Question

Consider the following information on Stocks A, B, C and their returns (in decimals) in each state: State Prob. of State A B C Boom 20% 0.32 0.2 0.17 Good 45% 0.12 0.09 0.08 Poor 25% 0.04 0.01 0.03 Bust 10% -0.08 -0.06 -0.01 If your portfolio is invested 25% in A, 40% in B, and 35% in C, what is the standard deviation of the portfolio in percent? Answer to two decimals, carry intermediate calcs. to at least four decimals.

Answer 1

State	Probability(P)	Expected return   (X)	A=(X.2905)^2	Variance = A*P
Boom	20%	[.32*.25]+[.20*.40]+[.17*.35] .08+ .08+.0595 .2195	(.2195-.2905)^2 .005041	.0010082
Good	45%	[.12*.25]+[.09*.40]+[.08*.35] .03+ .036+ .028 .094	(.094-.2905)^2 .038612	.0173754
Poor	25%	[.04*.25]+[.01*.40]+[.03*.35] .01+ .004+ .0105 .0245	(.0245-.2905)^2 .070756	.017689
Bust	10%	[-.08*.25[+[-.06*.40]+[-.01*.35] -.02- .024- .0035 - .0475	(-.0475-.2905)^2 .114244	.0114244
		.2905		.047497

Standard deviation =square root of variance

           =SR(.047497)

           = .2179 (rounded to .22)   (or 21.79% in % terms)