Question

A stock’s returns have the following distribution:

Probability	Stock Return
0.1	–8%
0.8	18%
0.1	47%

The stock’s expected return is 18.3%. Calculate its standard deviation.

Answer 1

Expected return=Respective return*Respective probability

=(0.1*-8)+(0.8*18)+(0.1*47)

=18.3%

probability	Return	probability*(Return-Expected Return)^2
0.1	-8	0.1*(-8-18.3)^2=69.169
0.8	18	0.8*(18-18.3)^2=0.072
0.1	47	0.1*(47-18.3)^2=82.369
		Total=151.61%

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

=(151.61)^(1/2)

=12.31%(Approx)