exercised the exchange assigned option writer pays cash to the option buyer and there will be no delivery of any share. The money value of the stock index underlying an index option is equal to the current cash index value multiplied by contracts multiple.Rupee value of the underlying index = cash index value*contract multiples. For example:- the contract multiple for the S&P 100 is $100. Assume that cash index value for the S&P 100 is 750 then the dollar value of S&P 100 contracts is 750*100 = $75,000

Module 5

Elementary investment strategiesThe use of options enables an investor to achieve unique risk-return patterns which cannot be achieved by taking investment positions on-ly in the underlying assets. This is in fact the economic rationale for the existence of options. The two investment strategies well known are long and short position.

Investment strategies1. Long position:- a position created by a person by buying an asset without taking any off setting position. The above buyer will gain when the price rises and lose due to the fall in price. on the other hand if the stock price remains unchanged or declines the invest-or makes no profit or incurs a loss (ignoring transaction

2. Short position:- a short position involves selling the asset first (without actually owning it) and buying it back later. The investor who short sells hopes that the price will decline during the time he is short.

3. Long call:- long call refers to the purchase of a call. The similarity between the long position in the underlying asset and long call position is that the investor concerned must be bullish on the underlying asset.

4. Short call:-The strategy involves writing a call without owning the underlying asset. The call writer makes a profit if the option expires worthless on the expiration date.

5. Long put:- This strategy involves buying a put- right to sell the underlying asset at a specified price. The put buyer anticipates a decline in the price of an underlying asset.

6. Short put:- This is a strategy of writing a put. In contrast to the put buyer the put writer is bullish on the underlying asset and earns an income (in the form of put premium) by speculating on his prediction. He is also prepared to accept ownership should the put owner decide to exercise.

Caps, Floors And CollarsCaps (interest rate caps):- a cap is a series of interest rate options, which guarantees a fixed rate payable on a borrowing over a specific time period at specific future dates. If interest rates rise above the agreed cap rate then the seller pays the difference between the cap rate and the interest rate to the purchaser.A cap is usually bought to hedge against a rise in interest rate and yet is not a part of the loan agreement and may be bought from a completely different bank/writer. In a cap usually an upfront fee is to be paid to the bank/writer. the cap guarantees that the rate charged on a loan will never exceed the current existing rates.Floors:- a floor is an agreement where the seller agrees to compensate the buyer if interest rates fall below the agreed up to a on floor rate. It is similar to a cap but ensures that if the interest rate falls below a certain agreed floor limit interest rate will be paid.Collars:- a collar is a combination of a cap and a floor where you sell a floor at a lower strike rate and buy a cap at a higher strike rate. Thus they provide protection against a rise in interest rates and some benefit from a fall in interest rates.

StraddleA straddle involves a call and a put option with the same exercise price and the same expiration date. A straddle buyer buys a call and a put option and the seller sells a call and a put option at the same exercise price and the same expiration date. The maximum loss associated with the long straddle is the premium paid /cost of optionProfit potential is unlimited when the prices of the underlying asset rise significantly and limited when it falls significantly. it is a case when investor purchasing a straddle makes profit at prices which are significantly lower/ higher than the prevailing market price.This strategy will appeal to an investor who wants to take a position in an underlying asset that is volatile but does not have a clue whether it will rise or fall in the short run. the investor however only anticipates a sharp movement in the price of the asset.

The graph has been drawn connecting the daily high-low prices. the triangular formation reveals that there has to be a break out either upwards or downwards. it is difficult to predict the direction in which the stock will move because the successive tops are lower than the preceding tops which is a bearish signal.

Also the successive lows are higher than the preceding low which is a bullish signal. if the investor knows that the stock is a volatile z tock he can profit from this scenario by buying a straddle on the stock. Obviously the writer of a straddle anticipates no major fluctuation in the prices of assetsStrangleIt is a combination of a call and a put with the same expiration date and different strike prices. If the strike prices of the call and the put options are x1 and x2 then a strangle is chosen in such a way that

x1>x2. Assume that we buy a call and put option on a particular stock with strike prices $35 & $30. Let the cost of call and put option be $3 and $ 5 respectively. our initial out flow is $8. If we have to benefit the total payoff should exceed $8.we will exercise the call option only when the price of the stock at expiration goes above $38.similarly put option only if price is below $25.To break even the stock’s price at expiration should be below $22 0r above $43. If the price falls between $22 and $43 then we do not benefit from the strategy by having a loss. Outside this range we have a profit potential. So profit and loss on a short position in a strangle is reverse of that of the long position.

Strips and strapsA strip consists of a long position in one call and two puts with the same exercise price and expiration date. The buyer of a strip believes that there will be a big stock price move but the stock price is more likely to fall than it is to rise.A strap consists of a long position in two calls and one put with the same strike price and expiration date. A strap is like a strip that is skewed in the opposite direction. The buyer of a strap expects bullish and bearish possibilities for the optioned security with a price rise being more likely.

Spread strategiesThese are employed for exploiting moderately bullish or bearish beliefs about the market. They involve use of options.1. Vertical spreads or price spreads:These involve buying an option and selling another option of the same type and time to expiration but with different exercise price2. Horizontal spread (time) involves buying an option and selling another option of the same type with same exercise price but with a different time of expiration.3. Diagonal spread involves buying an option and selling another of the same type with a different exercise price and different time to expiration.

Bulls and bear spread

If we wish to buy a bull spread using calls then we buy a call with a lower strike price and sell a call at a higher strike price. This strategy is called a spread because it involves buying an option and selling a related option to limit the risk. this strategy also limits the profit potential. The cost of a bull spread is cost of the option bought less the cost of the option sold.

Box spreadIt is a combination of bull and bear spreads with calls and puts respectively with the same set of exercise prices. if x1 and x2 are strike prices available with calls and puts then a box spread involves

buying and selling a put with strike prices x2 and x1.for a risk averse investor this strategy is ideal as it gives a payoff of the difference between the higher and the lower strike prices i.e. X2-x1.

Butterfly spreadA butterfly spread can be executed by using four identical options with the same underlying stock but with different exercise prices. A trader who is long on the butterfly spread buys a call with a low exercise price, buys a call with a high exercise price and sells two calls at intermediate exercise price

Option pricing model

Determinants of option prices:-The following are the important factors which influence the option pricing.1. Current price of the option: the option price will change as the stock price changes. The option price increases if the stock price increases and vice versa.

2. Strike price of the options:-The strike price is fixed for the life of the option. Other things remaining same in case of call option the lower the strike price the higher will be the option price and vice versa.

3. Time to expiration of the option:-Options are wasting assets. As it has a fixed time period. The longer the time period to expiration the higher is the option price. This is because as the time to maturity decreases lesser time remains for the stock price to fall/increase.4. Expected stock price volatility:-Fluctuations in stock prices in future is a major factor to influence the option price as greater the expected volatility of the price of the stock the more an investor would be willing to pay for the option and more premium the writer would demand.

5. Risk free interest rate:- interest rate is an important factor which creates impact on the option price. The higher the interest rate (short term risk free) the greater the cost of buying the underlying and carrying it to the expiration date of the call option. Hence the higher the interest rate the greater the price of the call option. 6. Anticipated cash payments on the stock:-it tends to decrease the price of a call option because the cash payments make it more attractive to hold stock than to hold the option. on the other hand for put option cash payments on the stock tend to increase the price.

Parameters explaining behavior of stock prices1. Expected return from the stock:-this is the annualized average return earned by the investors in a short period denoted by u. The expected return desired by invest-ors from stock depends on the riskiness of the stock. Higher the risk higher the return, and the market interest rate.2. Volatility: - the volatility of stock, ς is a measure of uncertainty about the returns provided by the stock. Volatilities are expressed in % per annum. it is defined as “ the volatility of a stock price is the

standard deviation of the return provided by the stock in one year when the return is expressed using continuous compounding”.The sd of the proportional change in stock price in time‘t’:- assume ς on a stock is 30%pa.to find the change in six months then ς =30√0.5 =21.2% and for 3 months it is 30√0.25 =15%.so sd will increase as the period lengthen. Graphically the curve becomes flatter and wider.

Models of valuation of options1. Binomial option pricing model:-1. Binomial option pricing model:-This model was developed by Cox, Ross and Rubinstein in 1979.thisThis model was developed by Cox, Ross and Rubinstein in 1979.this model assumes that the prices change in follow a binomial distribution.model assumes that the prices change in follow a binomial distribution. It follows the European call options. It solves the problem numericallyIt follows the European call options. It solves the problem numerically rather than analytically. rather than analytically.

Binomial pricing model –assumptionsBinomial pricing model –assumptions11.. There are no transaction costs, no bid/ask spread ,no margin There are no transaction costs, no bid/ask spread ,no margin requirements, no restriction on short sales, no taxes requirements, no restriction on short sales, no taxes 22.. There is no risk of default by the other party in the contract. There is no risk of default by the other party in the contract.33.. Markets are competitive, i.e. Market participants act as price takers Markets are competitive, i.e. Market participants act as price takers and not makers.and not makers.4. There are no arbitrage opportunities. Prices have adjusted in such a4. There are no arbitrage opportunities. Prices have adjusted in such a way so that there are no arbitrage opportunities in the market.way so that there are no arbitrage opportunities in the market.5. There is no interest rate uncertainty. This is assumed to reduce the5. There is no interest rate uncertainty. This is assumed to reduce the complexity of the pricing problems.complexity of the pricing problems.

