Question

Variance and standard deviation (expected). Hull Consultants, a farrous think tank in the Midwest, has provided probability estimates for the four potential economic states for the coming year in the following table: The probability of a boom economy is 13%, the probability of a stable growth economy is 20%, the probability of a stagnant economy is 45%, and the probability of a recession is 22%. 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 retum? 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? |% (Round to six decimal places.) What is the standard deviation of the stock investment? % (Round to two decimal places.) What is the variance of the corporate bond investment? % (Round to six decimal places.) What is the standard deviation of the corporate bond investment? 1% (Round to two decimal places.) What is the variance of the government bond investment? 1% (Round to six decimal places.) What is the standard deviation of the government bond investment? % (Round to two decimal places.) 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 retum? (Select the best response.) O A. The corporate bond would be the best choice because it has the highest expected return and the lowest risk. OB. There is not enough information to make this decision. OC. The goverment bond would be the best choice because it has the lowest risk. OD. The stock investment would be the best choice because it has the highest volatility and therefore the best chance of a high ratum.

Answer 1

Below are the calculations:

States	Probability	Stock	Probability Weighted Return	P(X - Expected return of I)^2
Boom	0.13	27.00%	0.13x27%=3.51%	0.13(0.27-0.0401)^2=0.68710213%
Stable	0.2	10.00%	0.2x10%=2%	0.2(0.1-0.0401)^2=0.0717602%
Stagnant	0.45	4.00%	0.45x4%=1.8%	0.45(0.04-0.0401)^2=0%
Recession	0.22	-15.00%	0.22x-15%=-3.3%	0.22(-0.15-0.0401)^2=0.79503622%
Expected Return= Sum of Probability Weighted Return			4.010%
Variance=Sum of P(X - Expected return of Stock)^2				1.553899%
Standard deviation = Square root of variance				12.465549%
			Return/Standard deviation	0.322
States	Probability	Bond	Probability Weighted Return	P(X - Expected return of Bond)^2
Boom	0.13	10.00%	0.13x10%=1.3%	0.13(0.1-0.0583)^2=0.02260557%
Stable	0.2	7.00%	0.2x7%=1.4%	0.2(0.07-0.0583)^2=0.0027378%
Stagnant	0.45	5.00%	0.45x5%=2.25%	0.45(0.05-0.0583)^2=0.00310005%
Recession	0.22	4.00%	0.22x4%=0.88%	0.22(0.04-0.0583)^2=0.00736758%
Expected Return= Sum of Probability Weighted Return			5.830%
Variance = Sum of P(X - Expected return of Bond)^2				0.035811%
Standard deviation = Square root of variance				1.892379%
			Return/Standard deviation	3.08
States	Probability	Gov	Probability Weighted Return	P(X - Expected return of Gov)^2
Boom	0.13	9.00%	0.13x9%=1.17%	0.13(0.09-0.0483)^2=0.02260557%
Stable	0.2	6.00%	0.2x6%=1.2%	0.2(0.06-0.0483)^2=0.0027378%
Stagnant	0.45	4.00%	0.45x4%=1.8%	0.45(0.04-0.0483)^2=0.00310005%
Recession	0.22	3.00%	0.22x3%=0.66%	0.22(0.03-0.0483)^2=0.00736758%
Expected Return= Sum of Probability Weighted Return			4.830%
Variance = Sum of P(X - Expected return of Gov)^2				0.035811%
Standard deviation = Square root of variance				1.892379%
Return/Standard Deviation				2.55

To decide which is the best out of the three, we need to calculate the return/standard deviation, which would imply the return generated per unit of risk.

We calculated the same and saw that the corporate bond has the highest number and therefore it is the best option and the correct answer is A.

Government bond has the same risk as corporate bond but lower return so C is not correct

Stock has very low risk adjusted return so option D is incorrect

We can make a decision with this much information so option B is incorrect