Question

Stock A has a standard deviation of return of 40%; Stock B 30%. Stock A has a return correlation coefficient with the S&P500 of 0.32; Stock B 0.85. S&P 500 has an expected return of 12.5% and a standard deviation of return of 20%, while T-bill rate is 3.8% What is the un-diversifiable risk of Stock A? Stock B? Which stock has greater risk? 1. 2. What is the beta of Stock A? Stock B? 3. What is the risk premium for S&P500? Stock A? Stock B? 4. What is the required rate of return for Stock A? Stock B? Stock A is expected to pay a dividend of $1.25 in a year and is expected to have a price of $25 in a year. Stock B is expected to pay a dividend of $0.50 each year for the next three years and is expected to have a price of $30 in three years. 1. Determine the current value of Stock A. (Hint: find the present value of future cash flows using the required rate of return derived from above for Stock A.) Determine the current value of Stock B. (Hint: find the present value of future cash flows using the required rate of return derived from above for Stock B.) If Stock A has an expected return of 8.5%, will you invest in Stock A? Why or why not? If Stock B has an expected return of 15%, will you invest in Stock B? Why or why not? 2. 3. 4.

Answer 1

a) Beta of A =Correlation*Standard Deviation of A/Standard Deviation of Market =0.32*40%/20% =0.64
Beta of B =Correlation*Standard Deviation of A/Standard Deviation of Market =0.85*30%/20% =1.275


Systematic Risk of A=Beta A^2*Standard Deviation of M^2=0.64^2*20%^2
Firm Specific risk of A =Variance of Risk A-Systematic Risk=40%^2-0.64^2*20%^2=14.36%

Systematic Risk of B=Beta A^2*Standard Deviation of M^2=1.275^2*20%^2
Firm Specific risk of B=Variance of Risk B-Systematic Risk=30%^2-1.275^2*20%^2 =2.50%

Stock A has greater risk

b)Beta of A =Correlation*Standard Deviation of A/Standard Deviation of Market =0.32*40%/20% =0.64
Beta of B =Correlation*Standard Deviation of A/Standard Deviation of Market =0.85*30%/20% =1.275
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c)Risk Premium of S&P 500 =12.5%-3.8% =8.7%
Risk Premium of A =Market Risk Premium *Beta =8.7%*0.64 =5.57%
Risk Premium of B =Market risk Premium/Beta =8.7%/1.275 =6.82%

d) Required Rate of A =Risk Free rate+beta*Market Risk premium=3.8%+0.64*8.7% =9.37%
Required Rate of B =Risk Free rate+beta*Market Risk premium=3.8%+1.275*8.7% =14.89%