Question

1. You are considering the purchase of two stocks, A and B. The initial price of each stock is $100. The price of the stocks at the end of the year depend on the state of the economy over the year as follows (neither stock pays a dividend):

      Price in One Year

State of Economy                Probability                            Stock A                  Stock B

     Boom                                                   .15                                          115                         125

     Moderately Growth                           .65                                          108                         112

     Recession                                            .20                                           92                           85

1. What are the expected rates of return and standard deviations for A and B?
2. If the risk-free rate is 2.50%, what is the risk premium on stock A? What is the risk premium on stock B? Which stock has the better risk-reward tradeoff as measured by the Sharpe ratio?
3. Assess your own risk tolerance using the questionnaire in your text on page 164. If you are a conservative investor, (i.e. you got 9 points or less) set A=6. If you are a moderate investor (i.e. you got 10 to 17 points) set A=4. If you are an aggressive investor, (i.e you got 18 points or more) set A=2. Your utility function is U = r^e – ½ As². You can invest in either Stock B or T-bills (risk-free rate = 2.50%). What is your certainty equivalent rate of return? Which will you choose?   What is the level of risk aversion for which you would be indifferent between Stock B and T-bills? (Within your group, there should be a moderate, a conservative and an aggressive investor. Please give me answers for all three types of investor.)

Answer 1

		Return in one year
State of economy	Probability	Stock A	Stock B
Boom	0.15	15%	25%
Moderately growth	0.65	8%	12%
Recession	0.20	-8%	-15%

a. E(R_A) = 0.15(0.15) + 0.65(0.08) + 0.20(-0.08) = 0.0585 = 5.85%

E(R_B) = 0.15(0.25) + 0.65(0.12) + 0.20(-0.15) = 0.0855 = 8.55%

Std. Dev. A = (0.15(0.15-0.0585)² + 0.65(0.08-0.0585)² + 0.20(-0.08-0.0585)²)^1/2 = 0.073435 = 7.3435%

Std. Dev. B = (0.15(0.25-0.0855)² + 0.65(0.12-0.0855)² + 0.20(-0.15-0.0855)²)^1/2 = 0.126193 = 12.6193%

b. Risk premium on stock A = 5.85% - 2.50% = 3.35%

Risk premium on stock B = 8.55% - 2.50% = 6.05%

Sharpe ratio of A = 3.35% / 7.3435% = 0.4562

Sharpe ratio of B = 6.05% / 12.6193% = 0.4794

Stock B has better risk-reward tradeoff as measured by the Sharpe ratio.