Question

Ex-Ante Standard Deviation An analyst estimates a 19% probability of a recession next year, a 43% probability of normal economic growth and a 38% probability of a strong recovery. If a recession occurs a stock is projected to have a -15.4% return. With normal growth the stock will generate a 10.4% return and if the strong recovery occurs the stock will have a 25.4% rate of return. This stock's standard deviation is

Multiple Choice 11.20% 11.76% 11.49% 14.54%

Answer 1

Expected return=Respective return*Respective probability

=(0.19*-15.4)+(0.43*10.4)+(0.38*25.4)

=11.198%

probability	Return	probability*(Return-Expected Return)^2
0.19	-15.4	0.19*(-15.4-11.198)^2=134.416185
0.43	10.4	0.43*(10.4-11.198)^2=0.27382572
0.38	25.4	0.38*(25.4-11.198)^2=76.6447855
		Total=211.334796%

Standard deviation=[Total probability*(Return-Expected Return)^2/Total probability]^(1/2)

=[211.334796]^(1/2)

=14.54%(Approx)