The market price of a security is $50. Its expected rate of return is 14%. The risk-free rate is 6% and the market risk premium is 8.5%. 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

The market price of the security is $31.81

Explanation:

In order to calculate the market price of the security if its correlation coefficient with the market portfolio doubles we would have to calculate first the following:

First, calculate the dividend expected after one year with the following formula:

D=P*E(ri)

D=$50*0.14

D=$7

Next, we would have to calculate the beta of the security using the CAAPM Equation:

βi= E(ri)-rf/E(rm)-rf

=0.14-0.06/0.085

=0.9412

Next, we have to calculate the new beta due to the change in the correlation coefficient with the following formula:

β=correlation coefficient/σm*σs

=2*0.941

=1.882

Next, Calculate the new expected return as follows:

E(ri)=rf+βi(E(rm)-rf)

=0.06+(1.882)(0.085)

=0.22

Finally we calculate the new piece of the security as follows:

P=D/E(ri)

=$7/0.22

=$31.81

The market price of the security is $31.81