Question

The shares ABC Ltd, a non-dividend paying stock, are currently selling for $25.00 per share. You have developed the following probability distribution of the price one year from now.

state of market	probability	price
awful	0.3	$32.50
normal	0.4	$30.00
awesome	0.3	$25.00

The variance of returns for CBC Ltd shares is closest to:

a) 0.0054. b) 0.0141. c) 0.0737 d) 0.1187

Answer 1

Return=(End price-Beginning price)/Beginning price

	Probability	Return
Awful	0.3	(32.5-25)/25=30%
Normal	0.4	(30-25)/25=20%
Awesome	0.3	(25-25)/25=0%

Expected return=Respective Return*Respective probability

=(0.3*30)+(0.4*20)+(0.3*0)=17%

probability	Return	probability*(Return-Expected Return)^2
0.3	30	0.3*(30-17)^2=50.7
0.4	20	0.4*(20-17)^2=3.6
0.3	0	0.3*(0-17)^2=86.7
		Total=141%

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

=11.874%(Approx).

Hence variance=Standard deviation^2

=0.0141