Question

Consider the following scenario analysis: 

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. (Do not round intermediate calculations. Enter your answers as a percent rounded to 1 decimal place.) 

Answer 1

Answer a)

The correct answer is YES.

Interest rate tends to rise in boom periods and falls in boom period. Now, bond prices are inversely proportional to interest rates and hence, bonds return will be more in recession time than in boom period.

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Answer b)

Return = $\sum$ Probability of a state * Return in that state

Stock Return = [ 0.2 * (-5%) ] + (0.6 * 15%) + (0.2 * 25%)

Stock Return = -1% + 9% + 5%

Stock Return = 13%

Bond Return = [ 0.2 * (14%) ] + (0.6 * 8%) + (0.2 * 4%)

Bond Return = 2.80% + 4.80% + 0.80%

Bond Return = 8.4%

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Variance of Stocks = [ 0.2 * (-5% - 13%)^2 ] + [ 0.6 * (15% - 13%)^2] + [ 0.2 * (25%   - 13%)^2 ]

Variance of Stocks = [ 0.2 * 1.96% ] + (0.6 * 0.16%) + (0.2 * 0.64%)

Variance of Stocks = 0.616%

Standard Deviation = Sqrt (Variance) = 7.8%

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Variance of Bonds = [ 0.2 * (14% - 8.40%)^2 ] + [ 0.6 * (8% - 8.40%)^2] + [ 0.2 * (4%   - 8.40%)^2 ]

Variance of Stocks = [ 0.2 * 0.31% ] + (0.6 * 0.13%) + (0.2 * 0.58%)

Variance of Stocks = 0.256%

Standard Deviation = Sqrt (Variance) = 5.1%