Question

You believe that next year there is a 20​% probability of a recession and 80​% probability that the economy will be normal. If your stock will yield negative 12​% in a recession and 18​% in a normal​ year, what is the standard deviation of the​ stock?

The standard deviation of the stock is __​%. ​(Round to two decimal​ places.)

Answer 1

Expected return=Respective return*Respective probability

=(0.2*-12)+(0.8*18)

=12%

Probability	Return	Probability*(Return-Expected return)^2
0.2	-12	0.2*(-12-12)^2=115.2
0.8	18	0.8*(18-12)^2=28.8
		Total=144%

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

=(144)^(1/2)

=12%