Question

Consider the following scenario analysis:

		Rate of Return
Scenario	Probability	Stocks		Bonds
Recession	0.20	–5	%	19	%
Normal economy	0.60	20		10
Boom	0.20	27		4

a. 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.)

	Expected Rate of Return	Standard Deviation
Stocks	?%	?%
Bonds	?%	?%

Answer 1

(a) Calculation of expected return of stocks:
	Probability(a)	Return(%) (b)	(a)*(b)
Recession	0.2	-5	-1
Normal	0.6	20	12
Boom	0.2	27	5.4
	Expected Return		16.4
Therefore expected return of stock is 16.4%
(b) Calculation of standard deviation of stock:
	Probability(a)	Return	(return- expected return)	(return- expected return)^2 (b)	(a*b)
Recession	0.2	-5	-21.4	457.96	91.592
Normal	0.6	20	3.6	12.96	7.776
Boom	0.2	27	10.6	112.36	22.472
					121.84
Standard deviation of stock= (121.84)^1/2= 11%
Calculation of expected return of bonds:
	Probability(a)	Return(%) (b)	(a)*(b)
Recession	0.2	19	3.8
Normal	0.6	10	6
Boom	0.2	4	0.8
	Expected Return		10.6
Therefore expected return of bond is 10.6%
(b) Calculation of standard deviation of bond:
	Probability(a)	Return	(return- expected return)	(return- expected return)^2 (b)	(a*b)
Recession	0.2	19	8.4	70.56	14.112
Normal	0.6	10	-0.6	0.36	0.216
Boom	0.2	4	-6.6	43.56	8.712
					23.04
Standard deviation of bond= (23.04)^1/2= 4.8%