Consider the following scenario analysis Rate of Return Prob

Consider the following scenario analysis Rate of Return Probability Stocks Bonds 14% Recession Normal economy Boon 0.20 0.60 0.20 -5% 15 25 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 deviahön for each investment. (Do not round intermediate calculations. Enter your answers as a percent rounded to 1 decimal place. Expected Rate Standard of Return Deviation Stocks Bonds

Solution

a)

Yes

Interest rates tend to fall at the outset of a recession and rise during boom periods. Because bond prices move inversely with interest rates, bonds provide higher returns during recessions when interest rates fall.

b)

Expected return of stocks = [0.20 × (?0.05)] + (0.60 × 0.15) + (0.20 × 0.25)

Expected return of stocks = [ -0.01 + 0.09 + 0.05 ]

Expected return of stocks = 0.13 or 13%

Expected return of Bonds = [0.20 × (0.14)] + (0.60 × 0.08) + (0.20 × 0.04)

Expected return of Bonds = [ 0.028 + 0.048 + 0.008 ]

Expected return of Bonds = 0.084 or 8.4%

Variance of stocks = [0.20 × (?0.05 ? 0.13)²] + [0.60 × (0.15 ? 0.13)²] + [0.20 × (0.25 ? 0.13)²]

Variance of stocks = 0.00648 + 0.00024 + 0.00288

Variance of stocks = 0.0096

Standard deviation of stock = ( 0.0096)^1/2

Standard deviation of stock = 0.09798 or 9.8%

Variance of Bonds = [0.20 × (0.14 ? 0.084)²] + [0.60 × (0.08 ? 0.084)²] + [0.20 × (0.04 ? 0.084)²]

Variance of Bonds = 0.000627 + 0.00001 + 0.000387

Variance of Bonds = 0.001024

Standard deviation of Bonds = ( 0.001024)^1/2

Standard deviation of Bonds = 0.032 or 3.2%