Question

A stock will provide a rate of return of either −29% or 32%.

a.	If both possibilities are equally likely, calculate the stock's expected return and standard deviation. (Do not round intermediate calculations. Enter your answers as a percent rounded to 1 decimal place.)

Expected return	%
Standard deviation	%

b.	If Treasury bills yield 1.5% and investors believe that the stock offers a satisfactory expected return, what must the market risk of the stock be? (Enter your answer as a whole percent.)

Market risk

%

Answer 1

Given:

Rate of return = -29% or 32% with equal probability

Expected rate of return = 0.5 * -29% + 0.5 * 32%

Expected rate of return = -0.1450 + 0.160

Expected rate of return = 0.0150

Expected rate of return = 1.5%

Standard deviation

Variance of the stock = weight1 * (return1 - expected rate of return)² + weight2 * ( return2 - expected rate of return)²

Variance of the stock = 0.5 * ( -29% - 1.50%)² + 0.5 * ( 32% - 1.50%)²

Variance of the stock = 0.5 * 0.093025 + 0.5 * 0.093025

Variance of the stock = 0.046513 + 0.046513

Variance of the stock = 0.093025

Standard deviation = sqrt( variance)

Standard deviation = sqrt ( 0.093025)

Standard deviation = 30.5%

b) Given T yield Rf= 1.5%

Expected return = 1.5%

market risk of the stock = Rms

E(R) = Rf + Rms

1.5% - 1.5% = Rms

Market risk = 0%