Suppose the risk-free interest rate is 2%, and the stock market will return eith

ID: 2784738 • Letter: S

Question

Suppose the risk-free interest rate is 2%, and the stock market will return either +21% or 10% each year, with each outcome equally likely. Compare the following two investment strategies: (1) invest for one year in the risk-free investment, and one year in the market, or (2) invest for both years in the market.
a. Which strategy has the highest expected final payoff?
b. Which strategy has the highest standard deviation for the final payoff?
c. Does holding stocks for a longer period decrease your risk?

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Explanation / Answer

Return in 2 years will be either = (1 + 2%) * (1 + 21%) = 1.2342 - 1

Return in 2 years will be either = (1 + 2%) * (1 + 21%) = 23.42%

or Return in 2 years = (1 + 2%) * (1 - 10%) = 0.918 - 1

or Return in 2 years = (1 + 2%) * (1 - 10%) = -8.2%

Option 2:

Return in 2nd year = 1.212 - 1 = 46.41%

Return in 2nd year = 1.21 * 0.9 - 1 = 8.9%

Return in 2nd year = 0.9 * 1.21 - 1 = 8.9%

Return in 2nd year = 0.9 * 0.9 - 1 = -19%

Part A:

Expected Return in option A = (23.42% - 8.2%)/ 2

Expected Return in option A = 7.61%

Expected Return in option B = (46.41% + 8.9% + 8.9% - 19%)/ 4

Expected Return in option B = 11.30%

Part B

Standard deviation = (0.5 * (23.42% - 7.61%)2 + 0.5 * (-8.2% - 7.61%)2)0.5

Standard deviation = 15.81%

Standard deviation = (0.25 * (46.41% - 11.30%)2 + 0.5 * (8.9% - 11.30%)2 + 0.25 * (-19% - 11.30%)2)0.5

Standard deviation = 23.25%

Part C

No holding stocks for a longer period decrease your risk

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Suppose the risk-free interest rate is 2%, and the stock market will return eith

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