Question

North Around, Inc. stock is expected to return 22 percent in a boom, 13 percent in a normal economy, and −15 percent in a recession. The probabilities of a boom, normal economy, and a recession are 6 percent, 92 percent, and 2 percent, respectively. What is the standard deviation of the returns on this stock? Please explain your answer.

Answer 1

Expected return=Respective return*Respective probability

=(0.06*22)+(0.92*13)+(0.02*-15)=12.98%

probability	Return	probability*(Return-Expected Return)^2
0.06	22	0.06*(22-12.98)^2=4.881624
0.92	13	0.92*(13-12.98)^2=0.000368
0.02	-15	0.02*(-15-12.98)^2=15.657608
		Total=20.5396%

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

=(20.5396)^(1/2)

=4.53%(Approx).