managing risk

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MANAGING RISK

Brealey-Myers Ch. 27 & Ch. 28

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Contents

1. Why manage risk?2. Insurance3. Forward & futures contracts4. Swaps5. Setting up a hedge6. Case: Metallgesellschaft7. Should cos. trade in derivatives?8. International risks

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1. Why Manage Risk?

A. Reducing risk of cash shortfalls / financial distress

B. Mitigating agency costsC. Evidence on risk management

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1A: Reducing Risk of Cash Shortfalls

Cash shortages resulting from risk factors result in:• Inability of the firm in meeting its expenses &

other dues on time• Foregoing profitable investment / business

opportunities • Not hedging certain types of risk can result in

such large potential outflow of funds that firm will face bankruptcy

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1A: Reducing Risk of Cash Shortfalls

• Lenders are aware of all risks in any industry and require the firms to arrange hedging / insurance arrangements, to protect themselves

• It is only by hedging risks, as required by the lenders, a firm can avail of the benefits of debt financing

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1B: Mitigating Agency Costs

• Agency costs relate to the behaviour of managers & the decisions they take

• In order to increase their incentives they may try to improve profitability by taking very high risks – this can affect the existence of the firm

• In order to protect their jobs they may not even take the reasonable risks – this can affect the growth of firm

• Managers can be better monitored & motivated in the presence of hedging

• In the presence of hedging their performance can be separately identified from the impact of market volatility

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1C: Evidence on Risk Management

Risks Hedged Hedging ToolsFire, accidents, theft InsuranceMarket risks: Currency DerivativesMarket risks: Commodities: input / output

Derivatives

Market risks: Interest rates

Derivatives

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1C: Evidence on Risk Management

• Hedging tends to be common practice when top management holds large personal equity shareholdings in the co.

• Hedging is less common when top management holds stock options instead of equity positions. Why?

• Firms that hedge tend to have high debt ratios

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2. Insurance• Firms use insurance to protect against specific risks –

fire, accidents, natural calamities• Insurance is a risk transfer mechanism• Insurance cannot be used to cover macroeconomic

risks• Buying insurance is not a Zero-NPV deal for the insured

because the premium charged by insurer has to compensate for: 1. Losses on risk covered, 2. Admin. costs 3. Adverse selection 4. Moral hazard 5. Profit

• When the costs related with 1, 2, 3 & 4 above are large, insurance is an expensive tool of protection

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2. Insurance…• Most of the risks faced by the insurance cos. follow

a jump process (jump risks): a sudden strike of hurricane & widespread damages, sudden terrorist attack causing widespread loss of life & property

• Insurers have started to protect themselves from such large risks by issuing catastrophe bonds (Cat Bonds)

• These bonds are a means of sharing catastrophic risks with investors

• Payment on a Cat Bond depends on whether a specified catastrophe occurs & how much is lost

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2. Insurance: Cat Bonds

• Public issue of 1st Cat Bond was made by Winterthur, Swiss Auto-insurance giant

• Purpose: To protect itself from storm damage which generally leads to large no. of claims

• The Cat Bonds had an embedded condition: Interest payments will not be made if there was a hailstorm in which 6000 or more cars insured by it, were damaged

• Effectively the investors in the Cat Bonds had coinsured the insurance co’s risks

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2: Caselet: British Petroleum (BP)• Conventional practice of cos is to buy insurance against

large potential losses & do not buy insurance against routine losses because large losses can cause financial distress but not the small ones

• BP questioned the conventional practice & changed its insurance strategy

• It allowed local managers to buy insurance against routine risks (those risks in which insurance cos. were more efficient in assessing & pricing risk, & charge competitive premiums due to intense competition)

• It decided not to buy insurance for losses over $10 m

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2: Caselet: British Petroleum (BP)• According to BP insurance cos. were less efficient in

assessing such large & specialised risks than BP itself & hence less effective in advising on the protective measures

• Hence the insurance premiums charged on such large risks were not competitively priced