The binomial modelThe binomial modelThe model is based on the assumption that if a share price is observedThe model is based on the assumption that if a share price is observed at the start and end of a period of time it will take one of the twoat the start and end of a period of time it will take one of the two values at the end of that period i.e the model assumes that the sharevalues at the end of that period i.e the model assumes that the share price would move up or down to a predetermined level. price would move up or down to a predetermined level.

One step binomial modelOne step binomial modelConsider a situation where a stock price is currently rs 20 and it isConsider a situation where a stock price is currently rs 20 and it is known that after 3 months it may be either rs 22 or rs 18. We alsoknown that after 3 months it may be either rs 22 or rs 18. We also assume a European call option to buy the stock for rs 21 in 3 months inassume a European call option to buy the stock for rs 21 in 3 months in this option we are estimating two values i.e. Rs 22 and rs 18, if thethis option we are estimating two values i.e. Rs 22 and rs 18, if the value turns up to 22 the option value will be re 1 and if 18 it is 0. value turns up to 22 the option value will be re 1 and if 18 it is 0. The situation=The situation=So = initial stock price rs 20So = initial stock price rs 20S1 = stock price after periodS1 = stock price after periodU0 = up factorU0 = up factorD0 = down factorD0 = down factorS1 = u0(s0) when stock price =22 and s1 = d0(s0) when stock price =S1 = u0(s0) when stock price =22 and s1 = d0(s0) when stock price = 18.18.

When the initial stock price =20,When the initial stock price =20,uo = 22-20=2/20, 1.10 and the downuo = 22-20=2/20, 1.10 and the down fact-or do= 20-18=2/20, 0.90. These are called as price relatives. Thefact-or do= 20-18=2/20, 0.90. These are called as price relatives. The assumption that the stock price can take only one of the two possibleassumption that the stock price can take only one of the two possible values at the end of each interval is referred as the binomial model.values at the end of each interval is referred as the binomial model.Consider a portfolio consisting of a long position in Consider a portfolio consisting of a long position in δδshares of the stockshares of the stock an a short position in call option. We can find out the value of portfolioan a short position in call option. We can find out the value of portfolio which is riskless. If the share price moves up from 20 to 22 the value ofwhich is riskless. If the share price moves up from 20 to 22 the value of shares will be 22shares will be 22δδ and the value of the option will be 1 i.e. 22-21. and the value of the option will be 1 i.e. 22-21.The total value of the option will be 22The total value of the option will be 22δδ – 1. If the price falls to 18 the – 1. If the price falls to 18 the value of the shares is 18value of the shares is 18δδ and the value of the option is zero so that and the value of the option is zero so that the total value of the port-folio is 18the total value of the port-folio is 18δδ+0 = 18+0 = 18δδ. The portfolio is riskless. The portfolio is riskless if the value of if the value of δδ is chosen so that the final value of the portfolio is the is chosen so that the final value of the portfolio is the same for both of the alternative stock prices.same for both of the alternative stock prices.This means 22This means 22δδ – 1=18 – 1=18δδ 4 4 δδ = 1, = 1, δδ= 0.25 = 0.25 A riskless portfolio is, therefore:-A riskless portfolio is, therefore:-Long: 0.25, short: 1 option. If the stock price moves upward to 22Long: 0.25, short: 1 option. If the stock price moves upward to 22 the value of the portfolio will be 22*0.25-1 =4.5. If the stock pricesthe value of the portfolio will be 22*0.25-1 =4.5. If the stock prices moves downward to 18 the value is 18*0.25 = 4.5.moves downward to 18 the value is 18*0.25 = 4.5.So irrespective of whether the stock price moves up or down, the valueSo irrespective of whether the stock price moves up or down, the value of the portfolio is always 4.5 at the end of the life of the option.of the portfolio is always 4.5 at the end of the life of the option.Analyzing the risk free portfolio must earn risk free interest. AssumingAnalyzing the risk free portfolio must earn risk free interest. Assuming risk free interest @ 12%pa, the value of the portfolio today must be therisk free interest @ 12%pa, the value of the portfolio today must be the present value of 4.5 or 4.5epresent value of 4.5 or 4.5e-0.12*o.25-0.12*o.25 =4.367 =4.367 The current price of the stock is 20, assuming option price denoted by fThe current price of the stock is 20, assuming option price denoted by f the value of the portfolio today is 20*0.25 – f = 5 – f. It follows that 5 –the value of the portfolio today is 20*0.25 – f = 5 – f. It follows that 5 – f =4.367 or f= 0.633.f =4.367 or f= 0.633.This means that current value of option must be 0.633. If the value ofThis means that current value of option must be 0.633. If the value of the option were more than 0.633 the portfolio would cost less thanthe option were more than 0.633 the portfolio would cost less than 4.367 to set up and would earn more than the risk free rate and vice4.367 to set up and would earn more than the risk free rate and vice versa. versa.

Black and scholes option pricing modelBlack and scholes option pricing modelThis is the most commonly used option pricing model in finance. it wasThis is the most commonly used option pricing model in finance. it was developed in 1973 by fisher black and myron scholes and wasdeveloped in 1973 by fisher black and myron scholes and was designed to price European options on non-dividend paying stocks.designed to price European options on non-dividend paying stocks. Later it was modified for American options, options on dividend payingLater it was modified for American options, options on dividend paying stock, and for future contracts. stock, and for future contracts. 11.. It assumes that the expected return and standard deviation are It assumes that the expected return and standard deviation are constant. (constant. (u and u and ςς are constant) are constant)22.. There are no taxes and transaction costs. There are no taxes and transaction costs.33.. All securities/stocks are perfect-ly divisible. All securities/stocks are perfect-ly divisible.4. No dividend payments on stock during the life of the option.4. No dividend payments on stock during the life of the option.5. There is no risk less arbitrage opportunities.5. There is no risk less arbitrage opportunities.6. Stock trading is continuous.6. Stock trading is continuous.7. Investors can borrow or lend at the same risk free rate of interest7. Investors can borrow or lend at the same risk free rate of interest

8. The short term risk free interest rate ‘r’ is constant. 8. The short term risk free interest rate ‘r’ is constant. The foundation of the model is the construction of a hypothetical riskThe foundation of the model is the construction of a hypothetical risk free portfolio, consisting of long call options and short positions in thefree portfolio, consisting of long call options and short positions in the underlying stock on which an investor earns the risk less return. it isunderlying stock on which an investor earns the risk less return. it is analogous to the no arbitrage analysis. analogous to the no arbitrage analysis. The reason why a risk less portfolio can be set up is because the stockThe reason why a risk less portfolio can be set up is because the stock price and the option price are both affected by the same underlyingprice and the option price are both affected by the same underlying source of uncertainties and factors. In short period the stock price issource of uncertainties and factors. In short period the stock price is perfectly correlated with the option price and the price of a put optionperfectly correlated with the option price and the price of a put option is perfectly negatively correlated with the price of the underlying stock.is perfectly negatively correlated with the price of the underlying stock. In this way in both cases when an appropriate portfolio of the stockIn this way in both cases when an appropriate portfolio of the stock and option is created, profit and loss from stock position will offset theand option is created, profit and loss from stock position will offset the profit and loss from option position so that the overall value of theprofit and loss from option position so that the overall value of the portfolio at the end of the short period of time is known with certainty.portfolio at the end of the short period of time is known with certainty.C=sn(d1)-keC=sn(d1)-ke-rt-rt n(d2) (call option) n(d2) (call option)P= keP= ke-rt-rt n(-d2) – sn(-d1) (put option) n(-d2) – sn(-d1) (put option)D1 = D1 = ln(s/k) + rtln(s/k) + rt + 0.5ς√t ς√tD2 = ln(s/k) + rtln(s/k) + rt - 0.5ς√t ς√t or d2=d1- ς√t

C= call option, p=put option, s= stock price, k= strike price, e=C= call option, p=put option, s= stock price, k= strike price, e= exponential ( constant value 2.7182818), r=risk free interest rateexponential ( constant value 2.7182818), r=risk free interest rate annual, t= time to expiry in years,annual, t= time to expiry in years,ςς=sd of returns (volatility) as a=sd of returns (volatility) as a decimal, edecimal, e-rt-rt is present value of a future sum of money, ln= natural is present value of a future sum of money, ln= natural log,nd1 is the area under the distribution to the left of d1 and nd2 islog,nd1 is the area under the distribution to the left of d1 and nd2 is left of d2.left of d2.

