BUS 431a: Investment and Portfolio Management
SPRING 2013

Problem Set #5 (team work)

1. (15 points) Suppose the economy can be .in one of the following two states: (i) Boom or “good” state and (ii) Recession or “bad” state. Each state can occur with an equal opportunity (50%). The annual return on the market and a certain security X in the two states of the economy are as follows: • Market: at the end of the year, the market is expected to yield a return of 30% in the good state and a return of (-10%) in the bad state; • Security X: at the end of the year, the security is expected to yield a return of 40% in the good state and a return of (-35%) in the bad state; Furthermore, assume that annual risk-free rate of return is 5%. A. (5 points) Calculate the beta of security X relative to the market. B. (5 points) Calculate the alpha of security X. C. (5 points) Draw the security market line (SML). Please, label the axes and all points (including the market portfolio, the risk-free security, and security X) in the graph clearly. Identify alpha in the graph.

Solution:
1. (5 points) Beta of security X is:
Market portfolio: (1/2) probability of getting 30% and (1/2) probability of getting -10%. So, expected/mean return and the standard deviation of the market are:

[pic]
[pic]

Security X: (1/2) probability of getting 40% and (1/2) probability of getting -35%. So, expected/mean return and the standard deviation of security X are:

[pic]
[pic]

The covariance between the market return and the security X return is:

[pic] (a formula that comes from CF classes)

Therefore, the beta of security X will be: [pic]

2. (5 points) Security’s alpha is:

[pic]

The first term in the equation above is the actual return and the second term is the CAPM predicted (required) return of security X.

3. (5 points)