Question

Risk and Return Suppose that the entire security market is made of only three types of assets: a risk-free asset, with a return of 3%, and two risky stocks A and B. There are 500 A stocks trading in the market, at a price of $10 per stock. Stock A has an expected return of 8% and a volatility of 10%. There are 375 B stocks trading in the market at a price of $8 per stock. Stock B has a volatility of 16%. The correlation between the returns of stock A and stock B is 0.15. 1. Compute the volatility of the market portfolio. (8 points)

2. Compute the β of stock B. (8 points)

3. Compute the expected return of stock B. (8 points) Hint: let rB denote the expected return of stock B, write the expected return of the market portfolio as a function of rB and use the CAPM.

Answer 1

given following data,

expected return of stock A = 8%.

risk of A = 10 %.

risk of B = 16%

correlation of stock A and stock B = 0.15.

porportion of stock A = 62.5 %

porportion of stock B = 37.5 %

1. Value of market portfolio = 500*10 + 375*8

= 5000+3000

= 8000.

we have for market volatility i.e standard deviation = of (62.5 %)^2* (10%)^2+ (37.5)^2* (16%)^2+2*62.5*37.5*0.15*10%*16.

Therefore the market volatility = 9.2904.

2. calculation of beta

we know that beta = correlation of stocks *( standard deviation of stock A / standard deviation of stock B)

= 0.15*(10%/16%)

= 0.09375

3. According CAPM model We have

expected return = risk free return + beta( market risk - risk free return)

= 3% + 0.09375(9.29 %-3%)

= 3.589%.