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 10%, the probability of a stable growth economy is 17%, the probability of a stagnant economy is 53%, and the probability of a recession is 20%. Calculate the variance and the standard deviation stock?
What is the variance of the stock investment? (ROUND TO FIVE DECIMAL PLACES)

What is the standard deviation of the stock investment? (ROUND TO TWO DECIMAL PLACES)

Investment	Boom	Growth	Stagnant	Recession
Stock	21%	10%	5%	-11%
Corporate Bond	10%	8%	6%	4%
Government Bond	9%	7%	5%	3%

Answer 1

State	Probability	Stock Return
Boom Economy	10%	21%
Stable Growth Economy	17%	10%
Stagnant Economy	53%	5%
Recession Economy	20%	-11%
Calculation of Expected return of stock investment
State	Probability (a)	Stock Return (b)	a X b
Boom Economy	10%	21%	2.10%
Stable Growth Economy	17%	10%	1.70%
Stagnant Economy	53%	5%	2.65%
Recession Economy	20%	-11%	-2.20%
Expected Return	4.25%
Expected Return = sum of (a X b)
Expected Return of stock investment= 4.25%
Calculation of Variance of stock investment
State	Probability (a)	Stock Return (b)	Mean Return(c)	{Square of (b-c)}*a
Boom Economy	10%	21%	4.25%	0.28056%
Stable Growth Economy	17%	10%	4.25%	0.05621%
Stagnant Economy	53%	5%	4.25%	0.00298%
Recession Economy	20%	-11%	4.25%	0.46513%
Variance	0.80488%
Variance = sum of [{Square of (b-c)}*a]
Variance of stock investment= 0.80488%
Calculation of Standard Deviation of stock investment
Standard Deviation = Sqaure root of [sum of {Square of (b-c)}*a]
Standard Deviation of stock investment = Square root of 0.80488%
Standard Deviation of stock investment = 8.97%
Therefore answer would be 0.80488% and 8.97 %