Question

The market price of a security is $25. Its expected rate of return is 12%. The risk-free rate is 4% and the market risk premium is 6.0%. What will be the market price of the security if its correlation coefficient with the market portfolio doubles (and all other variables remain unchanged)? Assume that the stock is expected to pay a constant dividend in perpetuity. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

Given Information:

Market price of security = $25

Expected rate = 12%

Risk-free rate = 4%

Market risk premium = 6%

Answer:

New market price of security = $15.03

Explanation:

The new market price of security can be calculated by,

P = Dividend/Expected return

Where Dividend is given by

Dividend = Market price*Expected rate

D = $25*0.12

D = 3$

Expected return is given by

Expected return = Risk-free rate + β*(market risk premium)

β can be calculated as

β = (Expected rate - Risk-free rate)/market risk premium

β = (12 - 4)/6

β = 1.33%

Since it is given that correlation coefficient with the market portfolio doubles, therefore, β will get doubled too because they are directly proportional.

β = 2*1.33%

β = 2.66%

So the Expected return is

Expected return = 4 + 2.66*(6)

Expected return = 19.96%

So the new market price of security is,

P = Dividend/Expected return

P = 3/0.1996

P = $15.03