Consider the following scenario analysis:Rate of Return Scenario Probability Stocks BondsRecession 0.20 -4 % 16 %Normal economy 0.50 18 % 9 %Boom 0.30 29 % 6 %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. c. Which investment would you prefer?

Answer and Explanation:

a. Here it is reasonable to presume that the treasury bond generates high returns when there is a recession.  

b. The calculation of the expected rate of return and the standard deviation for each investment is shown below:

For stocks

= (Expected return of the boom × weightage of boom) + (expected return of the normal economy × weightage of normal economy) + (expected return of the recession × weightage of recession)  

= (29% × 0.30) + (18% × 0.50) + (-4% × 0.20)  

= 8.7% + 9% - 0.80%

= 16.9%

For bonds  

= (Expected return of the boom × weightage of boom) + (expected return of the normal economy × weightage of normal economy) + (expected return of the recession × weightage of recession)  

= (6% × 0.30) + (9% × 0.50) + (16% × 0.20)  

= 1.8% + 4.5% + 3.2%

= 9.5%

Now the standard deviation calculation is to be shown in the excel spreadsheet

For the stock it is 11.48%

And, for the bond it is 3.5%

c. The investment that should be prefer could be computed by determine the coefficient of variation which is shown below:

Formula i.e. used is

= Standard deviation ÷ expected return

For stock, it is

= 16.9% ÷ 11.48%

= 1.47

And, for bonds it is

= 9.5% ÷ 3.5%

= 2.71

Since for the bonds the coefficient of variation is greater so the same is to be considered

Therefore the bond should be prefer

b is the correct answer