Question

Consider the following expectations for the market and two particular stocks in two possible equally likely states: (Please show the work step by step)

State                          Market Return                                  Stock A                                    Stock B

Boom                                 25% 38% 12%

Recession 5% -2% 6%

A. What is the beta of each stock? Remember that beta can be computed as the covariance of the stock’s return with the market return divided by the variance of the market return.

B. What is the expected return on each stock?

C. Given that the risk-free rate is 6%, draw the Security Market Line (SML) for this economy, and plot the two securities on the graph.

D. Assuming that the CAPM holds, by how many percentage points are the securities located above or below the security market line? State for each of the two stocks if the stock is overvalued, correctly priced, or undervalued according to CAPM?

Answer 1

a) Beta of A = Change in Stock A Price / Change in Market = (38 - -2) / (25 - 5) = 2

Beta of B = (12 - 6) / (25 - 5) = 0.3

b) E(R) for A = (38% - 2%) / 2 = 18%, E(R) for B = (12% + 6%) / 2 = 9%

c) Expected Market Return = (25% + 5%) / 2 = 15%

Plot SML by connecting points (0, 6%) and (1, 15%)

d) Using CAPM, Required Return for A = Rf + beta x (Rm - Rf) = 6% + 2 x (15% - 6%) = 24%

And RR for B = 6% + 0.3 x (15% - 6%) = 8.7%

As Stock A has higher required return (24%) than its expected return (18%), it is overvalued. And for Stock B, it is the other way around and hence, it is undervalued.