Question

1. The market and Stock J have the following probability distributions.  Calculate the standard deviations for the Stock J.

   Probability	r M	r J
   0.3	-10%	10%
   0.4	20%	18%
   0.3	25%	30%

   		6.22%
   		14.87%
   		12.50%
   		3.85%
   		7.81%

Answer 1

Standard deviation of stock J

Answer: 7.81

Where,

P = Probability

x̅ = Expected return of the stock

X = Return on investment of the stock

                       

Standard deviation of the return

Probability (P)	Rate of return (%)	(X - x̅)	P(X - x̅)2
(I)	(II)	(III)	(IV) = (I) * (III)2
.30	10	10 – 19.20 = -9.20	.30 * (-9.20)2 = 25.392
.40	18	18 – 19.20 = -1.20	.40 * (-1.20)2 = 0.576
.30	30	30 – 19.20 = 10.80	.30 * (10.80)2 = 34.992
Total ( ∑P(X - X̅)2)			60.96

Expected Return (x̅) = Probability * Return

                                    = 0.30 * 10 +0.40 * 18 +0.30 * 30

                                    = 19.20%                                     

SD =

                                                            SD =7.8076

                                                            SD =7.81