tutorial question 1-13

UBFF3293 Risk Management (MAY 2016)

UNIVERSITI TUNKU ABDUL RAHMANFACULTY OF BUSINESS AND FINANCE

ACADEMIC YEAR 2016/2017

BACHELOR OF FINANCE (HONS)BACHELOR OF ECONOMICS (HONS) FINANCIAL ECONOMICS

BACHELOR OF BUSINESS ADMINISTRATION (HONS) BANKING AND FINANCEBACHELOR OF SCIENCE (HONS) STATISTICAL COMPUTING AND

OPERATIONS RESEARCH

UBFF 3293 RISK MANAGEMENTTUTORIAL QUESTIONSTUTORIAL QUESTIONS

Tutorial 1

1. Objective The focus is on risk management issues and therefore focuses on the essential concepts underlying the risk analytics of existing models. It provides knowledge of causes of increased volatility of financial risks, fundamentals of pricing principles, risk management techniques and derivative markets. It details analytics without attempting to provide a comprehensive coverage of each existing model

2. Learning Outcome On completion of this unit, a student shall be able to: Explain the role and scope of risk management in organization and justify the need

for a holistic approach to risk management Recognize and apply the principles which underpin the identification, measurement

and management of financial risks in large organizations Identify and apply various risk quantification measures and risk management tools

that are available in the market Undertake a critical analysis of risks from the viewpoint of the individual

transaction, the business module and the organization Describe and evaluate the effectiveness of a variety of approaches to risk

financing, risk transfer and risk control and the factors that the corporate should take into account in respect of such approaches and be able to make appropriate conclusions and recommendations thereon

3. Reading List

Main Text:a. Chance, D. & Brooks, R. (2010) Introduction to Derivatives and Risk

Management (8th ed.). Cengage Learning South-Western – Main Text

Additional Text:b. McDonald, R.L. (2006) Derivatives Markets, (2nd ed.). Pearson Education

Addison Wesley

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c. Horcher, K.A. (2005) Essentials of Financial Risk Management. John Wiley & Sons

d. Sundaresan, S (2002) Fixed Income Markets and Their Derivatives (2nd ed.). Thomson Learning South-Western

e. Crouchy, M., Galai, D. & Mark, R. (2002). Risk Management. New York: McGraw-Hill.

f. Hull, J. (2006). Options, Futures and Other Derivatives (6th ed.). New Jersey: Pearson Prentice Hall.

g. Gitman, L.J. (2009). Principles of Managerial Finance (12th ed.). Boston: Pearson Addison Wesley.

4. Method of Assessment No. Method of Assessment Total1. Coursework

a) Mid-term Test 20% (50 marks)b) Group Assignment 20% (50 marks) Total 40% 100 marks

40%

2. Final Examination 60%GRAND TOTAL 100%

5. AssignmentRefer to Assignment instructions

6. Reminder on DeadlinesMid-term Test Week 8 (23 July 2016, 10am & Venue to be informed)Submission of Assignment Week 7 Friday (15 July 2016, 12:30pm)

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Tutorial 2 (Topic 1)Introduction to Risk Management

Question 1What do you understand by the word ‘risk’?

Question 2Give an example of a situation that entails uncertainty but not exposure, and hence no risk.

Question 3Give an example of a situation that entails exposure but not uncertainty, and hence no risk.

Question 4Risk management is sometimes described as the process of identifying and evaluating the trade-off between risk and expected return, and choosing the appropriate course of action. Describe the risk management process.

Question 5Explain four aspects that determine whether financial risk management is successful in an organization.

Question 6Explain the advantages for senior management having detailed written policies on financial risk management.

