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%.

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