Question

Given the following information, what is the standard deviation of Stock "C"?

		Rate of Return if State Occurs
State of Economy	Probability of State of Economy	Stock A	Stock B	Stock C
Boom	45%	0.20	0.45	0.32
Bust	55%	-0.10	-0.35	-0.21
Asset Weights		50%	25%	25%

Answer 1

Solution:
	Standard deviation of Stock "C"	26.37%
Working Notes:
Notes:	First of all we compute expected return of stock C returns , then Variance and at last standard deviation.
	Expected return of Stock C (Er C) = Sum of ((prob of each state) x (Return of Stock C at each state))
	=45% x 0.32 + 55% x (-0.21)
	=0.028500
	2.85%
	The variance of this Stock C = Sum of [(Prob. Of each state) x ( Return of the Stock C at each state - Expected return of the Stock C)^2 ]
	=45% x (0.32 - 0.02850)^2 + 55% x (-0.21 - 0.02850)^2
	=0.069522750
	0.069522750
	The standard deviation of Stock C = Square root of the variance of Stock C
		=(0.069522750)^(1/2)
		=0.263671671
		26.37%
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