Question

There are only two possible states of the economy. State 1 has a 45% chance of occurring. In State 1, Asset A returns 9.25% and Asset B returns 12.25%. In State 2, Asset A returns -4.70% and Asset B returns -7.70%. A portfolio of just these two assets is invested 65% in Asset A (with Asset B comprising the remainder without any negative weights). What is the standard deviation of the portfolio's returns?

Answer 1

B's Weight = 1 - A's Weight = 1 - 0.65 = 0.35

	A		B
	Return	Weight	Return	Weight	Portfolio Return [{R(a)*W(a)}+{R(b)*W(b)}]
State 1	0.0925	0.65	0.1225	0.35	0.103
State 2	-0.047	0.65	-0.077	0.35	-0.0575

State 2's Probability = 1 - State 1's Probability = 1 - 0.45 = 0.55

	Probability	Return	Probability* Return	Return- Expected Return[D]	Probability*D*D
State 1	0.45	0.103	0.04635	0.088275	0.003506614
State 2	0.55	-0.0575	-0.031625	-0.072225	0.002869048
		Expected Return = Sum of Probability*Return	0.014725	Variance =Sum of [D^2]	0.006375662
				Standard Deviation =Variance^1/2	0.079847742 = 7.9848%