Question 1 (CAPM)

Consider the following data representing security analyst's estimates of the expected return on two stocks, A and D, as well as the market expected return in each of the two possible states of the economy:

Suppose that assumptions of the CAPM are satisfied in this economy and that the risk free rate is 6%. (a) What is the expected rate of return on each stock according to the analyst's estimates?

(b) What are the betas for stocks A and D? Explain and show your calculations.

(c) What should be the expected rates of return on each stock according to CAPM?

(d) Write down the equation for the Security Market Line (SML) and draw it on a graph.

(e) Plot the returns on A and D calculated in (a) on the SML graph. What are the alphas for each stock?

Question 2 (CAPM)

Consider an investment project which requires an initial outlay of 10 million dollars and is expected to generate a cash flow of 12 million dollars one year later. Suppose that the risk free rate is 8% and that the expected market rate of return is 16%.

(a) Compute the net present value of the project if the project beta is equal to 1.2.

(b) Find the range of all possible values of beta for which this project should be implemented.

State

Probability

Market

A

D

Normal growth

0.5

5%

-2%

6%

Boom

0.5

25%

38%

12%

Question 3 (APT)

Suppose the returns on all well-diversified portfolios are determined by the following two factor model rE(r) (FE(F)) (FE(F))

w w w11 1 w22 2

Consider the following statement: if any two well-diversified portfolios, A and B, have the same betas

on each factor, they must have the same expected returns.

That is, if we have A B and A B , then it must be the case that E(rA ) E(rB ) .

w1 w1 w2 w2 w w

Use an absence of arbitrage argument (similar to the one used in class) to prove this statement. Please make sure you write down and carefully explain each step of the proof.