Hedging with optionsHedging with optionsHedging through financial derivatives is an important strategy ofHedging through financial derivatives is an important strategy of financial institutions, traders, and other dealers. The ultimate economicfinancial institutions, traders, and other dealers. The ultimate economic function of financial derivatives is to provide means of risk reduction.function of financial derivatives is to provide means of risk reduction. As seen earlier hedgers using futures basically attempt to lock in aAs seen earlier hedgers using futures basically attempt to lock in a specific price. specific price. In case of options hedgers seek to set a specific floor or ceiling price.In case of options hedgers seek to set a specific floor or ceiling price. For ex:- an option hedger can establish a floor price for a long putFor ex:- an option hedger can establish a floor price for a long put position and in case of a long call position a ceiling price is established.position and in case of a long call position a ceiling price is established. So options can be regarded as means of insurance against adverseSo options can be regarded as means of insurance against adverse price movementsprice movementsAnyone who is at a risk from a price change can use options to offsetAnyone who is at a risk from a price change can use options to offset that risk. For ex:- a call option can be used as a means of ensuring athat risk. For ex:- a call option can be used as a means of ensuring a maximum purchase price in which if the market price exceeds themaximum purchase price in which if the market price exceeds the strike price then the option can be exercised in order to buy at thestrike price then the option can be exercised in order to buy at the strike price and vice versa.strike price and vice versa.

The concept of fixed hedgeThe concept of fixed hedgeWhen the size of the option being hedged matches the amount of theWhen the size of the option being hedged matches the amount of the underlying covered by the options the hedge is referred to as a fixedunderlying covered by the options the hedge is referred to as a fixed hedge. A fixed hedge with option retains an exposure and entails ahedge. A fixed hedge with option retains an exposure and entails a cost. while protection is obtained from a stock price movement in onecost. while protection is obtained from a stock price movement in one direction exposure is retained to a movement in other direction.direction exposure is retained to a movement in other direction.This profit potential is paid for in the form of option premium. So itThis profit potential is paid for in the form of option premium. So it should be decided whether hedging is really desirable. If so whethershould be decided whether hedging is really desirable. If so whether options constitute the appropriate hedging instrument. Because ifoptions constitute the appropriate hedging instrument. Because if there is no intention to sell then there is no need to hedge.there is no intention to sell then there is no need to hedge.

Naked and covered positionNaked and covered positionOne strategy open to the hedger is to do nothing. This involves what isOne strategy open to the hedger is to do nothing. This involves what is known as a naked option. A naked call option is also termed as a callknown as a naked option. A naked call option is also termed as a call option that is not used for hedging an existing exposure. An alternativeoption that is not used for hedging an existing exposure. An alternative is covered position. This involves buying the stock as soon as theis covered position. This involves buying the stock as soon as the option has been sold.option has been sold.If the option is exercised this strategy works well. If the option is notIf the option is exercised this strategy works well. If the option is not exercised the covered position could price to be expensive. Howeverexercised the covered position could price to be expensive. However neither a naked position nor a covered position provides a satisfactoryneither a naked position nor a covered position provides a satisfactory hedge.hedge.

A stop - loss strategyA stop - loss strategyThis is an interesting hedging strategy where the stocks are purchasedThis is an interesting hedging strategy where the stocks are purchased and sold against writing a call or put option. for ex:- a firm which has aand sold against writing a call or put option. for ex:- a firm which has a call option with exercise price of x to buy one unit of stock. Thecall option with exercise price of x to buy one unit of stock. The hedging strategy is to buy the stock as soon as the prices rise over xhedging strategy is to buy the stock as soon as the prices rise over x and sell at fall.and sell at fall.The objective of this strategy is to hold a naked position whenever theThe objective of this strategy is to hold a naked position whenever the stock price is less than x and covered position if the stock price isstock price is less than x and covered position if the stock price is higher than x. The strategy is designed to ensure that the firm ownshigher than x. The strategy is designed to ensure that the firm owns the stock when the option is in the money and does not own it if thethe stock when the option is in the money and does not own it if the option is out of the money. option is out of the money.

Zero-cost option strategyZero-cost option strategyThis strategy involves when an opt-ion is purchased at a particularThis strategy involves when an opt-ion is purchased at a particular premium and at the same time, selling an option which gives samepremium and at the same time, selling an option which gives same size to the receipt of premium. It means paying the premium on onesize to the receipt of premium. It means paying the premium on one option and receiving the premium on the other option and thus bearingoption and receiving the premium on the other option and thus bearing zero cost on the option. zero cost on the option. Zero cost options are instruments which can be broken down into:-Zero cost options are instruments which can be broken down into:-1.participting forwards:- all the constituents have the same strike1.participting forwards:- all the constituents have the same strike price. For hedging against price fall a purchase of out of the moneyprice. For hedging against price fall a purchase of out of the money puts could be financed by the sale of a smaller number of in theputs could be financed by the sale of a smaller number of in the money calls. money calls.

In this strategy put options will fully cover against the price fallIn this strategy put options will fully cover against the price fall whereas the call option would not fully negate the benefits of a pricewhereas the call option would not fully negate the benefits of a price rise. So in this situation net effect is that of a forward contract thatrise. So in this situation net effect is that of a forward contract that allows some participation in the benefits of a price rise.allows some participation in the benefits of a price rise.2. Range forwards:- this is also call-ed as cylinder or split synthetic. In2. Range forwards:- this is also call-ed as cylinder or split synthetic. In these technique constituents options have different strike prices. ex:-these technique constituents options have different strike prices. ex:- in case of falling prices, hedging can be by buying a put option with ain case of falling prices, hedging can be by buying a put option with a strike price below the stock price and financing the same by writing astrike price below the stock price and financing the same by writing a call option with a strike price above stock price. call option with a strike price above stock price. As a result there will be advantage of allowing some profit from a riseAs a result there will be advantage of allowing some profit from a rise in the stock price, but at the cost of having no protection against ain the stock price, but at the cost of having no protection against a price fall until the stock price reaches the strike price of the put option.price fall until the stock price reaches the strike price of the put option.

Delta hedgingDelta hedgingDelta hedging is the strategy used to immunize portfolios from smallDelta hedging is the strategy used to immunize portfolios from small changes in the prices of the under-lying asset in the futures smallchanges in the prices of the under-lying asset in the futures small interval of time. The delta of an option is the ratio of the change. If theinterval of time. The delta of an option is the ratio of the change. If the delta is 0.50 it means that the option premium will change by 50% fordelta is 0.50 it means that the option premium will change by 50% for the change in the price of stock.the change in the price of stock.If an option with a delta of 0.50 is used a hedge then two options mustIf an option with a delta of 0.50 is used a hedge then two options must be held for every unit of the asset in order to equate both the optionbe held for every unit of the asset in order to equate both the option and asset portfolios. The minimum VARiance hedge ratio is theand asset portfolios. The minimum VARiance hedge ratio is the reciprocal of the option delta if delta is 0.50 then the hedge rat-io isreciprocal of the option delta if delta is 0.50 then the hedge rat-io is 2.as an option delta changes the hedge ratio will be changed2.as an option delta changes the hedge ratio will be changedΔΔ = = δδc/ c/ δδs where s where δδ is delta, is delta, δδc is change in call price, c is change in call price, δδs is change ins is change in asset (stock) price. A delta equal to 0.7 for a call option implies that forasset (stock) price. A delta equal to 0.7 for a call option implies that for a one unit change in the stock price or index the option would movea one unit change in the stock price or index the option would move 0.7 points. Also a 0.7 points. Also a δδ= -0.8 for a put option means that the put option= -0.8 for a put option means that the put option premium will decline by 8o paise if the stock rises by re 1.premium will decline by 8o paise if the stock rises by re 1.In terms of the b-s model for a call option the delta is given by n(d1),In terms of the b-s model for a call option the delta is given by n(d1), while for a put option it is equal to n(d1)-1.ex if n(d1) = 0.6443 thewhile for a put option it is equal to n(d1)-1.ex if n(d1) = 0.6443 the delta for call option is 0.6443-1 = 0.3557. So if the price of the assetdelta for call option is 0.6443-1 = 0.3557. So if the price of the asset rises by re 1 the price of the call option will rise by 64 paise while therises by re 1 the price of the call option will rise by 64 paise while the price of put option will fall by 35 paise. price of put option will fall by 35 paise. Evidently the call delta would always be greater than zero and lessEvidently the call delta would always be greater than zero and less than one. Deep in the money call options would have delta close tothan one. Deep in the money call options would have delta close to unity while deep in the money put options would show a delta neari-ngunity while deep in the money put options would show a delta neari-ng -1.options that are far out of the money have delta values close to-1.options that are far out of the money have delta values close to zero.zero.

Theta Theta θθOption values increase with the length of time to maturity. The expec-Option values increase with the length of time to maturity. The expec-ted change in the option premium from a small change in the time toted change in the option premium from a small change in the time to expiration is termed as theta, i.e. It is a rate of change in the optionexpiration is termed as theta, i.e. It is a rate of change in the option portfolio value as time passes. it is also called as time delay of theportfolio value as time passes. it is also called as time delay of the portfolio. portfolio.

Theta is calculated as the change in the option premium over theTheta is calculated as the change in the option premium over the change in time. change in time. ΘΘ = = δδ premium/ premium/ δδ time timeThe option premiums deteriorate at an increasing rate as theyThe option premiums deteriorate at an increasing rate as they approach expiration. It is also observed that most of the optionapproach expiration. It is also observed that most of the option premiums depending on the individual option is lost in the final 30premiums depending on the individual option is lost in the final 30 days to expiration. That is why theta is based on square root of time.days to expiration. That is why theta is based on square root of time.This exponential relationship between option premium and time isThis exponential relationship between option premium and time is seen in the ratio of option value between the four month and the oneseen in the ratio of option value between the four month and the one month at the money maturities. It will be:- month at the money maturities. It will be:- premium of 4 months premium of 4 months premium of 1 monthpremium of 1 month= = √√4/4/√√1 =2/1 = 2 times.1 =2/1 = 2 times.