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Tutorial 3 (Topic 2)Risk and Return

Question 1Consider the following assets:-

Market Asset 1 Asset 2Condition Probability Return Return Good 0.25 16% 4%Average 0.50 12% 6%Poor 0.25 8% 8%

i) Solve for the expected return and the standard deviation of return for each investment.

ii) Solve for the covariance and the correlation coefficient between Asset 1 and Asset 2.

iii) If your investment is divided equally between Asset 1 and Asset 2, what is your portfolio expected return and standard deviation?

iv) How should you divide your portfolio among Asset 1 and Asset 2 if you wish to minimize the standard deviation of your investment portfolio?

Question 2Below is price and dividend data for two companies for each of five months.

Security A Security BTime Price Dividend Price Dividend1 5.7 3.32 5.9 3.63 5.8 0.7 3.7 1.34 5.5 3.85 5.6 3.9i) Compute the rate of return for each company for each month.ii) Compute the average rate of return for each company.iii) Compute the standard deviation of the rate of return for each company.iv) Compute the covariance and correlation coefficient between security A and

security B.v) Assuming you invest 30,000 in security A and 40,000 in security B, compute

the average return and standard deviation for your portfolio.

Question 3To what extent can the overall risk of a portfolio be reduced? Explain with the help of correlation coefficient.

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Question 4An investor holds a portfolio consists of 10,000 shares of Kerzhakov Berhad and 12,000 shares of Lazovic Berhad. Details for each of the two companies are as follows:

Kerzhakov Berhad Lazovic BerhadExpected Return 15% 20%Dividend end of this year RM0.45 RM0.30Dividend growth rate 6% 8%Book value per share RM3.60 RM2.40Beta 2.88 0.83Calculate the portfolio’s systematic risk.

Question 5Given that a stock has daily volatility of 0.257, calculate its annual volatility using square root of time rule. (Assuming 250 trading days per year) What is your assumption about the stock’s volatility?

Question 6The volatility of a stock price is 25% per annum. What is the standard deviation of the percentage price change in one trading day? In eight trading days? In thirty trading days? Assume 252 trading days

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Tutorial 4 (Topic 3)Fixed Income Securities

Question 1Paul has recently inherited RM1, 000 and is considering purchasing 10 bonds of the Octopus Corporation. The bond has a par value of RM100 with 10 percent coupon rate and will mature in 10 years. Does Paul have enough money to buy 10 bonds if the required rate of return is 12 percent? (Note: calculation of bond’s intrinsic value is not needed).

Question 2a) IPM Company has an issue of $1,000 par value bonds with a 14 percent

coupon interest rate outstanding. The issue pays interest semiannually and has 10 years remaining to its maturity date. Bonds of similar risk are currently selling to yield a 12 percent rate of return. What is the value of these IPM Company bonds? What is the bond’s current yield?

b) The Coffee Plantation Company issued a 30-year bond 15 years ago with a face value of $1,000 and a coupon rate of 6%. The bond is currently selling for $850. What is the yield-to-maturity to an investor who buys it today at that price? (Assume semiannual coupon).

Question 3Describe the relationship between bond’s prices and interest rates using your own example.

Question 4Calculate the yield-to-maturity (YTM) and current yield for each of the bonds below:

Bond

Par Value Market Price Coupon rate (%) per period Years to maturity

X RM1,000 RM820 9% annually 8Y RM100 RM118 3% semiannually 5Z RM500 RM560 12% annually 12

Question 5Suppose you observe the following effective annual zero-coupon bond yields: 0.030 (1-year), 0.035 (2-year), 0.040 (3-year), 0.045 (4-year) and 0.050 (5-year)For each of the maturity year, compute the zero-coupon bond prices, continuously compounded zero-coupon bond yields, the par coupon rate and the 1-year implied forward rate.

Question 6Suppose you observe the following par coupon bond yields:3.30% (1-year), 3.55% (2-year), 3.87% (3-year)For each maturity year, compute zero-coupon bond prices, effective annual and continuously compounded zero-coupon bond yields and one-year implied forward rate. Assume the bond has a par value of RM 100.

