Question

Consider the following scenario analysis

Rate of Return

Scenario Probability Stocks Bonds

recession 0.20 -5% 14%

Normal economy 0.60 15 8

Boom 0.20 25 4

Is it reasonable to assume that treasury bonds will provide higher returns in recessions than in booms?

Calculate the expected rate of return and 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

			Stocks	Bonds
Expected rate of return			13.0%	8.4%
Standard deviation			9.8%	3.2%
Working:
Stocks:							Bonds:
# 1	Calculation of expected return						# 1	Calculation of expected return
	Scenerio	Probability	Rate of return					Scenerio	Probability	Rate of return
		a	b	a*b					a	b	a*b
	Recession	0.20	-0.0500	-0.0100				Recession	0.20	0.1400	0.0280
	Normal Economy	0.60	0.1500	0.0900				Normal Economy	0.60	0.0800	0.0480
	Boom	0.20	0.2500	0.0500				Boom	0.20	0.0400	0.0080
	Total			0.1300				Total			0.0840
# 2	Calculation of variance:						# 2	Calculation of variance:
	Scenerio	Probability	Rate of return	Expected return				Scenerio	Probability	Rate of return	Expected return
		a	b	c	d=((b-c)^2)*a				a	b	c	d=((b-c)^2)*a
	Recession	0.20	-0.0500	0.1300	0.00648			Recession	0.20	0.1400	0.0840	0.00063
	Normal Economy	0.60	0.1500	0.1300	0.00024			Normal Economy	0.60	0.0800	0.0840	0.00001
	Boom	0.20	0.2500	0.1300	0.00288			Boom	0.20	0.0400	0.0840	0.00039
	Total				0.00960			Total				0.00102
# 3	Calculation of standard deviation						# 3	Calculation of standard deviation
	Standard deviation		=	Variance	^ (1/2)			Standard deviation		=	Variance	^ (1/2)
			=	0.00960	^ (1/2)					=	0.00102	^ (1/2)
			=	0.09798						=	0.032