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