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A LEVEL 4 MODULE, AUTUMN SEMESTER 2019-2020 

BUSI4519 CAPITAL MARKET ANALYSIS

ANSWER THREE QUESTIONS

Question 1: COMPLETE ALL PARTS OF THIS QUESTION

a) A security analyst works for a large institution that uses the Single-Index Model as part of its portfolio-management scheme. The security analyst believes the values on returns (in percentage), Betas and unique risks for the three stocks she follows, and the risk-free rate (in percentage) and the variance in the market index are below:

Stock number i	Mean Return	Beta	Unique Risk
1	12	1.1	35
2	8	0.8	10
3	6	0.9	20
4	15	1.6	50

R_F = 5;  

The cutoff rate C_i of for an optimum portfolio can be found by the following equation:

Which asset(s) should be included in the optimum risky-asset portfolio?      (40%)

b) Using the academic literature on insider trading, discuss the evidence of the semi-strong and the strong-form of market efficiency. 

     (40%)

c) Assume that the average variance of return for an individual security is 50 and that the average covariance is 10. What is the expected variance of an equally weighted portfolio of 100 securities? How many securities need to be held for the portfolio to have minimum risk?

     (20%)

    Total (100%)

Question 2: COMPLETE ALL PARTS OF THIS QUESTION

a) Consider the following returns:

Period	US	UK	Exchange Rate
1			$1.30 = £1
2	6%	5%	$1.35 = £1
3	12%	-5%	$1.32 = £1
4	-5%	15%	$1.30 = £1
5	15%	8%	$1.35 = £1
6	10%	10%	$1.30 = £1

What is the average return in each market from the point of view of an American investor and of a British investor?

(40%)

b) Compare the risk preference of three investors A, B and C who are believed to have the following utility function  ,   and respectively.

     (30%)

c) Discuss the purposes of performance evaluation. Compare the Sharpe measure with the Treynor measure. You should also discuss potential problems in using single-parameter measures.  

     (30%)

   Total (100%)

Question 3: COMPLETE ALL PARTS OF THIS QUESTION

a) An investor is considering the following investments.

Investment A			Investment B
Return (%)	Probability		Return (%)	Probability
6	0.3		5	0.2
8	0.6		10	0.6
9	0.1		12	0.2

i) If the level below which the investor does not wish returns to fall, or the lower limit, is R_L = 4%, what is the preferred investment using Roy’s safety-first criterion? 

ii) If the probability of a return below the lower limit is α = 5%, what is the preferred investment using Kataoka’s safety-first criterion?

     (30%)

b) Discuss the similarities and differences between the CAPM and the APT.            (40%)

c) Compare the performance of Factor Fund (Fund A) with that of Churchill Fund (Fund B) using the Sharpe measure, the Treynor measure and the Jensen measure. The following data on the two funds have been collected: 

     (30%)

(Total: 100%)

Question 4: COMPLETE ALL PARTS OF THIS QUESTION

a) 

i) Compare the equations of the efficient frontier with riskless lending and borrowing and short sales for a combination of a domestic portfolio represented by the S&P Index and a portfolio of US Long-term Bonds; and a combination of the S&P Index and an emerging market equity index (EF). The estimated inputs for the returns (in percentage), standard deviations (in percentage), correlation coefficients of the indices and the risk-free rate (in percentage) are as follow:

15 20

9 12

21 25

0.3 0.2

R_F = 5

ii) Drawing on the academic literature, compare the equations in part i) with the equation of the efficient frontier with riskless lending and borrowing and short sales for a combination of the following indexes: S&P Index, US Long-term Bonds, European (excluding UK) equities, UK equities and emerging market equities. No calculation for part ii) is necessary.

(60%)

b) How do you use a fair gamble to define an investor’s choice for risk? Discuss the differences between absolute and relative risk aversion.

    (40%) 

                  Total (100%)

Question 5: COMPLETE ALL PARTS OF THIS QUESTION

a) Assume that the following assets are correctly priced according to the security market line.       

   

i) Derive the security market line.

 

ii) What is the expected return on an asset with Beta of 2?

 

iii) Assume that an asset exists with  and . Using the security market line derived in part i) to design an arbitrage opportunity.

     (30%)

b) Assume that the following two-index model describes returns:

Assume that the following three portfolios are observed.

Portfolio Expected Returns b_i1 b_i2

A 12 1 1

B 15 -2 2

C 18 3 2

i) Find the equation of the plane that must describe equilibrium returns.

 

ii) If , find the value for  and that would make the above expected returns of Portfolios A, B and C consistent with equilibrium determined by the standard Sharpe-Lintner-Mossin CAPM.

     (40%) 

c) Use the extant literature to compare and contrast active and passive investment management.

     (30%)

      Total (100%)

Question 6: COMPLETE ALL PARTS OF THIS QUESTION

a) Using the Single-Index Model, a security analyst has obtained the following estimates for stock A and stock B:

Stock

A 0.5% 1.8 15%

B 0.3% 1.2 9%

The analyst also estimates that the expected return on the market portfolio is 10%, the standard deviation of the market portfolio is 8%, and the riskless rate is 5%.

 

i) Based on the Single-Index Model, what are the expected returns and standard deviations of stock A and stock B?

 

ii) Based on the Security Market Line, what are the expected returns of stock A and stock B?

 

iii) Based on the ratio of the rate of return per unit of risk calculated in the Single-Index Model, are stocks A and B overpriced, underpriced or fairly priced?

     (30%)

b) Discuss how the behavioral finance approach challenges the efficient market hypothesis.      

     (40%)

c) Firm A has a stock price of $50 per share, an expected dividend for next year of $1.8 per share, an expected constant growth rate of 12% per year, and a beta of 1.2 on its stock. Firm B has a stock price of $50 per share, an expected dividend for next year of $1.8 per share, a retention rate of 65%, a historical rate of return on investment of 22%, and a beta of 1.5 on its stock. If the riskless rate is 10% and the expected return on the market portfolio is 15%, show whether these stocks are underpriced or overpriced. What is the assumption behind your calculation?

     (30%)

    Total (100%)