• BP assessed large losses of over $ 500 m have a very low probability of occurrence (once in 30 years ). For smaller cos. this would mean bankruptcy. But for a giant like BP, such loss after tax adjustment would be less than 1% of its equity value

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2: Caselet: British Petroleum (BP)

• Before implementing the new insurance strategy BP was paying $ 115 m a year in premiums & receiving $ 25 m a year in claims

• Assume that $ 35 m of premiums & the entire amount of claims were for routine risks and its opportunity cost of capital is 10%

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• Que 1: What would be the value of savings made by the change in strategy without considering the expected cost of not insuring for the big risks?

• Que 2: What would be the expected cost of not taking insurance protection for the big risks?

• Que 3: Is the change in insurance strategy justified financially?

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• Conclusion: For very low-probability risks investors themselves can eliminate the impact by holding diversified portfolios (thus stock market could absorb the risk more efficiently than the insurance industry)

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3. Forward & Futures Contracts

A. What is a forward contract?B. What is futures contract?C. Pricing of financial futures contractsD. Commodity spot & futures pricesE. Option ContractsF. Related mattersG. Concept of forward interest rates

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3A: What is a Forward Contract?

• It is a contract of purchase & sale of a specified asset for delivery & payment to be made in future

• The specified price is for future delivery: hence called forward price in contrast with the price for immediate delivery called spot price

• The buyer is said to have a long position; seller is said to have a short position

• Both parties eliminate their business risks: buyer fixes the costs & seller fixes the revenues

• However both are exposed to counterparty risk

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3B: What is a Futures Contract?

• A futures contract is a standardised forward contract

• Futures contracts are traded on futures exchanges

• Futures contracts are marked to market• Each day the profits / losses on the position are

calculated & the parties pay to the exchange any losses incurred in a day or receive any profits earned in the day from the exchange

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3B: What is a Futures Contract?

• Effectively each day the parties close out their position at a profit / loss and reopen a new contract at the prevailing market price for the same delivery date

• The futures exchange settles each futures contract on a daily basis with the resulting cash flows from profits / losses paid & received

• By this mechanism the futures exchange guarantees the contracts & eliminates counterparty risk

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3C: Pricing of Financial Futures

• An index futures contract is an example of a financial futures

• For a specified maturity index futures are sold at a specified price and each index futures contract is for a specified multiple of the index

• So if the index is an artificial asset then the multiple represents the quantity of the asset

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• If a person sells an index futures to you for delivery of the index after six months then the seller has to:

1. Buy the index today at the spot price2. In order to pay for the spot price he has to arrange

for money & incur financing cost at the prevailing interest rate

3. Hold the index for six months4. Earn any income the index distributes during the 6-

month holding period

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• So the price of the index futures contract today should be equal to:

Spot price of index today + (Interest on the spot price - Any income/dividends generated by the index during the period up to the maturity)

tft yrSF )1(0

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• Eg 4: Calculate the price of 6-month DAX index futures contract if the current value of the index is 3970.22, risk-free interest rate is 3.5% pa and the dividend yield on the index is 2% pa. Assume semi-annual compounding.

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3D: Commodities Spot & Futures Prices

Differences between buying commodities spot & futures:• Buying futures allows the buyer to save on the cost of

financing • There is no need of storage; so futures buyer can save

on the storage costs, wastage, security etc• But buyer of commodity futures loses the gains from

any opportunities which require immediate availability of the commodity: convenience yield

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So the price of a commodities futures contract today should be equal to:

Spot Price + (Interest on spot price + Storage costs - Convenience Yield) up to the maturity of contract

Exception: There is no convenience yield for commodities like electricity

tft YieldeConveniencCostStoragerSF ) - 1(0

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Eg 5: In Jan 2006 the spot price of coffee was Rs. 102 / kg & 3 month futures price was Rs. 98 / kg. The interest rate was 6% pa. Calculate net convenience yield (convenience yield – storage costs).

