Answer:
a. Yes. It is reasonable to assume that Treasury bonds will provide higher returns in recessions than in booms. In booms, stocks perform better and yield higher rewards.
b. Expected rate of return and Standard Deviation for each investment
Stocks Bonds
Expected rate of return 0.13% 8.4%
Standard Deviation 0.096% 5.83%
c. I prefer investment in Treasury bonds. Its expected rate of return of 8.4% is higher than Stock's 0.13%, even with its standard deviation of 5.83%.
Explanation:
a) Data and Calculations:
Rate of Return Scenario
Probability Stocks Bonds
Recession 0.20 −5% 14%
Normal economy 0.60 15 8
Boom 0.20 25 4
b) Expected Rate of Return and Standard Deviation for Stocks:
Rate of Return Scenario
Probability Stocks Expected Mean Squared
Rate Difference Difference
Recession 0.20 −5% -0.01% -0.14% 0.0196%
Normal economy 0.60 15 0.09% -0.04% 0.0016%
Boom 0.20 25 0.05% -0.08% 0.0064%
Expected rate of return 0.13% 0.0276%
Variance of squared differences = 0.0276%/3 = 0.0092%
Standard Deviation = 0.096%
c) Expected Rate of Return and Standard Deviation for Bonds:
Rate of Return Scenario
Probability Bonds Expected Mean Squared
Rate Difference Difference
Recession 0.20 14% 2.8% 5.6% 31.36%
Normal economy 0.60 8 4.8% -3.6% 12.96%
Boom 0.20 4 0.8% -7.6% 57.76%
Total expected rate of return 8.4% 102.08%
Variance = mean of squared differences = 102.08%/3 = 34.03%
Standard Deviation = 5.83%
