Answer:
The market price of the security if its correlation coefficient with the market portfolio doubles (and all other variables remain unchanged) will be $44.10.
Explanation:
Note: This question is not complete. The complete question is therefore presented before answering the question as follows:
The market price of a security is $74. Its expected rate of return is 20.2%. The risk-free rate is 3% and the market risk premium is 6.5%. 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.
Explanation of the answer is now given as follows:
Since the correlation coefficient with the market portfolio doubles (and all other variables remain unchanged), it implies that beta and also the risk premium will also double.
From the question, we can obtain:
Current risk premium = Expected rate of return - Market risk premium = 20.2% - 6.5% = 13.70%
As the current risk premium will double, we have:
New risk premium = Current risk premium * 2 = 13.70% * 2 = 27.40%
Also, we have:
New discount rate = New risk premium + Market risk premium = 27.40% + 6.5% = 33.90%
Since it is assumed that the stock is expected to pay a constant dividend in perpetuity, the dividend can therefore e calculated as follows:
Dividend = Current market price * Current expected rate of return = $74 * 20.2% = $14.95
The new market price of the security can now be calculated as follows:
New market price of the security = Dividend / New discount rate = $14.95 / 33.90% = $44.10
Therefore, the market price of the security if its correlation coefficient with the market portfolio doubles (and all other variables remain unchanged) will be $44.10.
