# FIN201 Investment Management- Manage a Risky Portfolio

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### Question 1

1. On the options market, both the call options and put options on Woolworths’ shares currently have strike (or exercise) prices of \$45.00 and maturities (or expiries) of four months.

a. What will be the profit or loss per share to an investor who buys the call today for \$3.00 per share under each of the following scenarios – that is, where the price of Woolworths’ shares in four months is:

A. \$40.00

B. \$45.00

C. \$50.00?

b. What will be the profit or loss per share, in each of the above scenarios, to an investor who buys  the put today for \$7.00?

2. If Coles’ shares are now selling at \$16.00 each, why could a call option on those shares with an exercise price of \$18.00 and expiring in six months, sell at a positive price? Explain, with the aid of a hypothetical example.

3. What is the after-tax percentage return to an investor who buys shares in BHP Ltd a year ago for \$35.00, receives a dividend of \$1.75 yesterday and sells the shares for \$38.85 today? The tax rate on both dividends and capital gains is 30%.

4. What is the difference between a call option and a long position on a futures contract, both on the same company’s shares?

5. Explain, with supporting reasons, which of the two strategies in d. above you would recommend to a risk averse investor seeking to buy shares in a company where the share price history has been slow but steady growth and little volatility?

### Question 2

1. Laurie Lawrence Ltd, a tourist operator in Queensland, was founded in 1995. Over the last six years, it has reported annual returns of 7%, 9%, 6%, 11%, 12% and -3% respectively. Over that period, the riskfree rate averaged 3% per annum. Calculate the following measures for the company over the last 6 years.

a. The arithmetic average return.

b. The standard deviation.

c. The geometric average annual return.

d. The Sharpe ratio

2. Based on the above calculations, and having regard to the industry in which the company is operating, would you recommend that an investor buy shares today in Laurie Lawrence Ltd? Give reasons.

3. Assume that you manage a risky portfolio with an expected return of 15% and a standard deviation of 24%. The T-bill money market risk-free rate is 5%. Jenny Li chooses to invest 60% of her portfolio in your fund and 40% in a T-bill money market fund.

a. What is the expected return and standard deviation of Jenny’s portfolio?

b. Suppose you risky portfolio includes the following investments in the given proportions:

Stock X, 20%; Stock Y, 35%; and Stock Z, 45%.

What are the investment proportions of each stock in Jenny’s overall portfolio, including the investment in the T-bill money market fund?

4. Suppose, instead of investing the proportions stated under c. above, Jenny decides to invest a proportion (x) of her total portfolio in your risky portfolio and the balance in the T-bill money market fund so that the overall portfolio will have an expected return of 12%. What is the proportion, x?

### Question 3

1. Mildred Downes wishes to invest \$400,000 in an Australian banking stock for 5 years, but is unsure as to which of two banking stocks, A Bank Ltd or B Bank Ltd, to select. She seeks your advice. You discover the following information.

A. A Bank Ltd has a beta of 0.7 and a standard deviation of 18%.

B. B Bank Ltd has a beta of 1.1 and a standard deviation of 28%

C. The market has an expected return of 13%.

D. The risk-free rate is 5%

Assuming that the capital asset pricing model applies,

i. calculate the expected return of each bank;

ii. advise which bank Mildred should invest in, assuming that she is risk averse (a moderately conservative investor), stating your reasons for your choice; and

iii. if you discover that Mildred is single, aged 35 years, lives in a rental apartment, has no dependents, earns an annual salary of \$80,000, has a permanent job with a large company, is debt-free and the above \$400,000 represents her total wealth, what alternative investment advice would you provide to her? Describe fully, with reasons for your advice.

2. In the following problem, assume that the market is in equilibrium, both portfolios are efficient and that the capital asset pricing model holds. Bright Fund and Best Fund are two well diversified portfolios: Best Fund has an expected return of 15% and a beta of 1.3, while Bright Fund has an expected return of 11% and a beta of 0.9. Calculate the following measures, showing each answer as a percentage, correct to 2 decimal places.

i. The expected market return.

ii. The risk-free rate.

### Question 4

1. The following describes several Treasury bonds issued by the Australian Government.

a. Face value, \$1,000; market price, \$1,000; term to maturity, 10 years, yield to maturity, 4% per annum; annual coupons. What is the coupon rate? Show answer as a percentage, correct to 2 decimal places.

b. Face value \$1,000; market price, \$900; term to maturity 9 years; yield to maturity 4.5% per annum; annual coupons. What is the coupon rate? Show answer as a percentage, correct to 2 decimal places.

c. Face value, \$1,000: market price \$900, term to maturity, 9 years; yield to maturity, 4.5% per annum (nominal rate); half-yearly coupons; What is the coupon rate? Show answer as a nominal percentage annual rate, correct to 2 decimal places.

d. Face value , \$1,000; market price \$750; term to maturity, 5 years; zero coupon bond. What is the yield to maturity? Show answer as a percentage annual rate, correct to 2 decimal places.

e. In answer d.., if the expected inflation rate over the next 5 years is 2.25% per annum, what will be the real yield to maturity (or the real annual return)? Show answer as a percentage, correct to 2 decimal places.

### Question 5

Following your graduation, you are employed by a bond trader who asks you to prepare an analysis of an Australian Treasury bond maturing in 4 years with a face value of \$100,000, a coupon of 5% per annum payable yearly and a yield to maturity of 3% per annum. The interest coupon payment due this year has just been paid. Your analysis should include the following calculations, with the accuracy specified in each part.

a. The current price of the bond. [Show answer correct to the nearer cent.]

b. The duration of the bond. [Show answer in years, correct to 4 decimal places.]

c. The convexity of the bond. [Show answer correct to 4 decimal places.]

d. Your employer has also advised that he considers that the yield to maturity is expected to increase very soon to 4% per annum. .On the assumption that the yield increase will occur later today, calculate the new bond price (correct to the nearer cent) by each of the following methods:

iii. The present value of future cash flows method (as used in a. above).

e. Which of the above 3 methods would you recommend as the most accurate? Why?

f. Referring to d. above, explain why method ii. gives a more accurate answer than method i.

### FIN201 Investment Management

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