GammaGammaThe gamma The gamma ẛ of the portfolio of opt-ions on an underlying asset may beẛ of the portfolio of opt-ions on an underlying asset may be defined as the rate of change of the portfolio’s delta with respect todefined as the rate of change of the portfolio’s delta with respect to the price of the underlying instrument. in other words it is the changethe price of the underlying instrument. in other words it is the change in delta per unit change in the price of the asset.in delta per unit change in the price of the asset.If the gamma is small and not significant it means that the deltaIf the gamma is small and not significant it means that the delta changes very slowly then adjustments for keeping delta neutral needchanges very slowly then adjustments for keeping delta neutral need relatively infrequently. If gamma is very high which means that delta isrelatively infrequently. If gamma is very high which means that delta is highly sensitive to stock price then the adjustment to make deltahighly sensitive to stock price then the adjustment to make delta neutral is needed.neutral is needed.

Vega (v)Vega (v)It may be defined as the rate of change of the value of the portfolio ofIt may be defined as the rate of change of the value of the portfolio of the options with respect to change (volatility) of the underlying asset.the options with respect to change (volatility) of the underlying asset. Volatility is stated in percentage per annum. it is the sd of dailyVolatility is stated in percentage per annum. it is the sd of daily percentage changes in the underlying stock price. I.e. The value of anpercentage changes in the underlying stock price. I.e. The value of an option is liable to change because of movements in stock prices overoption is liable to change because of movements in stock prices over the passage of time.the passage of time.If vega is high in absolute terms the portfolio value is very sensitive toIf vega is high in absolute terms the portfolio value is very sensitive to changes in volatility. If the stock’s volatility rising then the risk of thechanges in volatility. If the stock’s volatility rising then the risk of the option’s being exercised is increasing, the option’s premium would alsooption’s being exercised is increasing, the option’s premium would also be increasing.be increasing. vega = vega = δδ premium/ premium/ δδ volatility. volatility.

Rho and phiRho and phiThe rho of a portfolio of options may be defined as the rate of changeThe rho of a portfolio of options may be defined as the rate of change in the value of the portfolio option with respect to the interest rate. I.e.in the value of the portfolio option with respect to the interest rate. I.e. The expected change in the option premium from a small change inThe expected change in the option premium from a small change in the domestic interest rate. Rho = the domestic interest rate. Rho = δδ premium / premium / δδ domestic interest rate. domestic interest rate. In case of currency options we have domestic interest rate and foreignIn case of currency options we have domestic interest rate and foreign interest rate. When the change in the option value is due to foreigninterest rate. When the change in the option value is due to foreign interest rate it is called as phi.interest rate it is called as phi. phi = phi = δδ in option premium/ in option premium/δδ foreign interest rate. foreign interest rate.

MODULE -6MODULE -6Interest Rate MarketsInterest Rate Markets

Interest rate futures are the most popular and successful financialInterest rate futures are the most popular and successful financial derivative instrument today in the global fin. Markets. Both thederivative instrument today in the global fin. Markets. Both the borrowers and lenders face interest rate risk. If both dislike risk andborrowers and lenders face interest rate risk. If both dislike risk and uncertainty then they will seek such instruments through which theyuncertainty then they will seek such instruments through which they can reduce such risk. can reduce such risk.

Interest Rate FuturesInterest Rate FuturesInterest rate futures are such financial derivatives, which assist inInterest rate futures are such financial derivatives, which assist in reducing the interest rate risk of such persons. Interest rate futures arereducing the interest rate risk of such persons. Interest rate futures are such financial derivatives that are written on fixed income (return)such financial derivatives that are written on fixed income (return) securities or instruments here interest and principal are payable onsecurities or instruments here interest and principal are payable on predetermined dates. predetermined dates. Interest rate futures are such financial derivatives, which assist inInterest rate futures are such financial derivatives, which assist in reducing the interest rate risk of such persons. Interest rate future isreducing the interest rate risk of such persons. Interest rate future is such financial derivatives that are written on fixed income (return)such financial derivatives that are written on fixed income (return)

securities or instruments here interest and principal are payable onsecurities or instruments here interest and principal are payable on predetermined dates. predetermined dates. In the financial markets these debt obligations are often arbitrarilyIn the financial markets these debt obligations are often arbitrarily separated into short term(money market) and long term(capitalseparated into short term(money market) and long term(capital market) instruments. Money market instruments are those financialmarket) instruments. Money market instruments are those financial assets having initial maturity of one year or less and capital marketassets having initial maturity of one year or less and capital market more than one year.more than one year.An interest rate futures contract is a futures contract on an assetAn interest rate futures contract is a futures contract on an asset whose price is dependent solely on the level of interest rates. Interestwhose price is dependent solely on the level of interest rates. Interest rate futures are more complicated than other types of futures becauserate futures are more complicated than other types of futures because it requires description of both level of interest rates and maturity ofit requires description of both level of interest rates and maturity of interest rates. interest rates.

Types of interest ratesTypes of interest rates

1.1. Treasury rates Treasury rates: -: - it is the rate of interest applicable to borrowing by a govt. in its ownit is the rate of interest applicable to borrowing by a govt. in its own country. Ex: - Indian govt. can borrow in Indian rupees on treasurycountry. Ex: - Indian govt. can borrow in Indian rupees on treasury rates prescribed. Treasury rates are also regarded as risk free rate ofrates prescribed. Treasury rates are also regarded as risk free rate of interest.interest.

2. Libor rate2. Libor rate: - London inter bank offer rate is the rate at which: - London inter bank offer rate is the rate at which international banks are willing to lend money to another internationalinternational banks are willing to lend money to another international bank. LIBOR rates change as per the economic conditions, quantum ofbank. LIBOR rates change as per the economic conditions, quantum of money flows, market position of funds requirements etc. LIBOR ismoney flows, market position of funds requirements etc. LIBOR is higher than treasury rates.higher than treasury rates.

3. Repo rate3. Repo rate: -it is a contract where the owner of the funds agrees to: -it is a contract where the owner of the funds agrees to sell the to a counter party now and buy them back later at a slightlysell the to a counter party now and buy them back later at a slightly higher rate. so the counter party is giving a loan to other party. Thehigher rate. so the counter party is giving a loan to other party. The difference between the selling price and the repurchase price is calleddifference between the selling price and the repurchase price is called as interest earned or repo.as interest earned or repo.

4. Zero rate/ spot rate4. Zero rate/ spot rate:-it is the rate of interest earned on an:-it is the rate of interest earned on an investment that starts today and lasts for n years. It is called as n yearinvestment that starts today and lasts for n years. It is called as n year zero rate, n-year zero or n spot rate. All the amounts of accruedzero rate, n-year zero or n spot rate. All the amounts of accrued interest and principal are realized at the end of n years. There are nointerest and principal are realized at the end of n years. There are no intermediate payments intermediate payments The underlying marketsThe underlying marketsThere are a number of money markets operating in different segmentThere are a number of money markets operating in different segment collectively called as parallel markets. It comprises of :-collectively called as parallel markets. It comprises of :-11.. The inter bank rate. The inter bank rate.22.. The cd’s and cp markets. The cd’s and cp markets.33.. The local govt. securities market. The local govt. securities market. 1. Inter bank market:- it involves the borrowing and lending among1. Inter bank market:- it involves the borrowing and lending among banks and large entities like corp, govt. bodies, central banks, imf. It isbanks and large entities like corp, govt. bodies, central banks, imf. It is

a wholesale market where one single transaction is usually in millions.a wholesale market where one single transaction is usually in millions. Often money passes through many banks between original lender andOften money passes through many banks between original lender and the ultimate borrower. the ultimate borrower. The inter bank interest rate has become the benchmark for otherThe inter bank interest rate has become the benchmark for other interest rates. both the bid and offer rates are available here. Theinterest rates. both the bid and offer rates are available here. The difference between offer and bid rate is known as spread which isdifference between offer and bid rate is known as spread which is usually 1/8 %. usually 1/8 %. 2. Cd’s and cp market:-the cd’s are bearer certificates acknowledging a2. Cd’s and cp market:-the cd’s are bearer certificates acknowledging a deposit for a period, such as 3 or 6 months. it is a negotiabledeposit for a period, such as 3 or 6 months. it is a negotiable instrument which can be bought and sold between the date of issueinstrument which can be bought and sold between the date of issue and maturity. the market is dominated by banks and usually theand maturity. the market is dominated by banks and usually the discount houses operate market makers in this market. discount houses operate market makers in this market. The cp’s are issued by the corporate borrowers. Corporate firmsThe cp’s are issued by the corporate borrowers. Corporate firms directly approach the investors and can borrow at rates equal to ordirectly approach the investors and can borrow at rates equal to or even perhaps lower than the interest rates charged by the banks fromeven perhaps lower than the interest rates charged by the banks from them.them.3. Government borrowing:- govt. issues different instruments like3. Government borrowing:- govt. issues different instruments like treasury notes, treasury bills and bonds for financing their spendingtreasury notes, treasury bills and bonds for financing their spending and budget deficits. The local govt. authorities may find it cheaper toand budget deficits. The local govt. authorities may find it cheaper to take deposits directly rather than borrow from the banks and other fin.take deposits directly rather than borrow from the banks and other fin. Institution. Institution. The term structure of interest rates The term structure of interest rates The volatility of a debt instrument price is dependent on its maturity,The volatility of a debt instrument price is dependent on its maturity, the longer the maturity the greater the price volatility. Since thethe longer the maturity the greater the price volatility. Since the maturity of a bond is referred as its term to maturity or simply termmaturity of a bond is referred as its term to maturity or simply term the relationship between yield and maturity is referred to as the termthe relationship between yield and maturity is referred to as the term structure of interest rates. it is also called as yield curve. structure of interest rates. it is also called as yield curve. 1. Upward sloping yield: -yield rises as maturity increases. this is1. Upward sloping yield: -yield rises as maturity increases. this is referred as positive yield curve.referred as positive yield curve.2. Downward sloping yield: - where yield decreases as maturity2. Downward sloping yield: - where yield decreases as maturity increases.increases.3. Flat yield: - yield remains the same irrespective of changes in3. Flat yield: - yield remains the same irrespective of changes in maturity.maturity.