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3E: Option Contracts

• An option contract gives the holder the right to buy/sell the underlying asset by a specified future date for a specified price

• 2 types: Call & Put options• A call option gives the holder right to buy• A put option gives the holder right to sell • The writer of the option has the obligation to

take the opposite position of the holder• The holder may not exercise the right

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3F: Related Matter

• Trading in futures contracts happens in large volumes due to their liquidity. They are very liquid because they are standardised & have limited no. of maturity dates in a year

• If futures contracts on an asset do not suit the needs of an investor then forward contracts can be customised to the suit the specific requirements

• Forward contracts are also possible on: Electricity, Interest rates

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3G: Concept of Forward Interest Rates

Suppose the interest rates prevailing now are:• For 1 year: 10% pa• For 2 years: 12% pa

The interest rates available now are called spot rates• The spot interest rate for 2 years includes: (a) the spot

rate of interest for 1st year & (b) the rate of interest for the 2nd year decided now (called forward rate)

• Forward rate of interest is the rate applicable to a future time period decided now

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3G: Concept of Forward Interest Rates

So:(1 + 2-year spot rate)2 = (1 + Spot rate for year 1) X (1 + Forward rate for year 2)Hence: Forward interest rate for year 2 =

14.04% 0.1404 1 - 1.101.12

1 - rate)spot year -1 1(rate)spot year -2 (1

2

2

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3H: Creating a Synthetic Forward Lending

• A forward lending is a commitment given now for lending at a future point of time

• The interest rate applicable in a forward lending or forward borrowing commitment is a forward interest rate

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3H: Synthetic Forward Lending: Example

Eg. 6:• How will you create a synthetic forward lending

transaction for 1 year, given the following data?• Funds available now: 100 • Spot rate of interest for 1 year: 10%• Spot rate of interest for 2 years:12%• Demonstrate the transaction by showing the cash

flows.• Also calculate the rate of interest applicable to the

forward lending transaction

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3H: Synthetic Forward Lending: Eg. 6: Sol.

Steps:1. Borrow 100 now for 1 year at 10%2. Lend 100 now for 2 years at 12%3. Draw the net cash flows for now, year 1 & year 2

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• The net cash flows show: 1) There is no cash flow in year 0; 2) There is a synthetic forward lending of 110 at the end of year 1, for a period of 1 year

• Forward Rate of Interest =

Net cash Flows in Year 0, 1 & 2YEAR 0 YEAR 1 YEAR 2

Borrow for 1 year at 10% 100 -110 0Lend for 2 years at 12% -100 0 125.44Net cash flow 0 -110 125.44

%04.141404.01110

44.125

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• Conclusion: A synthetic forward lending transaction is created when you borrow now for a shorter term and lend now for a longer term.

• Question: How will you create a synthetic forward borrowing?

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4. Swaps

A. Interest rate swapsB. Currency swaps

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4A: Interest Rate Swap: Example• ABC Bank has made a 5-year Rs. 50 m loan carrying

interest rate of 8%, to a project• Interest receipts are of Rs. 4 m pa; the principal is to be

repaid in year 5• ABC Bank wants to receive interest payments at a

floating rate; so it wants to exchange the fixed interest receipts for floating interest receipts. How can we determine the amount of floating interest receipts?

• Given its credit rating ABC can borrow at 6% fixed rate for 5 years

• So its annual receipt of Rs. 4 m can support a fixed rate loan of: 4 / 0.06 = Rs. 66.67 m

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4A: Interest Rate Swap…Fixed-To-Floating Rate Swap thru a Swap Dealer:• Counterparty: Swap Dealer• Swap payments on a loan of Rs. 66.67 m at 6%

fixed rate for an equivalent loan with MIBOR floating rate to be received from counterparty

• Rs. 66.67 m principal is notional. It is never exchanged.

