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HOMEWORK HELP | How would his preferences affect the choice of securities in the optimal risky portfolio and the optimal complete portfolio?

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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Question 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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