Forward rate agreements (FRAs)Forward rate agreements (FRAs)These are also known as future rate agreements. These refer to aThese are also known as future rate agreements. These refer to a technique for locking in future short term interest rates. These aretechnique for locking in future short term interest rates. These are agreements that a certain interest rate will apply to a certain principalagreements that a certain interest rate will apply to a certain principal amount for a certain period in the future. amount for a certain period in the future.

Hedging the FRAHedging the FRAFRA can also be used to manage the risk by entering a notionalFRA can also be used to manage the risk by entering a notional agreement to lend or borrow in the futures at a rate of interestagreement to lend or borrow in the futures at a rate of interest determined in the present. A set of bid-offer spreads is publisheddetermined in the present. A set of bid-offer spreads is published showing rates of interest for different futures time periods. Theshowing rates of interest for different futures time periods. The customer and the banker may agree that the compensation will passcustomer and the banker may agree that the compensation will pass

between them in respect of any deviation of interest rates betweenbetween them in respect of any deviation of interest rates between the two dates.the two dates.

Treasury bill futuresTreasury bill futuresTreasury bill is major short-term interest rate securities and normallyTreasury bill is major short-term interest rate securities and normally issued 90 days 180 days respectively. The 90-day t-bills are mostissued 90 days 180 days respectively. The 90-day t-bills are most popular instrument. The t-bill futures market is the most liquid andpopular instrument. The t-bill futures market is the most liquid and contracts are widely traded. Treasury bill yield are quoted on acontracts are widely traded. Treasury bill yield are quoted on a discount basis with relation to the face value. discount basis with relation to the face value. As such the difference between the purchase price and the redemptionAs such the difference between the purchase price and the redemption value is the interest earned by the buyer. The discount on the facevalue is the interest earned by the buyer. The discount on the face value is always as a percentage of the face value. T- bills havevalue is always as a percentage of the face value. T- bills have maturity of less than one year. The difference between the purchasematurity of less than one year. The difference between the purchase price and its face value determines the interest earned by the buyer.price and its face value determines the interest earned by the buyer.

The discount on the face value is always as a percentage of the faceThe discount on the face value is always as a percentage of the face value. Price quotation for t-bill futures are on an index basis i.e. Thevalue. Price quotation for t-bill futures are on an index basis i.e. The index is 100 minus the annualized discount rate. If discount is say 7%index is 100 minus the annualized discount rate. If discount is say 7% then index price will be 93. The minimum price change allowed is onethen index price will be 93. The minimum price change allowed is one basis point, which amounts to $25 ($10,00,000*.01%*3/12) perbasis point, which amounts to $25 ($10,00,000*.01%*3/12) per contract. (Size of us Treasury bill = 10,00,000 dollars) contract. (Size of us Treasury bill = 10,00,000 dollars) The t-bill purchase price is: -The t-bill purchase price is: -Face value* (Face value* (1 – % discount)1 – % discount) * * days to maturity) days to maturity) 100 360100 360If discount is 7% the corresponding price paid for a 90 day t- bills =If discount is 7% the corresponding price paid for a 90 day t- bills = $10,00,000[ 1-0.07 *(90/360)] $10,00,000[ 1-0.07 *(90/360)] = $9,82,500 = $9,82,500 We can calculate the return on purchase of 90 day t-bill i.e.We can calculate the return on purchase of 90 day t-bill i.e. face value - issue priceface value - issue price * * 360 360 issue price days to maturityissue price days to maturity 10,00,000 - 982,50010,00,000 - 982,500 * * 360360 9,82,500 909,82,500 90 = 7.13%.= 7.13%.

Euro dollar futuresEuro dollar futuresEuro dollar is another most popular short-term instrument in theEuro dollar is another most popular short-term instrument in the money markets. Euro dollar deposits are us $ deposits held in amoney markets. Euro dollar deposits are us $ deposits held in a commercial bank outside the USA. These banks may be either foreigncommercial bank outside the USA. These banks may be either foreign banks or foreign branches of us based banks. The deposits are non-banks or foreign branches of us based banks. The deposits are non-transferable and they cannot be used as collateral securitytransferable and they cannot be used as collateral securityEuro dollar futures contracts are non-negotiable, 3-month timeEuro dollar futures contracts are non-negotiable, 3-month time deposits in dollars at banks located outside the US mainly in Europedeposits in dollars at banks located outside the US mainly in Europe with particular presence in London. London dominates the euro dollarwith particular presence in London. London dominates the euro dollar deposit market so LIBOR has become the benchmark short-termdeposit market so LIBOR has become the benchmark short-term interest rate for the traders.interest rate for the traders.

The LIBOR is quoted as an “add- on yield” basis, which means that it isThe LIBOR is quoted as an “add- on yield” basis, which means that it is a percentage of the time deposit purchase amount. it is an annualizeda percentage of the time deposit purchase amount. it is an annualized rate based on a 360 day a year. Ex:- if the 3 month LIBOR is 10%, therate based on a 360 day a year. Ex:- if the 3 month LIBOR is 10%, the interest on $1 million =interest on $1 million =(0.10)(90/360)($1 million) = $25,000.(0.10)(90/360)($1 million) = $25,000.

Factors for the speedy growth of euro $ futuresFactors for the speedy growth of euro $ futures11.. Most of the banks in the world depend on euro dollar market for Most of the banks in the world depend on euro dollar market for short-term loans.short-term loans.22.. Many corporate depend heavily on euro dollar market for their Many corporate depend heavily on euro dollar market for their borrowing requirements.borrowing requirements.33.. Euro$ futures are traded in Singapore, London and Chicago and can Euro$ futures are traded in Singapore, London and Chicago and can be used globally on 24 hours.be used globally on 24 hours.

Ted spreadTed spreadTed spread is the difference between the price of a 3 month t-billTed spread is the difference between the price of a 3 month t-bill futures contract and a 3 month euro dollar time deposit futuresfutures contract and a 3 month euro dollar time deposit futures contract both expiring at the same day. Given that the t-bills are lesscontract both expiring at the same day. Given that the t-bills are less risky than euro dollars the ted spread VARies considerably over the liferisky than euro dollars the ted spread VARies considerably over the life of the futures contracts.of the futures contracts.The t-bills being guaranteed by the US govt. are less risky than theThe t-bills being guaranteed by the US govt. are less risky than the guarantee given by the commercial banks issuing the euro dollar timeguarantee given by the commercial banks issuing the euro dollar time deposits. therefore the t-bills carry a lower rate of return than the eurodeposits. therefore the t-bills carry a lower rate of return than the euro dollars. so the treasury bills future prices are higher than the eurodollars. so the treasury bills future prices are higher than the euro dollar deposit futuresdollar deposit futures

Hedging interest rate with the interest rate futuresHedging interest rate with the interest rate futures1.1. Hedging a rise in interest rate for borrowing decisions or short term Hedging a rise in interest rate for borrowing decisions or short term hedging.hedging.2.2. Hedging a fall in interest rate for investing decisions or long term Hedging a fall in interest rate for investing decisions or long term hedging.hedging.There are two popular hedging strategies in futures used by investorsThere are two popular hedging strategies in futures used by investors to ensure the surety of their earnings for a longer period of time.to ensure the surety of their earnings for a longer period of time.

Two strategies for securityTwo strategies for security1.1. Strip hedging: -it involves buying VARious futures contracts with Strip hedging: -it involves buying VARious futures contracts with different delivery times, which are matching the investor's exposuredifferent delivery times, which are matching the investor's exposure dates. The basis risk is less here.dates. The basis risk is less here.2.2. Stack Stack hedging: buying VARious futures contracts, which are hedging: buying VARious futures contracts, which are concentrated in the nearby delivery months. Here the basis risk isconcentrated in the nearby delivery months. Here the basis risk is more the liquidity position is far superior to strip hedging.more the liquidity position is far superior to strip hedging.

Treasury bond futuresTreasury bond futuresThe most popular long-term interest rate futures contract is theThe most popular long-term interest rate futures contract is the Treasury bond futures contract traded on the Chicago board of trade.Treasury bond futures contract traded on the Chicago board of trade.

