Question

Hull​ Consultants, a famous think tank in the​ Midwest, has provided probability estimates for the four potential economic states for the coming year. The probability of a boom economy is 12%​, the probability of a stable growth economy is 18​%, the probability of a stagnant economy is 45​%, and the probability of a recession is 25​%. Calculate the variance and the standard deviation of the three​ investments: stock, corporate​ bond, and government bond. If the estimates for both the probabilities of the economy and the returns in each state of the economy are​ correct, which investment would you​ choose, considering both risk and​ return?   Investment Forecasted Returns for Each Economy Boom Stable Growth Stagnant Recession   Stock 23​% 14​% 33​% −15​%   Corporate bond 10​% 7​% 5​% 4​%   Government bond 9​% 6​% 4​% 3​% ​Hint: Make sure to round all intermediate calculations to at least seven​ (7) decimal places. The input​ instructions, phrases in parenthesis after each answer​ box, only apply for the answers you will type. What is the variance of the stock​ investment? What is the standard deviation of the stock​ investment? What is the variance of the corporate bond​ investment? What is the standard deviation of the corporate bond​ investment? What is the variance of the government bond​ investment? What is the standard deviation of the government bond​ investment?

Answer 1

Stock
Scenario	Probability	Return	'=rate of return * probability	Actual return -expected return(A)	(A)^2* probability
Boom	0.12	23.00%	2.76%	6.62%	0.000526
stable	0.18	14.00%	2.52%	-2.38%	0.000102
stagnant	0.45	33.00%	14.85%	16.62%	0.012430
recession	0.25	-15%	-3.75%	-31.38%	0.024618
	Expected return =	sum of weighted return =	16.38%	Sum=	0.037676
			Standard deviation of Stock	'=(sum)^(1/2)	19.41%
			Coefficient of variation=	STD DEV/RETURN=	1.18499348
Govt bond
Scenario	Probability	Return	'=rate of return * probability	Actual return -expected return(B)	(B)^2* probability
Boom	0.12	9%	1.08%	4.29%	0.000221
stable	0.18	6%	1.08%	1.29%	0.000030
stagnant	0.45	4%	1.80%	-0.71%	0.000023
recession	0.25	3%	0.75%	-1.71%	0.000073
	Expected return =	sum of weighted return =	4.71%	Sum=	0.000347
			Standard deviation of Govt bond	'=(sum)^(1/2)	1.86%
			Coefficient of variation=	STD DEV/RETURN=	0.395263859
corp bond
Scenario	Probability	Return	'=rate of return * probability	Actual return -expected return(C)	(C)^2* probability
Boom	0.12	10%	1.20%	5.29%	0.000336
stable	0.18	7%	1.26%	2.29%	0.000094
stagnant	0.45	5%	2.25%	0.29%	0.000004
recession	0.25	4%	1.00%	-0.71%	0.000013
	Expected return =	sum of weighted return =	5.71%	Sum=	0.000447
			Standard deviation of corp bond	'=(sum)^(1/2)	2.11%
			Coefficient of variation=	STD DEV/RETURN=	0.370099407

choose corporate bond as it has lowest coefficient of variation