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Tutorial 5 (Topic 4)Derivatives Markets

Question 1The key function of derivatives is in risk management. There are different types of risks found in today’s markets. Some of the commonly found risks are Market/Price Risk, Inflation Risk, Interest Rate Risk, Default/Credit Risk, Liquidity Risk, Currency/Exchange Rate Risk, and Operational Risk. Explain each type of risks.

Question 2What are the major functions of derivative markets in an economy?

Question 3Explain the difference between (a) forwards, (b) futures, and (c) options.

Question 4a. What are the three ways in which derivatives can be misused?b. Why is speculation controversial? How does it differ from gambling

Question 5What are the three limitations of forwards that led to the creation of futures?

Question 6What are the advantages of options over forwards and futures?

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Tutorial 6 (Topic 5 – Part I)Options

Question 1Why short puts and long calls are grouped together when considering position limits?

Question 2Discuss the three possible ways in which an open option position can be terminated. Is your answer different if the option is created in the over-the-counter market?

Question 3Consider an option that expires in 68 days. The bid and ask discounts on Treasury bill maturing in 68 days are 8.20% and 8.24%. Find the approximate risk-free rate.

Question 4The following option prices were observed for a stock on July 6, 2010. The stock is currently priced at RM165.13. The option’s expirations are July 17, August 21 and October 16. The risk-free rates are 0.0516, 0.0550 and 0.0588 respectively.Strike CALLS PUTS

Jul Aug Oct Jul Aug Oct155 10.50 11.80 14.00 0.20 1.25 2.75160 6.00 8.10 11.10 0.75 2.75 4.50165 2.70 5.20 8.10 2.35 4.70 6.70170 0.80 3.20 6.00 5.80 7.50 9.00Compute the intrinsic values and time values for the following American calls:a) July 160b) October 155c) August 170

Question 5The following option prices were observed for a stock on July 6, 2010. The stock is currently priced at RM165.13. The option’s expirations are July 17, August 21 and October 16. The risk-free rates are 0.0516, 0.0550 and 0.0588 respectively.Strike CALLS PUTS

Jul Aug Oct Jul Aug Oct155 10.50 11.80 14.00 0.20 1.25 2.75160 6.00 8.10 11.10 0.75 2.75 4.50165 2.70 5.20 8.10 2.35 4.70 6.70170 0.80 3.20 6.00 5.80 7.50 9.00Compute the intrinsic values and time values for the following American puts:a) July 165b) August 160c) October 170

Question 6

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The following option prices were observed for a stock on July 6, 2010. The stock is currently priced at RM165.13. The option’s expirations are July 17, August 21 and October 16. The risk-free rates are 0.0516, 0.0550 and 0.0588 respectively.Strike CALLS PUTS

Jul Aug Oct Jul Aug Oct155 10.50 11.80 14.00 0.20 1.25 2.75160 6.00 8.10 11.10 0.75 2.75 4.50165 2.70 5.20 8.10 2.35 4.70 6.70170 0.80 3.20 6.00 5.80 7.50 9.00Check the following combinations of European calls and puts to determine whether they are conform to the put-call parity rule. If you see any violations to the rule, suggest a strategy.a) July 155b) August 160c) October 170

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Tutorial 7 (Topic 5 – Part II)Options

Question 1List and discuss the six factors affecting stock option prices based on American calls and puts.

Question 2Calculate the price of a three month European call option on a non-dividend paying stock with a strike price of $50 when the current stock price is $52, the risk free interest rate is 10% per annum, and the volatility is 30% per annum.

Question 3What is the price of a European call option on a non-dividend paying stock when the stock price is $65, the strike price is $60, the risk-free interest rate is 12% per annum, the volatility is 20% per annum, and the time to maturity is six months?

