Question

Suppose that the market portfolio is equally likely to increase by 14% or decrease by 4%. Security "X" goes up on average by 22% when the market goes up and goes down by 14% when the market goes down. Security "Y" goes down on average by 32% when the market goes up and goes up by 26% when the market goes down. Security "Z" goes up on average by 4% when the market goes up and goes up by 4% when the market goes down. The expected return on security with a beta of 1.8 is closest to: 5.8% 4.8% 6.6% 5.0%

Answer 1

Expected return on market =

P = probability

R = reutrn

Expected return on market portfolio = (0.5*14%) + (0.5*(-4%)

= 7% - 2%

= 5%

calculation of risk free rate:

Risk free rate has beta = 0

beta = change in security return / change in market return

for security Z beta = (4% - 4%) / 18% = 0

so Security Z is risk free rate

risk free rate = 4%

market return = 5%

As per CAPM required return = risk free rate + beta*(market return - risk free rate)

= 4% + 1.8*(5% - 4%)

= 5.8%