Question

Please solve algebraically, not with excel:

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%	0.27	0.23	0.15
Good	45%	0.15	0.11	0.09
Poor	25%	0.03	0.02	0.04
Bust	10%	-0.1	-0.02	-0.03

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

	A		B		C
	Return	Weight	Return	Weight	Return	Weight	Portfolio Return [{R(a)*W(a)}+{R(b)*W(b)}+{Rc*Wc}]
Boom	0.27	0.25	0.23	0.4	0.15	0.35	0.212
Good	0.15	0.25	0.11	0.4	0.09	0.35	0.113
Poor	0.03	0.25	0.02	0.4	0.04	0.35	0.0295
Bust	-0.1	0.25	-0.02	0.4	-0.03	0.35	-0.0435

Economy	Probabilty	Return	Probability* Return	Return- Expected Return[D]	Probability*D*D
Boom	0.2	0.212	0.0424	0.115725	0.002678455
Good	0.45	0.113	0.05085	0.016725	0.000125877
Poor	0.25	0.0295	0.007375	-0.066775	0.001114725
Bust	0.1	-0.0435	-0.00435	-0.139775	0.001953705
		Expected Return = Sum of Probability*Return	0.096275	Variance =Sum of [D^2]	0.005872762
				Standard Deviation =Variance^1/2	0.076633947 = 7.66%