Question 4PYQ October 2007 Section B Q3(a)(a) What is the price of a European call option on a dividend paying stock when

the stock price is $105, the strike price is $90, the risk-free interest rate is 12% per annum, the dividend yield is 8% per annum, the volatility is 20% per annum, and the time to maturity is nine months?You are given the following formulae:

C = Se−δT N (d1 )−Ke−rTN (d2)

Whered1=

ln (S/K )+(r−δ+ 12 σ 2)Tσ √T

d2=d1−σ √T

(10 marks)(b) What are the assumptions that are required that make the Black-Scholes

formula for stock options valid (8 marks)

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Tutorial 8 (Topic 6)Value at Risk (VaR)

Question 1A company has a portfolio consisting of $20 million invested in Microsoft and $10 million invested in AT&T. The daily volatility of Microsoft is 3%, the daily volatility of AT&T is 2%, and the coefficient of correlation between the returns from Microsoft and AT&T is 0.3. Calculate the one-day and 10-day VaR of the investment in Microsoft-only, AT&T only and the portfolio of Microsoft and AT&T at the 99% confidence level.

Question 2Suppose a portfolio manager holds two distinct classes of stocks. The first class, worth $20 million, is identical to the S&P 500. It has an expected return of 12% and a standard deviation of 15%. The second class is identical to the Nikkei 300, an index of Japanese stocks, and is valued at $12 million. Assume that the currency risk is hedged. The expected return is 10.5% and the standard deviation is 18%. The correlation between the Nikkei 300 and the S&P 500 is 0.55. All figures are annualized. (Assume 250 days)With this information, calculate one-day VaR and VaR’ at the 95% confidence level for S&P 500, Nikkei 300 and the portfolio.

Question 3Consider a position consisting of a $300,000 investment in asset A and a $500,000 investment in asset B. Assume that the daily volatilities of the assets are 1.8% and 1.2% respectively, and that the coefficient of correlation between their returns is 0.3. What is the five-day 95% value at risk for the portfolio?

Question 4PYQ October 2007 Section A Q1(b)You are given the following additional information:

Asset A:Value of investment: RM30 millionExpected return: 15% p.a.Standard deviation: 10% p.a.

Asset B:Value of investment: RM20 millionExpected return: 12% p.a.Standard deviation: 8% p.a.

Correlation coefficient between returns on asset A and B is 0.3

Required:You have been asked by your boss to compute the one-day and ten-day VaR and VaR’ for the portfolio, and to interpret the results to him. You are to assume a 252-days trading year.

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Tutorial 9 (Topic 7)Bond Risk

Question 1a) Consider a $100,000 bond with 10% coupon payments made semiannually.

Calculate the value of the bond for combinations of the following maturities and zero-coupon yields for all maturities:Maturities: 5, 10, 15 and 20 yearsInterest rates: 8%, 10%, 12% and 14%

b) Consider the results in part (a) above. Describe how maturity and yield (discount rate) affect the value of a coupon-bearing bond. Explain these effects in as much detail and with as much intuition as you can

Question 2Compute the duration of the following bonds. All bonds have a face value of $100,000. They differ by their coupon and maturity. Assume coupon rates of 8%, 10%, 12% and 14%. Consider maturities of 5, 10, 15 and 20 years, and assume the yield curve is flat at 9%.

Question 3Suppose your company is in the US and has foreign portfolio investment with bonds worth €50 million. Assume that the current exchange rate is S = $1.2/€. You predict that risk factors affecting the bond portfolio are the daily price returns and movements in the exchange rate between $ and €. You are given the following information:

- Standard deviation of returns on the bonds is 0.5% per day- Standard deviation of the exchange rate is 1% per day- Correlation between the two risk factors is 0.25

Compute the 1-day VaR with 99% confidence levels for each risk factor and for the whole position.