The underlying instrument is a $1,00,000 par value hypothetic-al bondThe underlying instrument is a $1,00,000 par value hypothetic-al bond for a 20 year period. The notional coupon rate is at present 6% . Thefor a 20 year period. The notional coupon rate is at present 6% . The Treasury bond futures price is quoted at par of 100. Treasury bond futures price is quoted at par of 100. Quotes are in 32nds of 1%. So a quote of 94-16 means 94 and 16/32 orQuotes are in 32nds of 1%. So a quote of 94-16 means 94 and 16/32 or 94.50. So a buyer is prepared to accept delivery at 94.50% of par94.50. So a buyer is prepared to accept delivery at 94.50% of par value. Since the par value is $1,00,000 the hypothetical t-bond price isvalue. Since the par value is $1,00,000 the hypothetical t-bond price is $94,500 for buyer and seller. the minimum price fluctuation is 1/32nd$94,500 for buyer and seller. the minimum price fluctuation is 1/32nd of 1% i.e $31.25 for $1,00,000 par value.of 1% i.e $31.25 for $1,00,000 par value.

Treasury bills, notes and bonds.Treasury bills, notes and bonds.T-bills:- these are short term gilt edged securities sold by us treasuryT-bills:- these are short term gilt edged securities sold by us treasury at a discount.at a discount.T-notes:- these are medium term coupons bearing gilt edged securitiesT-notes:- these are medium term coupons bearing gilt edged securities sold through periodic auctions.sold through periodic auctions.T-bonds:-these are long term coupons bearing gilt edged securitiesT-bonds:-these are long term coupons bearing gilt edged securities sold at periodic auctions.sold at periodic auctions.

MODULE –7MODULE –7

Credit risk and derivativesCredit risk and derivatives

Credit derivatives are the financial instruments designed to transferCredit derivatives are the financial instruments designed to transfer the credit risk of one counterpart to another. Credit risk arises main-lythe credit risk of one counterpart to another. Credit risk arises main-ly due to the default of the debt-or or due to the deterioration of thedue to the default of the debt-or or due to the deterioration of the credit quality of the debtor. Due to the incidence of such risk thecredit quality of the debtor. Due to the incidence of such risk the creditor can only receive the amount that the debtor provides. creditor can only receive the amount that the debtor provides.

It is related to the offsetting of credit risk to be incurred in a firm. TheIt is related to the offsetting of credit risk to be incurred in a firm. The concept of derivative is to create a contract that derives from anconcept of derivative is to create a contract that derives from an original contract or asset. A credit derivative is a contract that involvesoriginal contract or asset. A credit derivative is a contract that involves a contract between parties in relation to a return from the credit asset.a contract between parties in relation to a return from the credit asset. Without transferring the asset.Without transferring the asset.

Credit derivativesCredit derivativesThere are such instruments which transfer either specific or all theThere are such instruments which transfer either specific or all the inherent risks of a credit position from one party to the other. Here theinherent risks of a credit position from one party to the other. Here the risk seller transfers its risk to the risk buyer against payment of arisk seller transfers its risk to the risk buyer against payment of a premium. These contracts are private and confidential which allow thepremium. These contracts are private and confidential which allow the user to manage their exposure to credit risk. user to manage their exposure to credit risk. They are also termed as off balance sheet financial instruments whichThey are also termed as off balance sheet financial instruments which permit one party (beneficiary) to transfer credit risk of a referencepermit one party (beneficiary) to transfer credit risk of a reference asset owned by it to another party (guarantor) without actually sellingasset owned by it to another party (guarantor) without actually selling

the asset. A credit derivative is a specific financial product designed tothe asset. A credit derivative is a specific financial product designed to mitigate or to assume specific forms of credit risk by hedgers andmitigate or to assume specific forms of credit risk by hedgers and speculators.speculators.The credit derivatives generally hedge directly to a particular debtor.The credit derivatives generally hedge directly to a particular debtor. The credit risk is typically debtor specific. Here the focus is placed onThe credit risk is typically debtor specific. Here the focus is placed on individual solutions specifically designed to fulfill customer specificindividual solutions specifically designed to fulfill customer specific desires with an eye on their balance sheet. the solutions are customerdesires with an eye on their balance sheet. the solutions are customer specific with no secondary market.specific with no secondary market.

Credit derivatives- featuresCredit derivatives- features1.1. It is a bilateral contract comprising two parties. One is the credit risk It is a bilateral contract comprising two parties. One is the credit risk protection buyer or beneficiary and the other is the credit riskprotection buyer or beneficiary and the other is the credit risk protection seller or guarantor.protection seller or guarantor.2.2. These These are traded on OTC market. OTC products are dealt with are traded on OTC market. OTC products are dealt with outside the regulated exchanges so they permit maximum flexibility inoutside the regulated exchanges so they permit maximum flexibility in designing the contract as per the needs of parties. designing the contract as per the needs of parties. 3. In credit derivatives contract the beneficiary(protection buyer) pays3. In credit derivatives contract the beneficiary(protection buyer) pays a fee called premium as in insurance business to the guarantora fee called premium as in insurance business to the guarantor (protection seller) i.e. a party which wants to protect itself from the(protection seller) i.e. a party which wants to protect itself from the future credit risk will pay fee to the other party which takes such risk.future credit risk will pay fee to the other party which takes such risk.4. The reference asset for which credit risk protection is purchased and4. The reference asset for which credit risk protection is purchased and sold is predetermined. Ex:-a bank loan, corporate bonds, debentures,sold is predetermined. Ex:-a bank loan, corporate bonds, debentures, trade receivables etc.trade receivables etc.5. The protection from credit risk regarding reference asset is arisen5. The protection from credit risk regarding reference asset is arisen due to VARious causes which are known as credit events. Ex:-due to VARious causes which are known as credit events. Ex:- bankruptcy, insolvency, payment default, price decline, ratings.bankruptcy, insolvency, payment default, price decline, ratings.6. VARious instruments are being used in the credit-derivatives market6. VARious instruments are being used in the credit-derivatives market like credit-default swaps, total return swaps, credit option, etc.like credit-default swaps, total return swaps, credit option, etc.7. The settlement between the counter-parties in such contract on the7. The settlement between the counter-parties in such contract on the credit event is settled on cash or in terms of physical financial assetscredit event is settled on cash or in terms of physical financial assets (loan/bond). If the guarantor is not satisfied with the pricing or(loan/bond). If the guarantor is not satisfied with the pricing or valuation he has a right to ask for physical settlementvaluation he has a right to ask for physical settlement8.in general credit derivatives guidelines are issued by international8.in general credit derivatives guidelines are issued by international swaps and derivatives association known as master agreement and theswaps and derivatives association known as master agreement and the legal format of a derivative contract.legal format of a derivative contract.Credit derivatives are the most important financial innovations whichCredit derivatives are the most important financial innovations which assist credit managers to realize their credit exposures and then to actassist credit managers to realize their credit exposures and then to act optimally to hedge and replicate credit risk.optimally to hedge and replicate credit risk.

Credit risk-conceptCredit risk-conceptRisk may be of two types:-Risk may be of two types:-11.. Market risk. Market risk. 2. Firm specific risk.2. Firm specific risk.

Market risk arises due to movements in interest rates, exchange rates,Market risk arises due to movements in interest rates, exchange rates, stock prices, commodity prices, trade restrictions, economic sanctions,stock prices, commodity prices, trade restrictions, economic sanctions, govt. policies etc in adverse directions creating an effect on the firms.govt. policies etc in adverse directions creating an effect on the firms.Firm specific risk refers to the possibility that an individual borrowersFirm specific risk refers to the possibility that an individual borrowers circumstances change for the worse resulting in failing to makecircumstances change for the worse resulting in failing to make obligated payments. The market risk is managed by entering intoobligated payments. The market risk is managed by entering into offsetting or hedging transaction but in the preview of firm specific riskoffsetting or hedging transaction but in the preview of firm specific risk common called as credit risk. common called as credit risk. Credit risk refers to the possibility that a borrower will fail to service orCredit risk refers to the possibility that a borrower will fail to service or repay a debt on time. It is also defined as the possibility of lossesrepay a debt on time. It is also defined as the possibility of losses associated with diminution in the credit quality of borrower or counterassociated with diminution in the credit quality of borrower or counter parties. For ex in a bank the party may refuse outright commitments,parties. For ex in a bank the party may refuse outright commitments, settlements etc.settlements etc.

Credit risk- formsCredit risk- forms1.1. Direct lending:- principal/ interest may not be repaid. Direct lending:- principal/ interest may not be repaid.2.2. In case of guarantee/letter of credit funds may not be coming. In case of guarantee/letter of credit funds may not be coming.3.3. Funds settlement may not be effected in securities trading. Funds settlement may not be effected in securities trading.4.4. in case of cross border exposure free transfer of funds may cease or in case of cross border exposure free transfer of funds may cease or bebe restricted by governments. restricted by governments.

