Question

Q3) Consider the following table, which gives a security analyst’s expected return on two stocks in two particular scenarios for the rate of return on the market. Assume that both scenarios are equally likely to happen (i.e., probability of scenario 1 = probability of scenario 2=0.5).

Q4) You are considering investing in stock S and you want to know how stock S is related to the market portfolio M. Given your research, you discovered the following information:

	Expected Return	Standard Deviation
Stock (S)	15%	25%
Market (M)	12%	20%
Risk-free	2%
Correlation of S and M	40%

1. What is the exposure of stock S to market risk? (3 points)
2. Discuss whether according to the CAPM, stock S is overvalued, undervalued or fairly valued. (2 points)
3. What is the level of systematic and idiosyncratic risk for stock S? (5 points)

1. What are the betas of the two stocks? (5 points)
2. Plot the two securities on the SML graph. Assume that T-bill rate is 6%. (5 points)
3. What are the alphas of each? (5 points)

Answer 1

A) Exposure of Stock S to market risk is Beta

r- Correlation Coefficient between stock and Market

Beta = 0.4 * 0.25 / 0.2

Beta = 0.5

B)

Re = Rf + (Rm - Rf) Beta

Rf, Risk Free Return - 0.02

Rm, Market Return - 0.12

Re = 0.02 + (0.12 - 0.02) 0.5

Re = 0.07 or 7%

Expected return of stock given is 15 % which is greater than Return as per CAPM (7%), Therefore, Stock is Undervalued.

C)

Total Risk = (Standard Deviation of stock)²

Total Risk = (25)² = 625

Systematic Risk = ( Standard Deviation of Market)² * (Beta)^{​​​​​​2}

Systematic Risk = (20)² * (0.5)² = 100

Idiosyncratic Risk = Total Risk - Systematic Risk

= 625 - 100

= 525

Another way to solve C)

Total Risk = (Standard Deviation of stock)

Total Risk = 25

Systematic Risk = ( Standard Deviation of Market) * (Beta)​​​​​​

Systematic Risk = (20) * (0.5) = 10

Idiosyncratic Risk = Total Risk - Systematic Risk

= 25 - 10

= 15