**Consider a risk-averse, passive investor. How would his preferences affect**

**the choice of securities in the optimal risky portfolio and the optimal complete**

**portfolio? Would he be able to invest in a portfolio above the capital market**

**line (CML)?**

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Write My Essay For MeQuestion 1

Ethan is seeking financing for a new car. The local bank has agreed to give him a

loan for 90% of the cost of the car (he will pay the rest in cash) and so he has just

taken out a 5-year loan for this amount. To repay the loan, he has agreed to pay

RM20,000 at the end of every year based on an APR of 8% compounded

quarterly. What is the price of Ethan’s car?

[5 marks]

Question 2

The returns on stock Yellow over the past 3 years were:

2009 2010 2011

Stock Yellow 6.8% 6.1% 9.5%

(i) Stock Green has a Sharpe Ratio of 0.4. The risk-free rate of return is 6%.

Calculate the historical return and volatility of stock Yellow and determine

which of the two stocks is the better investment.

[4 marks]

(ii) Stock Green has an expected return twice as large as stock Yellow. Given

that the two stocks have a correlation of 0.6, calculate the expected return

and volatility of a portfolio that has an equal amount invested in Green and

Yellow stocks.

[4 marks]

Question 3

Critically evaluate the differences between investing in exchange-traded funds

(ETFs) and mutual funds, considering the advantages and disadvantages of each.

[8 marks]

Question 4

Explain why margin payments are necessary in the context of short selling.

[4 marks]

Total [25 marks]

End of Section A

4

SECTION B

Answer ANY THREE questions.

Each question is worth 25 marks.

Question 1

A. Critically evaluate the effectiveness of the capital asset pricing model (CAPM)

as a tool in determining asset returns.

[10 marks]

B. The returns on asset Y are twice as sensitive to market changes compared to

the returns on asset X. The expected return on asset X is 12% and its

standard deviation of returns is 25%. The expected return on asset Y is 15%

and its standard deviation of returns is 35%. The market risk premium is 10%.

(i) Calculate the risk-free rate of interest and the Betas that would give the

expected returns of 12% and 15% for assets X and Y respectively.

[5 marks]

(ii) After proper analysis, you are now convinced that the betas for assets X

and Y should actually be 0.2 and 0.8 respectively. Calculate the alphas

for both asset X and asset Y and indicate whether they are underpriced,

over-priced or fairly-priced.

[4 marks]

(iii) Outline the basic idea behind the one-factor model of Arbitrage Pricing

Theory and use it to consider how and why the prices of asset X and

asset Y will change.

[6 marks]

Total [25 marks]

5

Question 2

A. Given a measure of the risk aversion of an investor, there are many possible

ways to calculate his/her utility. You are given that “A” measures the level of

risk aversion of an investor, E(r) is the expected return on a portfolio and σ is

the standard deviation of the portfolio returns.

(i) Alice is a risk-averse investor (with A = 1) and her utility function is

given by U = E(r) – ½ Aσ2

. A particular risky fund has σ = 0.25 and if

Alice invests 100% of her money in that fund, she will have a utility of

0.04. If she can borrow at the risk free rate of 6%, calculate the utility

she would get by investing 30% of her money in the risk-free fund and

70% in the risky fund. Suggest, with the aid of a diagram, how she can

adjust her portfolio to achieve a higher utility, giving reasons for your

suggestion.

[10 marks]

(ii) Explain, with the aid of appropriate diagrams, how the utility curves for

risk-averse, risk-loving and risk-neutral investors differ.

[6 marks]

B. Consider a risk-averse, passive investor. How would his preferences affect

the choice of securities in the optimal risky portfolio and the optimal complete

portfolio? Would he be able to invest in a portfolio above the capital market

line (CML)?

[5 marks]

C. Describe two main differences between the capital market line (CML) and the

security market line (SML).

[4 marks]

Total [25 marks]

6

Question 3

A. The price of a stock is RM80 and its price is expected to either go up by 20%

or down by 10% every 9 months. The stock pays dividends at a continuous

rate of 2% and the force of interest is 5%.

(i) What is the price of an 18-month, 90-strike European call option on

this stock?

[12 marks]

(ii) What would be the price of an 18-month, 90-strike European put

option on this stock?

[3 marks]

(iii) What would be the price of an 18-month, 90-strike American call

option on this stock?

[2 marks]

(iv) Consider the two call options in parts (i) and (ii) above, along with an

18-month at-the-money European call option and an 18-month at-themoney

American call option on the stock. Without further calculation,

rank the four call options from most expensive to least expensive,

giving reasons for your answer.

[3 marks]

B. Explain how it is possible for an individual to get the effect of risk-free lending

by using a stock along with call and put options on that stock. Clearly state

how much is being lent at the risk-free rate.

[5 marks]

Total [25 marks]

7

Question 4

A. Jonathan is contemplating call options on a particular stock. The prices for 3

month call options on the stock are RM4 and RM1.50 for those with strike

prices of 50 and 60 respectively. Jonathan is considering using a ratio call

backspread, created by selling 1 call with a strike price of 50 and buying 2

calls with a strike price of 60.

(i) On graph paper, draw the payoff and profit diagrams for this option

strategy, showing how the 3 call options are combined to create the

ratio call backspread.

[6 marks]

(ii) Use your graph to determine the maximum possible loss and the

range of stock prices that will give a profit at maturity. If Jonathan sold

a call option that was more out-of-the money than the one for RM4 and

bought the same two calls for RM1.50 each, what would happen to his

net premium, the profit range and maximum possible loss?

[5 marks]

(iii) What is Jonathan’s market outlook if he thinks that the ratio call

backspread is a suitable strategy to invest in?

[3 marks]

B. Explain and illustrate how the value of a put option changes if:

(i) the volatility of the underlying asset changes. [3 marks]

(ii) the price of the underlying asset changes. [3 marks]

C. The spot price for wheat is US$600 per bushel and the 18-month futures

price for wheat is $632 per bushel. The risk-free rate of return is 3.5%.

Calculate the arbitrage profit that exists and explain the necessary

transactions for an investor to turn a risk-less profit in the futures market for

wheat.

1. [5 marks]

Total [25 marks]

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