# FIN201 Investment Management- Market Risk Premium

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### FIN201 Investment Management

1. [(CALC’NS a. + b. + c. + d. = 4 + 4 + 4 + 4 = 16 Marks) + (REC’NS e. = 4 Marks)]

a. At 15 October, 2020, the share prices of Coal Ltd and Wood Ltd were \$30 and \$105 respectively. One year later, the respective share prices were \$35 and \$110.

i. Calculate the price-weighted percentage average return for these two stocks over the year to 15 October, 2021.

ii. Suppose instead, at 15 October, 2021, the final price of Coal Ltd was \$35 (as above),but the price of Wood Ltd had fallen to \$95. Calculate the revised price-weighted percentage average return for these two stocks over the year to 15 October, 2021.

b. What are both the payoff and the profit or loss per share for an investor in the following two situations?

i. Jean buys the June, 2022 expiration Paypal call option for \$6.40 with an exercise price of \$120, if the Paypal stock price at the expiration date is \$132?

ii. Joan buys a Paypal put option for \$4.50 with the same expiration date and exercise price as Jean’s call option, and the Paypal stock price is also \$132 at the expiration date?

i. State briefly two reasons why he/she should include international equities in his or her investment portfolio.

ii. Identify two risks which apply to the investor if he/she invests in international equities.

d. Two corporate bonds, issued respectively by F Ltd and G Ltd, have the same face value of \$10.000 and the same term to maturity of 7 years. F Ltd’s bonds have a coupon rate of 8% per annum, payable half-yearly, and G Ltd’s bonds have a coupon rate of 7.8% per annum, payable bi-monthly (that is, every 2 months). Calculate the effective annual return (EAR) on each bond.

[Show each answer as a percentage, correct to 2 decimal places.]

e. Asif is a fund manager with a share portfolio currently valued at \$1 billion under management. He considers that the share market is much over-priced and fears a sharp downturn of 20% in the market by June, 2022, which will badly affect his share portfolio’s value and performance, which he wishes to protect. He seeks your advice as to whether he should take a short position in futures or buy a put option, each with an exercise price of \$1 billion (the current value of his share portfolio). Explain each of the two strategies, and state your recommendation which Asif should follow, with reasons.

2. [(CALC’NS a. + b. = (3 + 3) + (2 + 2 + 2+2 + 2) = 16 Marks} + (REC’NS c. = 2 Marks}]

a. The expected return of the market index over 2022 is 10%. The standard deviation of returns of the market index is expected to remain at its long-term average of 18%. The risk-free rate is 4%. Calculate:

i. the degree of risk aversion (commonly denoted by ‘A’) for an investor in the market index.

ii. the Sharpe ratio of the market index portfolio.

b. The expected return of a risky portfolio in New Zealand over 2022 is 15%, while the risk-free rate is 7%. Terry wishes to set up a complete portfolio, with y (the proportion invested in the risky portfolio) = 0.75.

Required:

i. Define a “complete portfolio”.

ii. Describe the mix (or asset allocation) of Terry’s complete portfolio, including the percentages of each asset held.

iii. What is the expected return of Terry’s complete portfolio?

iv. What is the standard deviation of returns for Terry’s complete portfolio?

v. What is the Sharpe ratio for Terry’s complete portfolio?

c. Mabel is more risk averse than Terry, and her degree of risk aversion, A, is 4.0. Using the data supplied at the beginning of part b. above, calculate the percentages of each asset class you would recommend she should hold in her optimal complete portfolio. [Show percentages correct to 2 decimal places.]

3. [CALC’NS a. + b. + c. = (3+3) + (2+2+4) + 2 = 16 marks) + (REC’NS d. = 2 marks }]

a. Historical data for the All Ordinaries Index indicates that:

• the standard deviation of returns from the Index has been 17%; and
• the degree of risk aversion (A) of an investor in the Index is 3.6

Required:

i. What market risk premium is consistent with the above historical standard deviation?

ii. If the market risk premium is 12%, what would be the historical standard deviation?

b.The expected return of the market in Iceland is 15%. Stock H has a beta of 1.3 and the risk-free rate is 5%.

