Question

Quantitative Problem: You are given the following probability distribution for CHC Enterprises:

State of Economy	Probability	Rate of return
Strong	0.20	20	%
Normal	0.50	10
Weak	0.30	-4

What is the stock’s STD DEV?

Answer 1

Calculation of Expected return:

Particulars	Probability (1)	Return (2)	Expected return (3) (1*2)
Strong	0.2	20%	4%
Normal	0.5	10%	5%
Weak	0.3	-4%	-1.2%
		Expected return	7.8%

Calculation of Standard deviation:

Particulars	Probability (1)	Return-Expected return(2)	Square of Return-Expected return (3)	Variance (4) (1*3)
Strong	0.2	20%-7.8%=12.2% or 0.122	(0.122)^2 = 0.0149	0.00298
Normal	0.5	10%-7.8%=2.2% or 0.022	(0.022)^2 = 0.0005	0.00025
Weak	0.3	-4%-7.8%=-11.8% or -0.118	(-0.118)^2=0.0139	0.00417
			Variance	0.0074

Standard deviation = Square root of Variance

= Square root of 0.0074

= 0.086 or 8.6%

Standard deviation = 8.6%