Consider the following information about three assets:

Stock Mean Return Standard Deviation

Moose 10.00% 5.20%

Gnu 8.00% 2.70%

Wildebeest 12.00% 6.50%

a) What are the mean returns and risk of a portfolio if the investment manager invests in:

i. 25% in Moose and 75% in Gnu if the correlation between Moose & Gnu is 0.2?

ii. 60% in Moose and 40% in Wildebeest if the correlation between Moose and Wildebeest is -0.5?

iii. 50% in Gnu and 50% in Wildebeest if the correlation between Gnu and Wildebeest is -0.4?

b) What does a risk return diagram show? Draw the risk return diagram for investing in Gnu & Wildebeest. Show your working and tabulate your results as well as drawing the diagram.

c) What level of risk would an investor who has the highest level of risk aversion face and what would the expected return on their portfolio be? How might you suggest that they improve their portfolio?

Question 2

a) What does the capital market line show? How does this change the possible investment opportunities for an investor?

b) How does the capital market line differ from the securities market line?

c) Do you agree with the statement: “Adding assets to a portfolio will always be beneficial. One can reduce the risks of investing to zero”. Justify your answer.

Question 3

a) How might an insurance company immunize its liability of £1 million due in 10 years if:

i. There are zero coupon bonds, each paying £1000 at maturity, available for each of the years for the next 15 years? All the zero bonds have a yield of 8%.

ii. There is a 20 year bond with duration of 15 years, price is £525 and a 7 year bond with a duration of 4 years and a price of £615? How many of each bond should the insurance company buy?

b) What are the strengths and weaknesses of the Gordon Growth Model?

c) What are the main methods for investing in real estate? Why would one invest in such instruments?

d) “Commodities are an excellent form of diversification for an equity portfolio” Discuss this statement.

Question 4

a) What are the strengths and weaknesses of the Sharpe & Sortino ratios?

b) What is the definition of ‘maximum drawdown’? How is it used in the assessment of portfolios?

c) You have been given the following information and are asked to advise a client on the portfolios. How would you advise them? You should base your answer on the relevant performance measures.

Portfolio Expected Return Standard Deviation Beta Max-Drawdown

Doolittle 10.0% 12.0% 1.5 30.0%

Higgins 4.0% 5.0% 0.75 10.0%

Crichton 14.0% 14.0% 2.0 55.0%

Risk free Rate 2.0% 0.0%

Question 5

a) A swap pays LIBOR+1% for the floating counter-party and 5% for the fixed rate counter-party. If the nominal amount is £1500 and the payments are made every 6 months over the period of a year, what are the payments to each of the counter-parties if LIBOR is 6% in 6 months time and 3% at the end of the year?

b) If a (European) call option on a stock is priced at £20 with a strike of £50, what is the price of put option with the same strike if:

i. The interest rate is 6% and the underlying stock price is £40?

ii. The interest rate is 10% and the underlying stock is £50?

c) What is the pay-off diagram for the put option described above?

d) A fund manager wishes to use futures in her portfolio as she believes that the market is going to rise in the near future. Her portfolio is worth £100 million with a beta of 0.9 before implementing the futures strategy. She wants to move her portfolio’s beta to 0.975 and intends to use futures priced at £10,000 with a beta of 1.2.

i. How many futures contracts does she need to invest in?

ii. What is the effective beta if the market increases by 1% and the futures price rises to £10,100?

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Portfolio Management – What are the mean returns and risk of a portfolio if the investment manager invests
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