• Swap Dealer is quoting a rate of 6% against MIBOR• Example in Excel sheet: Fixed-to-Floating Swap

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4A: Interest Rate Swap…

• IRSs have no initial cost / value (NPV = 0) for both parties

• But the value of an IRS drifts away from 0 with time as long term interest rates change – one of the counterparty gains other loses

• Swap dealers try to protect their position by a series of forward / futures contracts / by an offsetting swap with a 3rd party

• Swaps are exposed to counterparty risk

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Example 6A:• Calculate the value of the previous swap if the

market interest rates for long term fixed rate debt, have increased to 7% with 3 yrs. remaining to maturity

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Example 6: Solution• PV(Fixed rate payments of 4m pa for 3 yrs &

maturity value 66.67m) at 7% discount rate = Rs. 64.92 m

• The value of swap = 66.67 – 64.92 = Rs. 1.75 m

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4B: Currency Swap: Example

• ABC Co. of US requires € 8m to finance its European operations. At present exchange rates € 8m = $ 10m

• EUR interest rate is 5%; USD interest rate is 6%• ABC is better known in US & not in Europe• What will happen if it borrows in Europe instead of

in US?• So ABC decides not to borrow Euros directly.• Instead it raises $ 10m by issuing 5-year 6% notes in

US & arranges for a swap with a counterparty, XYZ, to convert the USD loan to a EUR loan

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4B: Currency Swap…

• Under the currency swap arrangement XYZ agrees to pay ABC the USD amount to service its USD debt

• In exchange ABC agrees to make a series of annual payments in EUR to XYZ for servicing its EUR loan

USD EUR USD EUR USD EUR1. Issue USD Loan 10 -0.6 -10.62. Swap USD for EUR -10 8 0.6 -0.4 10.6 -8.43. Net Cash Flow 0 8 0 -0.4 0 -8.4

Year 0 Years 1-4 Year 5

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4B: Currency Swap…

The impact of the swap is:• Line 3 in table: Convert a 6% $ loan into 5% € loan• Line 2 in table: Year 1-4: A series of contracts to buy

USD by paying EUR i.e. Buying USD 0.6m by paying EUR 0.4m. Year 5: A contract to buy USD 10.6m by paying EUR 8.4m

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4C: Credit Derivatives• Protect lenders from default risks• A bank can give loan to a borrower with the credit risk

transferred to another bank• Common tool: Default Swap• Like an insurance on loans given with annual premiums• Can be applied to both individual / portfolio of loans• Bank A has given loan to customer X & enters into a

Default Swap with Bank B• Under this Bank A pays a fixed sum every year to Bank

B as long as Co. X has not defaulted. If X defaults then B compensates A for loss; otherwise pays nothing

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5. Setting Up a Hedge

• A position in an asset can be hedged by using derivatives: Futures or Options

• Setting up a hedge with Futures – corporate finance perspective

• Setting up a hedge with Options – corporate finance perspective

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5. Setting Up a Hedge With Futures: Example

• A farmer produces Type A potatoes & wants to hedge the price of his produce by selling potato futures.

• The potato futures are based on Type B potatoes• Historical data suggests that 1% change in the price of

potato futures (with Type B potatoes underlying) is associated with 0.8% change in price of Type A potatoes

• If the farmer wants to hedge the price for 100 MT Type A potatoes then he should sell 0.8 x 100 MT of potato futures = 80 MT worth of potato futures

• If 1 potato futures contract = 10 MT then this means farmer should sell: 80 / 10 = 8 potato futures contracts

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5. Setting Up a Hedge with Futures: Generalisation

• The hedging problem referred to in the example will not occur if the asset to be hedged & the asset underlying the futures contract are the same

• In that case generally a 1% change in the futures price of the underlying asset will be associated with 1% change in the value of the asset to be hedged

• So the quantity of asset sold by futures contracts should be exactly equal to the quantity of asset held

• The hedging problem referred to in the example is a situation of Cross Hedging – a common problem

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5. Setting Up a Hedge with Futures: Generalisation

• The problem of cross hedging occurs when the asset to be hedged is different from the one underlying the futures contract