Credit derivatives instrumentsCredit derivatives instrumentsThe basic feature of credit derivative instruments is that they separateThe basic feature of credit derivative instruments is that they separate the credit risk from the total risk allowing the trading of credit risk withthe credit risk from the total risk allowing the trading of credit risk with the purpose of replicating credit risk, transferring credit risk andthe purpose of replicating credit risk, transferring credit risk and hedging credit risk. the important instruments of credit derivativeshedging credit risk. the important instruments of credit derivatives are:- are:- 1. Credit default swaps:- (cds) is a bilateral derivative contract where1. Credit default swaps:- (cds) is a bilateral derivative contract where one party agrees to pay another party periodic fixed payments inone party agrees to pay another party periodic fixed payments in exchange for receiving “credit event protection” in the form ofexchange for receiving “credit event protection” in the form of payment for any adverse credit event over a pre agreed period. payment for any adverse credit event over a pre agreed period.

Credit derivatives instruments (cds)Credit derivatives instruments (cds)The typical credit events are bankruptcy, failure to pay, restructuring,The typical credit events are bankruptcy, failure to pay, restructuring, failure to pay, repudiation/ moratorium.failure to pay, repudiation/ moratorium.Features:- Features:- 1. It is a bilateral contract between protection buyer and seller.1. It is a bilateral contract between protection buyer and seller.2. The protection buyer pays a fee to the protection seller for receiving2. The protection buyer pays a fee to the protection seller for receiving the credit event protection. It is expressed in annualized basis points ofthe credit event protection. It is expressed in annualized basis points of a transactions nominal amount.a transactions nominal amount.3. The third party and the specific obligation if any on which even3. The third party and the specific obligation if any on which even protection is concurrently bought and sold are referred to as theprotection is concurrently bought and sold are referred to as the reference entity and reference obligation.reference entity and reference obligation.

4. Reference credit is the contingent amount which will be paid by the4. Reference credit is the contingent amount which will be paid by the seller in case adverse event occur. seller in case adverse event occur. 5. The reference credit must be nominated under the default swap5. The reference credit must be nominated under the default swap contract. Also the reference credit asset must also be specified in thecontract. Also the reference credit asset must also be specified in the default swap contract. Also to be mentioned is the asset value.default swap contract. Also to be mentioned is the asset value.6. The credit event triggers the obligation of the provider of default6. The credit event triggers the obligation of the provider of default protection to make payment either in cash or the underlying asset.protection to make payment either in cash or the underlying asset.

Basket linked credit swapsBasket linked credit swapsIn this type of swap contract credit default is based on a basket ofIn this type of swap contract credit default is based on a basket of underlying assets with different issuers. For ex a us$100 millionunderlying assets with different issuers. For ex a us$100 million transaction may comprise four underlying credit assets – a five yeartransaction may comprise four underlying credit assets – a five year German bond, a five year Canadian bond, a five year French bond andGerman bond, a five year Canadian bond, a five year French bond and 5 year Swiss bonds.5 year Swiss bonds.Here the default provider provides protection on any 4 assets up to aHere the default provider provides protection on any 4 assets up to a face value of us$100 million on a first to default basis is providingface value of us$100 million on a first to default basis is providing protection of us$400 million of credit assets. The important point inprotection of us$400 million of credit assets. The important point in this concept is first to default of any credit assets included in thethis concept is first to default of any credit assets included in the basket of credits.basket of credits.2. Total return swaps:- (trs) these are bilateral contracts designed to2. Total return swaps:- (trs) these are bilateral contracts designed to replicate the economic returns arising of underlying asset or areplicate the economic returns arising of underlying asset or a portfolio of assets for a pre-specified time. here one party pays theportfolio of assets for a pre-specified time. here one party pays the total return ( interest + capital appreciation) of a asset and in returntotal return ( interest + capital appreciation) of a asset and in return the other pays floating rate payments (LIBOR + spread). the other pays floating rate payments (LIBOR + spread). These floating payments represents a funding cost of the trs payer. AThese floating payments represents a funding cost of the trs payer. A trs contract allows the trs receiver to obtain the economic returns of antrs contract allows the trs receiver to obtain the economic returns of an asset without funding thereon its balance sheet. So trs is primarily offasset without funding thereon its balance sheet. So trs is primarily off balance sheet financial vehicle.balance sheet financial vehicle.Total return payers are typically such lenders and other investors whoTotal return payers are typically such lenders and other investors who want to reduce their exposure to an asset without removing it fromwant to reduce their exposure to an asset without removing it from their balance sheet.their balance sheet.Other return receivers are typically such institutions who want toOther return receivers are typically such institutions who want to invest funds on a leverage basis to diversify their portfolios or intend toinvest funds on a leverage basis to diversify their portfolios or intend to higher return by taking on risk exposure.higher return by taking on risk exposure.

Credit spreadsCredit spreads

It represents the margin between the risk free rate of returnIt represents the margin between the risk free rate of return designated to compensate the investor for the risk undertaken ondesignated to compensate the investor for the risk undertaken on default of the underlying asset. It is the difference between return ofdefault of the underlying asset. It is the difference between return of the underlying security and the return on the corresponding risk freethe underlying security and the return on the corresponding risk free security.security.It is to understand the relative credit value changes in contract toIt is to understand the relative credit value changes in contract to changes in the interest rates, credit spread expectation, and the termchanges in the interest rates, credit spread expectation, and the term structure of credit spread. This is required to design credit optionstructure of credit spread. This is required to design credit option

derivatives which would be the natural extension of financial marketsderivatives which would be the natural extension of financial markets to unbundled risk. to unbundled risk.

Credit optionsCredit options

It gives the option holder the right to sell a bond to the other partyIt gives the option holder the right to sell a bond to the other party (investor) at a certain strike price expressed in terms of a spread over(investor) at a certain strike price expressed in terms of a spread over a benchmark. On the expiration if the actual spread is lower than thea benchmark. On the expiration if the actual spread is lower than the strike price then the bond holder will not exercise the option, therebystrike price then the bond holder will not exercise the option, thereby the option is worthless.the option is worthless.If the actual spread is higher than the strike price then the bond holderIf the actual spread is higher than the strike price then the bond holder will deliver the bond and the investor pays the price whose yieldwill deliver the bond and the investor pays the price whose yield spread over the bench mark equals the strike spread. credit optionspread over the bench mark equals the strike spread. credit option may be put and call options. Put options are 1. Price options 2. Spreadmay be put and call options. Put options are 1. Price options 2. Spread options.options.In the price put options the option writer agrees to compensate theIn the price put options the option writer agrees to compensate the option buyer for a decline in value of the underlying asset below theoption buyer for a decline in value of the underlying asset below the strike price. Upon the exercise of the credit option the payoff isstrike price. Upon the exercise of the credit option the payoff is determined by subtracting the market price from the strike price of thedetermined by subtracting the market price from the strike price of the asset.asset.Strike price is usually determined by taking the present value of theStrike price is usually determined by taking the present value of the asset’s cash flow discounted at the risk free rate plus the strike creditasset’s cash flow discounted at the risk free rate plus the strike credit spread. The spread put options are based upon the spread betweenspread. The spread put options are based upon the spread between the bond yield and the corresponding treasury yield.the bond yield and the corresponding treasury yield.Second type of credit options are referred to as call options which areSecond type of credit options are referred to as call options which are based on the credit spread. These are structured in such a way thatbased on the credit spread. These are structured in such a way that the option is in the money when the credit spread exceeds thethe option is in the money when the credit spread exceeds the specified (strike) spread level. specified (strike) spread level.

Credit linked notesCredit linked notes

This instrument enables the invest-or to purchase an asset with aThis instrument enables the invest-or to purchase an asset with a return linked to the credit risk of the asset itself and the additionalreturn linked to the credit risk of the asset itself and the additional credit risk transferred by way of credit derivative between the parties.credit risk transferred by way of credit derivative between the parties. it is a combination of a regular note (bond) and a credit option.it is a combination of a regular note (bond) and a credit option.Being a regular note with coupon, maturity and redemption it is an onBeing a regular note with coupon, maturity and redemption it is an on balance sheet instrument just like credit default swap. the price orbalance sheet instrument just like credit default swap. the price or coupon of the note is based on the performance of a reference asset. Itcoupon of the note is based on the performance of a reference asset. It means the investor receives a coupon and redemption at par valuemeans the investor receives a coupon and redemption at par value unless there has been credit event by a reference credit.unless there has been credit event by a reference credit.If there is a credit event in that case the amount will be redeemed atIf there is a credit event in that case the amount will be redeemed at par value minus a contingent payment to the investor. the issuerpar value minus a contingent payment to the investor. the issuer receives a premium for taking exposure to the reference credit. Thereceives a premium for taking exposure to the reference credit. The premium forms part of the coupon that is paid to the investor. premium forms part of the coupon that is paid to the investor.