Question 4Suppose a 10-year zero coupon bond with a face value of $100 trades at $69.20205.

a. What is the yield to maturity and modified duration of the zero-coupon bond?

b. Calculate the approximate bond price change for a 50 basis point increase in the yield, based on the modified duration you calculated in part a). Also calculate the exact new bond price based on the new yield to maturity.

c. Calculate the convexity of the 10-year zero-coupon bond.

d. Now use the formula (equation 7.15) that takes into account both duration and convexity to approximate the new bond price. Compare your result to that in part b)

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Tutorial 10 (Topic 8 – Part I)Forwards, Futures, Swaps and Management of Interest Rate Risk

Question 1What are circuit breakers? What are their advantages and disadvantages?

Question 2Explain how the clearinghouse operates to protect the futures market.

Question 3Explain the differences among the three ways of terminating a futures contract: offsetting trade, cash settlement, and delivery. How is a forward contract terminated?

Question 4A major bread maker is planning to purchase wheat in the near future. Identify and explain the appropriate hedging strategy.

Question 5Explain the arguments against hedging.

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Tutorial 11 (Topic 8 – Part II) Forwards, Futures, Swaps and Management of Interest Rate Risk

Question 1Assume that in 5 months’ time, DEF Ltd will need to borrow $50 million for 8 months. DEF Ltd wants to hedge using a FRA. The relevant FRA rate now is 8%. Required:a) State what FRA is required – to quote the ‘x by y’ type. b) What is the total amount of interest payment and the effective annual cost of

borrowing (assume 365-day calendar year) with the FRA arrangement to hedge if in 5 months’ time, the interest rate is:

7% 11%

Question 2Suppose a company has RM10,000,000 loan with 6-months’ rollover. The company is worried that come next rollover in December, the interest rate would have increased. Current interest rate is 4% and 3-month December interest rate futures priced at 95.75. Show how the interest rate risk may be hedged using futures if in December, the loan is rolled over at 5% and 94.88. Given: 1 tick = 0.01%. Size per contract = RM1,000,000.Compute hedge efficiency ratio and effective annual cost of borrowing.

Question 3What are the differences between forward and futures contracts?

Question 4Assume that there are 2 companies, A and B that plan to raise RM10 million debt financing via issue of bonds. A and B have the following details

A is a highly rated company that prefers to borrow at a variable interest rate B is a lowly rated company that prefers to borrow at a fixed interest rate

The rates that these companies would pay for issuing either floating (variable) rate or fixed rate bonds are as follows:

Company Fixed rate bond Floating rate bondA 9% LIBOR + ½%B 11½% LIBOR + 1%

Using the principle of comparative advantage, advise how a swap arrangement would be beneficial to A and B. Assume A and B have equal bargaining power.

Question 5Assume that it is now 1 December. Your company expects to receive $7 million from a large order in four months’ time. This will then be invested in high quality commercial paper for a period of six months, after which it will be used to pay part of the company’s dividend. The company’s treasurer wishes to protect the short-term investment from adverse movements in interest rates, by using interest rate futures or forward rate agreements (FRAs).The current yield on high quality commercial paper is Bank Base Rate + 0.60%.

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CME $1,000,000 3 month $ futures. $25.00 tick size.March 96.25June 96.60

Futures contracts mature at the month end. Bank Base Rate is currently 4%.

FRA prices (%)4 v 6 4.35 – 4.304 v 10 4.08 – 4.036 v 10 4.00 – 3.95

Required:i) Devise a futures hedge to protect the interest yield of the short-term investment.

Explain how the futures hedge is expected to workii) Ignoring transactions costs, explain how a FRA would be set up for the short-term

investmentiii) If the Bank Base Rate fell by 0.5% points during the next four months and the

relevant futures price then is 96.65, show the expected outcomes of each hedge in the cash market, futures market and FRA market as appropriate

Question 6Your are the treasurer of a firm that will need to borrow $10 million at LIBOR plus 2.5 points in 45 days. The loan will have a maturity of 180 days, at which time all the interest and principal will be repaid. The interest will be determined by LIBOR on the day the loan is taken out. To hedge the uncertainty of this future rate, you purchase a call on LIBOR with a strike of 9 percent for a premium of $ 32,000. Determine the amount you will pay back and the annualized cost of borrowing for LIBORs of 6 percent and 12 percent. Assume the payoff is based on 180 days and a 360-day year. The current LIBOR is 9 percent.