• Suppose the following relation holds between Changes in Prices of Asset A and Changes in Futures Prices on Asset B (underlying asset)

Change in Price of A = α + δ (Change in Price of B)• The ‘δ’ is called hedge ratio.• Setting up a hedge requires estimating the hedge

ratio

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5. Setting Up Hedge with Options• Concept applied: Option Delta• Delta represents the change in the value of an

option that occurs with the change in the value of the underlying asset

• For a call option: Delta is +ve: This means an increase in the value of the asset results in an increase in the value of the option & vice versa

• Based on Delta a position in the asset can be hedged by taking a position in call option & a position in call option can be hedged by taking a position in the asset

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5. Setting Up Hedge with Options

• Because the Delta is +ve a long position in the asset can be hedged by taking a short position in a call option on the asset; short position in the asset can be hedged by a long position in the call

• Similarly a long position in a call option can be hedged by taking a short position in the asset; a short position in the call option can be hedged with a long position in the asset

• The value of Delta is used to determine the number of call options to be sold or bought

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6. Caselet: Metallgesellschaft • In 1993 the MGRM, US subsidiary of German Co.

Metallgesellschaft issued its customers price guarantees on gasoline, heating oil & diesel for up to 10 years. This way it aggressively attracted sales.

• It had sold > 150 million barrels of oils at prices 3-5 USD higher than the prevailing spot prices.

• It could not protect itself with futures contracts because for such long years futures contracts do not exist.

• So it bought a large no. of short dated futures contracts & rolled them over at the end of their maturity

• Since oil has +ve convenience yields generally, each time it rolled over its futures it used to sell the maturing contracts at a higher price than the price it had to pay for the new futures

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6. Caselet: Metallgesellschaft • In 1993 oil suddenly started showing negative

convenience yields. So the maturing futures contracts could be sold only at lower prices.

• So MGRM had to pay higher to roll over its short dated futures contracts

• Since these oil futures were marked to market & oil prices continued to fall in 1993, MGRM had to incur huge marked-to-market losses and had to pay large amounts in response to margin calls

• The fall in oil prices indicated that its long term forward contracts (guarantees) were appearing profitable, but this was only in books.

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6. Caselet: Metallgesellschaft • The BoD of the co. fired the CEO of its US subsidiary

& instructed it to cease all hedging activities & start negotiating with its customers to cancel the long term contracts.

• Almost at the same time the fall in oil prices reversed. If MGRM had held on to its long term contracts then they would have earned huge profits

Discussion Questions:• Was the CEO wrong or the BoD wrong?• Who’s mistake led to the massive losses?

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6A: Other Cases of Derivatives Disasters

Company EventShowa Shell, Japanese co. $1.5 billion loss on

positions in forex futuresBarings Brothers:Blue-chip British merchant bank with 200 year track record

$ 1.4 billion caused by one of its derivatives traders, Nick Leeson, at its Singapore office because of taking very large bets on the Japanese stock market index

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7. Should Cos. Trade in Derivatives?

• In 1970s & 80s cos. turned their treasury functions into profit centres by entering into derivatives trading & profits from such activities were also reported as part of their operations

• Losses arising out of indiscriminate trading occurred because cos. did not understand the risks of such activities & the potential losses that could result; they only focused on the profits they had earned

• Cos. should not cease derivatives trading. Rather they should exercise caution in doing so.

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7. Should Cos. Trade in Derivatives?

