Question

Variance and standard deviation (expected). Bacon and Associates, a famous Northwest think tank, 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 22%, the probability of a stable growth economy is 40%, the probability of a stagnant economy is 20%, and the probability of a recession is 18%. 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? 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 five decimal places.) Data Table - X (Click on the following icon 2 in order to copy its contents into a spreadsheet.) Investment Stock Corporate bond Government bond Boom 20% 10% 9% Forecasted Returns for Each Economy Stable Growth Stagnant 11% 4% 8% 6% 7% 5% Recession 10% 4% 3% Print Done

Answer 1

	Stock
Economy	Probabilty	Return	Probability* Return	Return- Expected Return[D]	Probability*D*D
Boom	0.22	0.2	0.044	0.122	0.00327448
Stable Growth	0.4	0.11	0.044	0.032	0.0004096
Stagnant	0.2	0.04	0.008	-0.038	0.0002888
Recession	0.18	-0.1	-0.018	-0.178	0.00570312
		Expected Return = Sum of Probability*Return	0.078 7.8%	Variance =Sum of [D^2]	0.009676 = 0.9676%
				Standard Deviation =Variance^1/2	0.098366661 = 9.83667%
			Co Efficient of Variation = Standard Deviation/Mean i.e. Expected Return	0.098366661/0.078	1.261111039

	Cortporate Bond
Economy	Probabilty	Return	Probability* Return	Return- Expected Return[D]	Probability*D*D
Boom	0.22	0.1	0.022	0.0268	0.000158013
Stable Growth	0.4	0.08	0.032	0.0068	0.000018496
Stagnant	0.2	0.06	0.012	-0.0132	0.000034848
Recession	0.18	0.04	0.0072	-0.0332	0.000198403
		Expected Return = Sum of Probability*Return	0.0732 = 7.32%	Variance =Sum of [D^2]	0.00040976 = 0.04098%
				Standard Deviation =Variance^1/2	0.020242529 = 2.02425%
			Co Efficient of Variation = Standard Deviation/Mean i.e. Expected Return	0.020242529/0.0732	0.276537288

	Government Bond
Economy	Probabilty	Return	Probability* Return	Return- Expected Return[D]	Probability*D*D
Boom	0.22	0.09	0.0198	0.0268	0.000158013
Stable Growth	0.4	0.07	0.028	0.0068	0.000018496
Stagnant	0.2	0.05	0.01	-0.0132	0.000034848
Recession	0.18	0.03	0.0054	-0.0332	0.000198403
		Expected Return = Sum of Probability*Return	0.0632 = 6.32%	Variance =Sum of [D^2]	0.00040976 = 0.04098%
				Standard Deviation =Variance^1/2	0.020242529 = 2.02425%
			Co Efficient of Variation = Standard Deviation/Mean i.e. Expected Return	0.020242529/0.0632	0.320293188

Co Efficient of Variation is Risk per unit of Return of Return.

Therefore, Considering Both Risk and Return, the Investment that should be choosen is the one with LOWEST CO EFFICIENT OF VARIATION i.e.  Corporate Bonds