Required:

i. What is the expected return of Stock H, according to the CAPM?

ii. What is the alpha of a stock? (Definition or explanation required.)

iii. What is the alpha of Stock H, if Iceland Stockbrokers, investors in – and researchers of the stock, believe that Stock H will provide a return this year of:

I.20%; or alternatively, if they consider the return this vear will be:

Ii.14%?

c. Based on your answers to part b iiii. above, is Stock H over-priced, underpriced or fairly priced-in each of the situations I. and II.? Would you recommend that Iceland Brokers buy more of – or sell – or just hold Stock H in each of these situations?

d. Jackie, an analyst with Betta Brokers, uses a two-factor (F1 and F2) CAPM index method to evaluate the expected return of stock in Z Ltd. The model uses the following data:

E(R) of F1 = 12%; E(R) of F2 = 8%; B (beta) of F1 = 1.3; ß (beta) of F2 = 0.4; and Rf (risk-free rate) = 5%.

What is the expected return of a share in Z Ltd?

4. [(CALC’NS (3 + 2 + 3) + (2 + 2) + (2 + 2) = 16 Marks}]

A. The yield curve for Government-guaranteed zero-coupon bonds is based as follows:

Term to maturity (years) & Yield to maturity(% per annum)

1 year – 8%

2 years – 9%.

3 years- 10%

Required:

i. What are the implied one-year forward rates for years 1, 2 and 3 respectively?

ii. If the expectations hypothesis of the term structure of interest rates is correct, in one year’s time, what will be the yield to maturity on a one-year zero-coupon bond?

iii.Based on the same hypothesis as in ii. above, in one year’s time, what will be the yield to maturity on a two-year zero-coupon bond?

b. On 15 January, 2021, you bought a Government bond, with a face value of \$1,000; a term to maturity of 5 years; a coupon rate of 6% per annum payable yearly, and a yield to maturity of 5% per annum. You paid the market price of \$1,043.76 for the bond.

On 15 January, 2022, you sold the bond to Jill, providing her with a yield to maturity of 4% per annum

[Note: You bought and sold the bond immediately after payment of the interest coupon due on 15 January each year – that is, the interest payments due on 15 January in 2021 and 2022 are not included in the bond prices.]

Require:

i. What price would Jill have paid for the bond? [Show answer correct to the nearer cent.]

ii. What is your holding period return for holding the bond for one year, receiving the January, 2022 interest coupon, then selling the bond? [Show answer as a percentage correct to 2 decimal places.]

c. With the aid of hypothetical illustrative examples, briefly explain each of the Expectations and the Liquidity preference hypotheses relating to the term structure of interest rates. Which of the two hypotheses do you consider to be the more relevant? Why?

5. CALC’NS a. + b. + c. + d. = (1 + 1 + 1) + (3 + 3) + (2 + 2 + 2) + 1 = 16 Marks) + { REC’NS e. = 2 Marks)]

A. Briefly explain the following concepts relating to bond portfolio management.

i. Duration.

ii. Convexity.

iii. Immunisation

B. Illustrate your answer to A. above with the calculation of the duration and convexity of a bond with a face value of \$1,000, term to maturity of 3 years, a coupon rate of 6% per annum, payable yearly, and a yield to maturity of 4% per annum.

[Note: As a by-product of these calculations, you should calculate the current market price of the bond, which price should be used as a base or starting point to your answers required in C.

i. and C. il. below.]

C. Calculate the expected price of the bond described in B. above, if the yield to maturity fell immediately to 3% per annum, by each of the following 3 methods.

iii.The present value of future cash flows method.

D. Which of the methods listed in C. above is most accurate? Why?

E. Explain how a pension fund can use zero-coupon bonds to immunize its obligation to pay out \$10 million a year in pensions in perpetuity, if the forecast long-term interest / discount rate is 5% a year forever.

### FIN201 Investment Management

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