Question

Consider the following information about Stocks I and II:

State of Economy	Probability of State of Economy	Return of Stock I if State Occurs	Return of Stock II if State Occurs
Recession	0.10	-0.02	-0.20
Normal	0.70	0.20	0.15
International exuberance	?	0.16	0.40

The expected market return is 10 percent, and the risk-free rate is 4 percent. Answer questions 16 to 18.

1) What is the beta for stock I?

2) What is the beta for stock II?

3) Which stock has more systematic risk? Explain.

Answer 1

Answer 1.

Stock I:

Expected Return = 0.10 * (-0.02) + 0.70 * 0.20 + 0.20 * 0.16
Expected Return = 0.17 or 17.00%

Expected Return = Risk-free Rate + Beta * (Market Return - Risk-free Rate)
17.00% = 4.00% + Beta * (10.00% - 4.00%)
13.00% = Beta * 6.00%
Beta = 2.12

Answer 2.

Stock II:

Expected Return = 0.10 * (-0.20) + 0.70 * 0.15 + 0.20 * 0.40
Expected Return = 0.1650 or 16.50%

Expected Return = Risk-free Rate + Beta * (Market Return - Risk-free Rate)
16.50% = 4.00% + Beta * (10.00% - 4.00%)
12.50% = Beta * 6.00%
Beta = 2.08

Answer 3.

Beta is the measure of systematic risk. Higher the beta, higher the systematic risk. Stock I has more systematic risk.