Precautions:1. Senior management should regularly monitor their

derivatives positions and should do sensitivity analysis of their impact on the firm on a regular basis

2. They should allow taking large positions only when they have superior information that increases the likelihood of profiting from the transactions

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8. International risks

A. Impact of interest rates on foreign exchange rates

B. Impact of inflation rates on foreign exchange rates

C. Relation between interest rates & inflation ratesD. Forward premium & changes in spot ratesE. Transaction exposure & Economic exposureF. International investment decisions

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8A: Interest Rates & Exchange Rates

• Country A: currency A• Country B: currency B• Exchange rate between currencies of A & B

expressed as: A / B (no. of units of A per unit of B)• Two types of exchange rates between currencies of

A & B: 1. Spot rate (S) & 2. Forward rate (F)• There are two interest rates in currencies A & B: rA & rB

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• At any point of time the two interest rates: rA & rB and the two exchange rates: S & F have to fulfill the following relationship:

• The above relationship is called Interest Rate Parity theory

• LHS denotes Difference in interest rates between the two countries / currencies

• RHS denotes Difference between forward & spot exchange rates

SF

rr

B

A

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• If the two interest rates: rA & rB and the two exchange rates: S & F, do not fulfill the above relationship then there will be opportunities for earning risk-free arbitrage profits.

• Market operators will continue doing arbitrage until the time the exchange rates (S & F) and the interest rates (rA & rB ) attain revised values which fulfill the above relationship

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Example: Verify whether the IRP theory holds for the following data:

• USD interest rate for 1 year: 1.22% pa• Mexican Peso interest rate for 1 year: 6.7% pa• Spot exchange rate (Peso/USD): Peso 10.9815/ USD• 1 year forward exchange rate (Peso/USD): Peso 11.5775 / USD

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8B: Inflation Rates & Exchange Rates

• Relation between changes in Spot exchange rates & inflation rates

• Arbitrage ensures that in general:a) Goods that can be bought more cheaply in the

foreign country will be imported and their domestic prices will be forced down

b) Goods that can be bought more cheaply in the domestic country will be exported and their foreign prices will be forced down

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8B: Inflation Rates & Exchange Rates…

• Country A: currency A• Country B: currency B• Exchange rate between currencies of A & B

expressed as: A / B (no. of units of A per unit of B)• S : Spot exchange rate between currencies A & B• E(S) : Expected spot exchange rate between

currencies A & B • iA : Inflation rate in country A (currency A)

• iB : Inflation rate in country B (currency B)

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• Due to differences in inflation rates between countries A & B the Spot exchange rate between currencies A & B will change over time

• Hence inflation rates in the two currencies, the spot exchange rate and the Expected spot exchange rate have to fulfill the following relationship:

• This relationship is called Purchasing Power Parity• LHS denotes Expected difference in inflation rates• RHS denotes Expected change in spot rate

B ofunit per A of units as expressed are S & E(S) where

)()1()1(

SSE

iEiE

B

A

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Example: Given the following data calculate the Expected spot rate between Peso & USD: Peso/USD

• Spot rate: 10.9815 Peso / USD• Inflation rate in Mexico (Peso): 6.5%• Inflation rate in US (USD): 1.5%

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8C: Interest Rates & Inflation Rates• Capital tends to flow where returns are highest• Investors are concerned with real returns – nominal

returns minus inflation• So capital will flow to countries which offer higher real

returns• So as long as the real return differs across countries there

will be flow of funds across countries until the real rates become equal in all countries

• This implies that real returns will be equal across countries

• Hence differences in nominal returns between countries will be equal to differences in inflation rates across them

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8D: Forward Premium & Changes in Spot Rates

• If investors do not care about risk then the forward exchange rate would be equal to what they expected the spot rate to be

• If 1 year forward Peso-USD rate is Peso 11.5775 / $ then it implies that traders expect the spot rate in 1 year to be Peso 11.5775 / $

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• If they expect the spot rate after 1 year to be Peso 12 / $ then nobody will by buy Peso forward by paying dollars because they will get more Pesos for each $ by waiting for 1 year & buying spot

• If they expect the spot rate after 1 year to be Peso 11 / $ then nobody will buy dollar forward by paying Pesos because they will pay less Pesos for dollars if they wait for 1 year & buy $ at spot rate

• Expectations theory: The percentage difference between forward rate & spot rate =

