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.)

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