The market price of a security is $43. Its expected rate of return is 20%. The risk-free rate is 3% and the market risk premium is 7.8%. 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.

45.95%

Explanation:

If the security's correlation coefficient with the market portfolio doubles then beta, and t the risk premium will as well double.

The current risk premium is: 20% - 3% = 17%

Therefore the new risk premium would be 34% while the new discount rate for the security would be: 34% + 3% = 37%

Hence if the stock pays a constant perpetual dividend, then we know from the original data that the dividend (D) must satisfy the equation for the present value of a perpetuity:

Price = Dividend/Discount rate

43 = D/0.2 - > D

= 43 x 0.2 = $8.6

At the new discount rate of 37%, the stock would be worth: $8.6/0.37 = $23.24

$23.24/43 - 1

=45.95%

Therefore the increase in stock risk has lowered its value by 45.95%.