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Expectations theory: • Between any two currencies, A & B, the percentage

difference between forward rate & spot rate = Expected change in spot rate

A/B of in terms expressed are S & Fboth Where

)(SSE

SF

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8E: Transaction & Economic Exposure

• Transaction exposure arises out of the risk that the exchange rate of a foreign currency may change adversely for any business, from the time it entered into a transaction with a foreign party to the time it is settled

• For importers an increase in the exchange rate of the foreign currency from the time of entering into the contract to the time the payment is made – it increases their cost

• For exporters a decrease in exchange rate from the time of contracting to the time of receiving the revenues – it decreases their revenues

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• Transaction exposure can be hedged by entering into forward contracts

• Importers should buy the currency of payment forward

• Exporters should sell the currency of receipts forward

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• Economic exposure: An exporter may be affected even when it is not having any receivables from its customers.

• Exchange rate volatility may make the products sold by its competitors in other countries, cheaper

• When such a thing happens the exporter will lose business to its foreign competitors

• This exposure is called economic exposure• It is difficult to measure

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8F: International Investment Decisions

• In the presence of currency risks investment decisions should be separated from the decision to hedge / take currency risks

• Two ways of deciding1. Calculate the cash flows in home currency (which

will be received if the currency risk were hedged) & discount them in home currency cost of capital

OR2. Forecast the cash flows in foreign currency &

discount them in foreign currency cost of capital

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8F: Example (BM/771-3)

• A Swiss pharma co. is planning to invest in a plant in India

• The forecasted cash flows in Rs. millions are:

• The rupee cost of capital is 12%• Spot rate: Rs. 38 / SFr.• Rupee risk-free interest rate: 6%• SFr. risk-free interest rate: 4%• Evaluate the project using both approaches

Year 0 1 2 3 4 5

Cash Flow

-1300 400 450 510 575 650

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8F: Sol: Approach 1

Step 1: Forecast the cash flows in Rs: GivenStep 2: Discount cash flows in Step 1 in Rupee

cost of capital & calculate NPV in Rs.Step 3: Convert NPV in Rs. to NPV in SFr. By

using Rs./SFr. Spot exchange rate

Refer to Excel sheet

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8F: Sol: Approach 2

Step 1: Estimate the forward exchange rate for conversion of Rs. to SFr. for each year during the lifetime of the project using the Interest Rate Parity theory

Step 2: Use the forward exchange rates for the various years to convert the cash flows in Rs. to cash flows in SFr.

Step 3: Estimate the cost of capital in SFr.Step 4: Calculate the NPV in SFr. Refer to Excel sheet

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8F: Sol: Approach 2

• Step 1: Estimating the projected forward rate:

• Step 3: Cost of Capital in SFr:

Rs./SFr.in are F & SBoth rate;spot is S :Where

r1r1S (F) Rate ForwardYear -t

t

SFr.

Rs.

RateInterest Rs.1

RateInterest SFr.1Return Rs.1Return SFr.1

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8F: Cost of Equity: Example (BM/773-4)

• A Swiss co. is planning to invest in a project in India• Swiss risk-free interest rate: 4%• Market risk premium in Switzerland: 8.4%• Beta of Indian cos. in that industry relative to Swiss

market index: 0.7• Indian risk-free interest rate: 6%• Calculate the cost of equity for the Swiss Co. in SFr.• Calculate the cost of equity for the Swiss Co. in INR

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8F: Cost of Equity: Example (BM/773-4)

• Cost of equity of Swiss Co. in SFr. = Required Return in SFr. = SFr. Risk-free Rate + (Beta wrt Swiss Index * Swiss Market Risk Premium) = 4 + (0.7 x 8.4) = 9.9%

• Cost of equity of Swiss Co. in INR (= Required Return in INR) should fulfill the following relationship:

• (1 + Rs. Return) = 1.099 x 1.06/1.04 = 1.12 So: Rs. Return = 1.12 – 1 = 0.12 = 12%

RateInterest SFr. 1

RateInterest Rs.1Return SFr. 1 Return Rs.1

managing risk

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