Question

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)

Answer 1

a. The exposure of stock to market risk means the position of the stock if the market goes down. Beta is used to measure the sensitivity of the stock in relation to market. It captures the effect of systematic risk i.e. the change in stock price due to change in market. The formula for beta is:

where, r is the correlation of stock and market

y is the standard deviation of Stock and x is the standard deviation of market.

In the question, it is given that standard deviation of the stock is 25% and that of market is 20%. The correlation of S and M is 40%.Therefore,

This means that if the market changes by 1% then the stock price changes by 0.5%.

b. Capital Asset Pricing Model(CAPM) works on the idea that a person is rewarded for the risk he is willing to take over the risk-free rate of return. In other words, by investing in a stock, a person takes risk instead of having a guaranteed risk-free return. This is called risk premium i.e. market return minus risk-free return. The formula for CAPM is:

E(R) = R_f +  (R_m-R_f)

where, E(R) is the expected return.

R_f is the risk free rate of return.

R_m is the market rate of return and is the sensitivity of the stock to market.

CAPM assumes that only systematic risk is relevant i.e. risk due to changes in economy and ignores unsystematic risk.

In the question, it is given that R_f =2%, R_m=12% and Beta as calculated in part a. is 0.5.

Putting these values in CAPM equation,

E(R) = 2% + 0.5(12%-2%) = 7%

It is given in the question that expected return of stock S is 15%. As per CAPM, the expected return of the stock is 7%. This means that taking into account the market factors, the stock is expected to give a return of only 7% which is less than the expected return of 15%. Hence, the stock is overvalued.

c. Systematic risk refers to changes in the stock price due to market volatility in general. This risk affects all stocks in the market or all stocks in a particular industry. This risk does not depend on how a company performs individually and thus cannot be nullified by excellent performance of a company. That is why, it is also called undiversifiable risk. The formula for calculating systematic risk is:

SR = m

where, SR is the sytematic risk,

m is the standard deviation of the market & is the sensitivity of the stock to market.

In this question, = 0.5 and m = 20%

Therefore, Systematic risk = 0.5 20 = 10%

Hence, the systematic risk for Stock S is 10%.

Idiosyncratic risk is the residual risk which arises due to a company's internal factors. This risk depends on the company's performance individually in the industry or market. It is also called diversifiable risk as it can be reduced by the excellent performance of the company.

Idiosyncratic risk = Total risk- Systematic risk

In the question it is given that Standard deviation of the stock is 25%. This is total risk. The systematic risk calculated above is 10%.

Therefore, idiosyncratic risk for stock S is 15% (25%-10%).