Consider the following scenario analysis:
Rate of Return | |||||
Scenario | Probability | Stocks | Bonds | ||
Recession | 0.20 | –6 | % | 18 | % |
Normal economy | 0.50 | 19 | 11 | ||
Boom | 0.30 | 26 | 8 |
a. Is it reasonable to assume that Treasury bonds will provide higher returns in recessions than in booms?
b. Calculate the expected rate of return and standard deviation for each investment.
Expected Rate of Return | Standard Deviation | |
Stocks | ? | ? |
Bonds | ? | ? |
RATE OF RETURN | ||||
SCENARIO | PROBABILITY | STOCKS | BONDS | |
Recession | 0.2 | -0.06 | 0.18 | |
Normal economy | 0.5 | 0.19 | 0.11 | |
Boom | 0.3 | 0.26 | 0.08 | |
a) Yes, treasury bonds will provide higher returns in recessions(18%) than in booms (8%). | ||||
b) | ||||
SCENARIO | PROBABILITY | RETURNS FOR STOCKS | PROB*RETURN | (RETURN - EXPECTED RETURN)^2 |
Recession | 0.2 | -0.06 | -0.012 | 0.048841 |
Normal economy | 0.5 | 0.19 | 0.095 | 0.000841 |
Boom | 0.3 | 0.26 | 0.078 | 0.009801 |
SUM | 0.161 | 0.059483 | ||
The expected return for stocks is 16.1%. | ||||
The variance for stocks is .059483 | ||||
Standard deviation = (Variance)^.5 | ||||
Standard deviation | (0.059483)^(.5) | |||
Standard deviation | 0.243891369 | |||
Standard deviation | 24.39% | |||
SCENARIO | PROBABILITY | RETURNS FOR BONDS | PROB*RETURN | (RETURN - EXPECTED RETURN)^2 |
Recession | 0.2 | 0.18 | 0.036 | 0.004225 |
Normal economy | 0.5 | 0.11 | 0.055 | -0.000025 |
Boom | 0.3 | 0.08 | 0.024 | 0.001225 |
SUM | 0.115 | 0.005425 | ||
The expected return for bonds is 11.5%. | ||||
The variance for bonds is .005425 | ||||
Standard deviation = (Variance)^.5 | ||||
Standard deviation | (0.005425)^(.5) | |||
Standard deviation | 0.073654599 | |||
Standard deviation | 7.37% | |||
Expected Return | Standard deviation | |||
Stocks | 16.10% | 24.39% | ||
Bonds | 11.50% | 7.37% |
Consider the following scenario analysis: Rate of Return Scenario Probability Stocks Bonds Recession 0.20...
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Consider the following scenario analysis: a. Is it reasonable to assume that Treasury bonds will provide higher returns in recessions than in booms? Yes No b. Calculate the expected rate of return and standard deviation for each investment.
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