Exam (Practice, with solutions)

Exam (Practice, with solutions)

Question 1

Consider a treasury bill with a rate of return of 5% and the following risky securities:

Security A: E(r) =.15; s2=.0400

Security B: E(r) =.10; s2=.0225

Security C: E(r) =.12; s2=.1000

Security D: E(r) =.13; s2=.0625

The investor must develop a complete portfolio by combining the risk-free asset with one of the securities mentioned above. Which would the investor choose as part of his complete portfolio?

Answer: Security A since it has the highest Sharpe ratio

Question 2

The market portfolio has a standard deviation of 10%. What fraction of your complete portfolio

should be invested in the risk-free asset if you want your complete portfolio to have a standard

deviation of 1%.?

Solution

Answer: = 90%

Question 3

Rose Hill Trading Company is expected to have EPS in the upcoming year of $8.00. The expected ROE is 18.0%.

The expected return on market portfolio is currently 15% and the risk-free rate is 3%.

The beta on the stock is estimated to be 1.5. If the firm's plow-back ratio is 30%,

what is the firm’s P/E ratio?

Solution

Answer: P/E = 4.49

Question 4

Consider the CAPM. The risk-free rate is 5% and the expected return on the market is 15%. What

is the beta on a stock with an expected return of 12%?

Solution

Answer: Beta = 0.7

Question 5

Consider the single factor APT. Portfolio A has a beta of 0.2 and an expected return of 13%.

Portfolio B has a beta of 0.4 and an expected return of 15%. The risk-free rate of return is 10%.

What is the arbitrage strategy?

Solution

Therefore, A is underpriced in comparison to B.

Answer: Long A, Short B

Question 6

Consider the multi-factor APT with two factors. The risk premiums on the factor 1 and factor 2

portfolios are respectively 5% and 3%. Stock A has a beta of 1.4 on factor 1, and a beta of 0.5 on

factor 2. The expected return on stock A is 14%.

If no arbitrage opportunities exist, what is the risk-free rate?

Solution

Answer: 5.5%

Question 7

Consider the following options for the same stock XYZ. Using the call and put options with the strikes of $30 and $35, evaluate the implied discount rate and stock price. Comparing to the options with the strike of $25, are there any arbitrage opportunities?

Solution

For the three options maturing in April, we have the following call-put parity relations

From the second and the third relations, we obtain

Substituting into the first call-put parity relation, we obtain

which means that the first call is overpriced in comparison to the put. Therefore, one arbitrage opportunity would be to short second call, buy second put and the underlying, and sell the bond.

Дата добавления: 2015-09-29