Question

Consider the following information on Stocks I and II:

 

State of Economy	Probability of State of Economy	Rate of Return if State Occurs
		Stock I	Stock II
Recession	.26	.025	−.21
Normal	.61	.325	.13
Irrational exuberance	.13	.185	.41

  

The market risk premium is 11.1 percent, and the risk-free rate is 4.1 percent.
a.	Calculate the beta and standard deviation of Stock I. (Do not round intermediate calculations. Enter the standard deviation as a percent and round both answers to 2 decimal places, e.g., 32.16.)
b.	Calculate the beta and standard deviation of Stock II. (Do not round intermediate calculations. Enter the standard deviation as a percent and round both answers to 2 decimal places, e.g., 32.16.)
c.	Which stock has the most systematic risk?
d.	Which one has the most unsystematic risk?
e.	Which stock is “riskier”?

Answer 1

Rate of return Stock II 2 State of econom 3 recession 4 normal 5 irrational exuberance probability Stock 0.26 0.61 0.13 -0.21Market risk premium 0.111 0.025 0.325 0.185 0.13 Risk-free rate 0.41 0.041 Stock I Stock II Expected return Variance Standard deviation beta Standard deviation(% 0.0780 0.04 0.1938 0.33 19.38 9 0.2288 0.02 0.1292 1.69 12.92 10 12 13 14 15 Since stock I has a higher beta, Stock I has the most systematic risk 16 17 Stock II has the most unsystematic risk

Rate of return 2 State of econo 3 recession 4 normal 5 irrational exuberance probability StockI 0.26 0.61 0.13 0.025 0.325 0.185 Stock II 0.21 0.13 0.41 Market risk Risk-free rate ium 0.111 0.041 Stock I Stock II return 10 Variance Standard deviation beta standard deviation(% -SQRT(C10 -SQRT(D10) 12 13 14 -Ci1 100 -D11 100

Answer 2

Probability Stock I Stock II

Recession 0.26 0.025 - 0.21

Boom 0.61 0.325 0.13

Irrational exuberence 0.13 0.185 0.41

Stock I

Expected Return = 0.26 * 0.025 + 0.61 * 0.325 + 0.13 * 0.185

= 0.0065 + 0.19825 + 0.02405

= 0.2288 or 22.88%

Variance = 0.26 (0.025 - 0.2288)2 + 0.61 (0.325 - 0.2288)2 + 0.13 (0.185 - 0.2288)2

= 0.0108 + 0.0056 + 0.00025

= 0.01665

Standard deviation = square root of 0.01665

= 0.1290 or 12.90%

0.2288 = 0.041 + beta * 0.111

0.1878 = beta * 0.111

beta = 1.69

Stock II

Expected return = 0.26 * - 0.21 + 0.61 * 0.13 + 0.13 * 0.41

= - 0.0546 + 0.0793 + 0.0533

= 0.078 or 7.8%

Variance = 0.26 (-0.21 - 0.078)2 + 0.61 (0.13 - 0.078)2 + 0.13 (0.41 - 0.078)2

= 0.0216 + 0.0016 + 0.0143

= 0.0375

Standard deviation = square root of 0.0375

= 0.1936 or 19.36%

0.078 = 0.041 + beta 0.111

beta = 0.33.