Mechanism of credit linked notesMechanism of credit linked notes

CLN’s are created through a trust or special purpose vehicle (spv)CLN’s are created through a trust or special purpose vehicle (spv) which is collateralized with AAA rated securities. It is a credit swapwhich is collateralized with AAA rated securities. It is a credit swap between a bank and the issuer. It can also be issued by a NBFC or abetween a bank and the issuer. It can also be issued by a NBFC or a bank directly. if the issuer is a trust it enters into a default swap with abank directly. if the issuer is a trust it enters into a default swap with a deal arranger (3deal arranger (3rdrd party) in return for a premium. party) in return for a premium.In case of a default the trust pays the dealer par amount the recoveryIn case of a default the trust pays the dealer par amount the recovery rate in exchange for an annual fee. this annual fee is passed on to therate in exchange for an annual fee. this annual fee is passed on to the investors in the form of higher coupon on the notes. The investorsinvestors in the form of higher coupon on the notes. The investors purchase the securities from the issuer which pays a floating or fixedpurchase the securities from the issuer which pays a floating or fixed coupon during the life. coupon during the life. Coupon reflects risk of issuer and the credit swap. At the time ofCoupon reflects risk of issuer and the credit swap. At the time of maturity the investors receive the par amount if no credit event occursmaturity the investors receive the par amount if no credit event occurs (referenced credit defaults) or declares bankruptcy. If the credit event(referenced credit defaults) or declares bankruptcy. If the credit event occurs the principal at par minus contingent payment will be paid tooccurs the principal at par minus contingent payment will be paid to investors. The investor is selling the credit protection in exchange forinvestors. The investor is selling the credit protection in exchange for higher yield in terms of coupon on the note.higher yield in terms of coupon on the note.

MODULE – 8MODULE – 8Value at risk (VAR) measureValue at risk (VAR) measureIt is a statistical measure of the maximum potential loss from uncertainIt is a statistical measure of the maximum potential loss from uncertain events in the normal business over a particular time horizon. It isevents in the normal business over a particular time horizon. It is measured in units of currency through a probability level. It is the lossmeasured in units of currency through a probability level. It is the loss measurement consistent with a confidence limit such as 99% on ameasurement consistent with a confidence limit such as 99% on a probability distribution.probability distribution.It implies that this is the measurement of a loss which has a chance ofIt implies that this is the measurement of a loss which has a chance of only 1% of being exceeded. That means if a trader mis hedges a deal itonly 1% of being exceeded. That means if a trader mis hedges a deal it is a must to know the chances of loss before they occur. VAR is definedis a must to know the chances of loss before they occur. VAR is defined as the maximum loss a portfolio of securities can face over a specifiedas the maximum loss a portfolio of securities can face over a specified time period with a specified level of probability. time period with a specified level of probability. Ex:- a VAR of $1 million for a day at a probability of 5% means that theEx:- a VAR of $1 million for a day at a probability of 5% means that the portfolio traded securities would expect to loose at $1 million in oneportfolio traded securities would expect to loose at $1 million in one day with a probability of 5%. Alternatively there is 95% probabilityday with a probability of 5%. Alternatively there is 95% probability that the loss from the portfolio in one day should not exceed $1that the loss from the portfolio in one day should not exceed $1 million. million. So losses may occur once in 20 trading days. VAR actually assigns aSo losses may occur once in 20 trading days. VAR actually assigns a probability to a dollar amount of happening of the loss. it is not theprobability to a dollar amount of happening of the loss. it is not the maximum loss that could occur but only a loss amount that couldmaximum loss that could occur but only a loss amount that could expect to exceed only at some percentage of time. The actual loss thatexpect to exceed only at some percentage of time. The actual loss that may occur could be much higher than at VAR.may occur could be much higher than at VAR.

Approaches to computing VAR Approaches to computing VAR There are various approaches to computing VAR, the most importantThere are various approaches to computing VAR, the most important ones are:-ones are:-the Variance co-Variance approachthe Variance co-Variance approachhistorical simulation approachhistorical simulation approachMonte Carlo simulation approachMonte Carlo simulation approach

VAR-Variance covariance approachVAR-Variance covariance approachThis allows an estimate to be made of the potential future losses of aThis allows an estimate to be made of the potential future losses of a portfolio through using statistics on volatility of risk factors in the pastportfolio through using statistics on volatility of risk factors in the past and correlations between changes in their values. Volatilities andand correlations between changes in their values. Volatilities and correlation risk factors are calculated for a selected period of holdingcorrelation risk factors are calculated for a selected period of holding the portfolio.the portfolio.This is done using historical data. VAR is computed as multiplyingThis is done using historical data. VAR is computed as multiplying expected volatility of the portfolio by a factor that is selected based onexpected volatility of the portfolio by a factor that is selected based on the desired confidence level. This is based on the assumption that thethe desired confidence level. This is based on the assumption that the underlying market factors follow a multivariate normal distribution. underlying market factors follow a multivariate normal distribution. As the portfolio return is a linear combination of normal Variables it isAs the portfolio return is a linear combination of normal Variables it is also normally distributed. The normal VAR is easy to handle becausealso normally distributed. The normal VAR is easy to handle because

the VAR multiple of the portfolio std deviation and the portfolio std devthe VAR multiple of the portfolio std deviation and the portfolio std dev is the linear function of individual volatilities and covariance.is the linear function of individual volatilities and covariance.The following facts are to be consi-dered.1.movements in marketThe following facts are to be consi-dered.1.movements in market prices do not always follow a normal distribution they sometime exhibitprices do not always follow a normal distribution they sometime exhibit heavy tails, which means a tendency to have a relatively moreheavy tails, which means a tendency to have a relatively more frequent occurrence of extreme values than following a normalfrequent occurrence of extreme values than following a normal distribution. distribution. 2. Models may not appropriately depict market risk arising from2. Models may not appropriately depict market risk arising from extraordinary events.extraordinary events.3. The past is not always a good guide to the future for example3. The past is not always a good guide to the future for example correlation forecast may not hold true.correlation forecast may not hold true.

VAR- historical simulation approachVAR- historical simulation approachThis approach uses historical data of actual price movements toThis approach uses historical data of actual price movements to determine the actual portfolio distribution. In this way the correlationsdetermine the actual portfolio distribution. In this way the correlations and volatilities are implicitly handled. the advantage here is that theand volatilities are implicitly handled. the advantage here is that the fat tailed nature of security’s distribution is preserved.fat tailed nature of security’s distribution is preserved.Fat tails refer to the fact that the large market moves occur moreFat tails refer to the fact that the large market moves occur more frequently than what would occur if the market returns was normallyfrequently than what would occur if the market returns was normally distributed. in using historical simulation changes that have been seendistributed. in using historical simulation changes that have been seen in relevant market prices and the risk factors are analyzed over 1 to 5in relevant market prices and the risk factors are analyzed over 1 to 5 years time.years time.The portfolio under examination is then valued using changes in theThe portfolio under examination is then valued using changes in the risk factors derived from the historical data to create the distribution ofrisk factors derived from the historical data to create the distribution of the portfolio returns. we then assume that this historical distribution ofthe portfolio returns. we then assume that this historical distribution of returns is also a good proxy for the distribution of returns of thereturns is also a good proxy for the distribution of returns of the portfolio over the next holding period.portfolio over the next holding period.The relevant percentile from the distribution of historical returns leadsThe relevant percentile from the distribution of historical returns leads to the expected VAR for the current portfolio. Of course if asset returnsto the expected VAR for the current portfolio. Of course if asset returns are normally distributed the VAR obtained under the historicalare normally distributed the VAR obtained under the historical simulation approach should be the same as that under Variancesimulation approach should be the same as that under Variance covariance approach.covariance approach.

Monte Carlo simulation approachMonte Carlo simulation approachTo apply this approach first we have to calculate the correlation andTo apply this approach first we have to calculate the correlation and volatility matrix for the risk factors. Then these correlations andvolatility matrix for the risk factors. Then these correlations and volatilities are used to drive a random number generator to computevolatilities are used to drive a random number generator to compute changes in the underlying risk factors. The resulting values are used tochanges in the underlying risk factors. The resulting values are used to re-price each portfolio position and determine trial gain or loss.re-price each portfolio position and determine trial gain or loss.This process is repeated for each random number generation and re-This process is repeated for each random number generation and re-priced for each random number generation and reprised for each trial.priced for each random number generation and reprised for each trial. the results are then ordered such that the loss corresponding to thethe results are then ordered such that the loss corresponding to the desired confidence level can be determined.desired confidence level can be determined.Monte Carlo simulation can be viewed as a hybrid of the VarianceMonte Carlo simulation can be viewed as a hybrid of the Variance covariance approach and the historical simulation approach. It uses thecovariance approach and the historical simulation approach. It uses the Variance covariance matrix to drive a simulation. this simulation worksVariance covariance matrix to drive a simulation. this simulation works

similar to the historical simulation but rather than simply using historysimilar to the historical simulation but rather than simply using history it creates the history (known as path). it creates the history (known as path). It is based on the Variance covariance matrix devised from the actualIt is based on the Variance covariance matrix devised from the actual historic market data. The greatest benefit of the Monte Carlohistoric market data. The greatest benefit of the Monte Carlo simulation VAR is the abilitysimulation VAR is the ability to use pricing models to revalue non-linear securities for each trial. In this way the non linear effects of option that were missed in the Variance covariance VAR can be captured in this approach.Monte Carlo simulation having its roots in random number generationMonte Carlo simulation having its roots in random number generation is exposed to sampling error. There is the risk of running too fewis exposed to sampling error. There is the risk of running too few simulations to adequately capture the distribution and this could resultsimulations to adequately capture the distribution and this could result in an inferior answer. However methods exist to estimate how far off ain an inferior answer. However methods exist to estimate how far off a simulation is so that we can decide whether to run or not to run trials.simulation is so that we can decide whether to run or not to run trials.