Question

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	?	?

Answer 1

		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%