Question

The market price of a security is $52. Its expected rate of return is 12.1%. The risk-free rate is 4% and the market risk premium is 7.3%. 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.)

Market price=

Answer 1

Firstly, we need to calculate the Beta of the Stock. We can calculate Beta with CAPM equation-

where

E(R) = Expected Return

Rf = risk free rate

Rm = Market return

Rm-Rf = market risk premium

B = Beta

Putting the values -

Now,

Cov(S,M) = Covariance between stock and Market

S = Stock

M = Market

Now if we double the correlation coefficient of Stock and Market, Then it also double to the Beta of Stock

Thus,

New Beta would be -

Now, Lets calculate the Constant Dividend with Constant dividend Model -

And,

New Expected Return-

Thus,

New Market Price -

Market Price = $31.15

Hope this will help, please do comment if you need any further explanation. Your feedback would be appreciated.