Question

You are considering buying a share of stock in a firm that has the following two possible payoffs with the corresponding probability of occurring. The stock has a purchase price of $50.00. You forecast the alternatives as follows:

a) There is a 40% chance that the stock will sell for $70 at the end of one year.

b) There is a 60% chance that the stock will sell for $30 at the end of one year.

What is the expected percentage return on this stock, and what is the standard deviation of returns on this stock?

Answer 1

Expected return=(End value-Beginning value)/Beginning value

Probability	Expected return
40%	(70-50)/50=40%
60%	(30-50)/50=-40%(Negative)

 

Expected return = Respective return*Respective probability

                                = (0.4*40)+(0.6*-40)

                                = -8%(Negative)

 

probability	Return	probability*(Return-Expected Return)^2
0.4	40	0.4*(40-(-8)]^2=921.6
0.6	-40	0.6*[-40-(-8)]^2=614.4
		Total=1536%

 

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

                                      = (1536)^(1/2)

                                     = 39.19%(Approx)

 

Expected return = -8%(Negative)

Standard deviation = 39.19%(Approx)