Question

Evaluating risk and return. Stock X has an expected return of 9.5 percent, a beta coefficient of 0.9, and a 30 percent standard deviation of expected returns. Stock Y has a 13 percent expected return, a beta coefficient of 1.3, and a 20 percent standard deviation. The risk-free rate is 5 percent, and the market risk premium is 5.5 percent.

a) Calculate the coefficient of variation of each stock.

b) Which stock is riskier for diversified investors? Which stock is riskier for undiversified investors?

c) Use the CAPM model to calculate each stock’s required rate of return.

d) On the basis of the two stocks’ expected and required returns, which stock would be more attractive to a diversified investor?

e) Calculate the required return of a portfolio that has $7,000 invested in Stock X and $3,000 invested in Stock Y.

f) If the market risk premium increased to 6.5 percent, which of the two stocks would have the larger increase in its required return? Why would the market risk premium increase?

Answer 1

Given:

Stock X:

Expected return (r1)= 9.5 %

beta coefficient (β1)= 0.9

standard deviation(d1) =30%

Stock Y:

expected return(r2)= 13 %

beta coefficient (β2)= 1.3

standard deviation(d2) =20%

R(f)= 5%            

MRP= 5.5%

1.

coefficient of variation (COV)= standard deviation/ expected return rate

for Stock X:

COV= 30/9.5 =3.16

for Stock Y:

COV= 20/13 = 1.54

2.

A diversified investor is the one who has reduced his risk by allocating the investment in several financial instruments. It aims at earning higher returns at the same risk.

A diversified investor will choose the stock which has low deviation from its price and thus they would avoid stock X, as it is riskier.

Same goes for un-diversified investors too, as they have not secured the risk, they would like to invest in stock that are less volatile, thus choosing stock with less COV, so they would choose stock Y and avoid stock X.

3. according to CAPM method,

Required rate of return = R(f)+ β*MRP

For stock X,

RRR= 5% + 0.9*5.5%

= 5%+ 4.95%

= 9.95%

For stock Y,

RRR= 5% + 1.3*5.5

= 5%+ 7.15%

= 12.15%

4.

On the basis of expected rate of return and required rate of return Stock Y would be more attractive to investors as it provide a higher return as compared to stock X.