Question

5. Stock X has a 10% expected return, a Beta coefficient of .9, and a 35% standard deviation of expected return. Stock Y has a 12.5% expected return, a bet coefficient of 2, and a 25% standard deviation. The risk free rate is 2% and the market risk premium is 5%

1. Calculate each stock’s coefficient of variation.
2. Which stock is riskier?
3. Calculate each stock’s required rate of return.
4. Calculate the required rate of return of a portfolio that has $7,500 invested in Stock X and $2,500 invested in Stock Y.

Answer 1

coefficient of variation = Standard deviation/Mean

coefficient of variation of X =35/10 i.e.3.5 or 350%

coefficient of variation of Y =25/12.5 i.e.2 or 200%

Risker stock is that whose  coefficient of variation is higher i.e Stock X

required rate of return = Risk free return + Market risk premium* Beta

Stock X = 2 +5*.9 i.e.6.5%

Stock Y =2+5*2 i.e.12%

Portfolio value = 7500+2500 i.e.10000

Weight of X =7500/10000 i.e.0.75

Weight of Y =2500/10000 i.e.0.25

required return of portfolio = Weighted average of required return

=0.75*6.5+0.25*12 i.e. 7.875%