Question 7A large, multinational bank has committed to lend a firm $25 million in 30days at LIBOR plus 100 bps. The loan will have a maturity of 90 days,at which time the principal and all interest will be repaid. The bank is concerned about falling interest rates and decides to buy a put on LIBOR with a strike of 9.5 percent and a premium of $ 60,000. Determine the annualized loan rate for LIBORs of 6.5 percent and 12.5 percent. Assume the payoff is based on 90 days and a 360-day year. The current LIBOR is 9.5 percent.

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Tutorial 12 (Topic 9)Interest Rate Models

Question 1Determine the zero-bond prices and generate the interest curve under the Vasicek model for 5 years (semi-annual intervals), given the following parameters

Kappa = 0.1Long-run r = 12%Sigma = 2%r = 10%

Question 2Construct a 4-period, 3-step (8 terminal node) binomial interest rate tree where the initial interest rate is 10% and rates can move up or down by 2% ; model your tree after that in figure 24.3. Compute prices and yields for 1-, 2-, 3- and 4- year bonds. Do yields decline with maturity? Why?

Question 3What are the 1-, 2-, 3- and 4-, and 5-year zero-coupon bond prices implied by the two trees? Given the following is the short rate.Tree #10.08 0.07676 0.0817 0.07943 0.07552

0.10362 0.10635 0.09953 0.090840.13843 0.12473 0.10927

0.1563 0.131430.15809

Tree #20.08 0.08112 0.08749 0.08261 0.07284

0.09908 0.10689 0.10096 0.089070.1306 0.12338 0.10891

0.15078 0.133170.16283

Question 4What volatilities were used to construct each tree? (You computed zero-coupon bond prices in the previous problem; now you have to compute the year-1 yield volatility for 1-, 2-, 3- and 4- year bonds.) Can you unambiguously say that rates in one tree are more volatile than the other?

Tutorial 13 (Topic 10)

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Management of Credit Risk

Question 1Read the attached write-up (Appendix A13) and answer the following questionsa) Describe the 3 issues that an institution (say, a bank) will have consider when

assessing credit risk from a single counterpartyb) What do you understand by the ‘credit quality’ of an obligation?c) Is there a difference between credit ratings used by banks relative to those used

by others?

Question 2a) What are the limitations to the use of external ‘ratings’ issued by companies like

Moody’s, JP Morgan etc?b) What is the relationship between stock/bond prices and credit risk?

Question 3Use of KMV modelSuppose you are given the following information regarding Monsanto in March 1998:

1. Book value of all liabilities: $7.2 billion2. Estimated default point (D): $5.7 billion3. Market value of equity: $33.9 billion4. Estimated market value of firm (V): $41.3 billion5. Estimated volatility of firm value σ: 20%

Estimate the firm’s distance-to-default (DD)

Question 4Rating To:

Rating From F FF FFFF 0.9 0.07 0.03FF 0.15 0.8 0.05FFF 0.1 0.3 0.6

Consider a firm with an F rating.a. What is the probability that after 4 years it will still have an F rating?b. What is the probability that after 4 years it will have an FF or FFF rating?c. From examining the transition matrix, are firms tending over time to become

rated more or less highly? Why?

Question 5Identify and explain the primary methods of managing credit risk for derivatives dealers.

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Question 6Comment on the current credit risk assumed for each of the following positions. Treat them separately; that is, not combined with any other instrument.

a. You are short an out-of-the-money interest rate call options.b. You entered into a pay fixed-receive floating interest rate swap a year ago.

Since that time, interest rates have increased. c. You are long an in-the-money currency put option.d. You are long a forward contract. During the life of the contract the price of the

underlying asset has decreased below the contract price.

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tutorial question 1-13

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