Question

# The market price of a security is \$54. Its expected rate of return is 13.2%. The...

The market price of a security is \$54. Its expected rate of return is 13.2%. The risk-free rate is 5% and the market risk premium is 9.2%. 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. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

Step 1:
According to capital asset pricing model equation:
Expected return = Risk free rate + Beta * Market Premium
Substituting the values, we get;
13.2% = 5%+ Beta * 9.2%
13.2% -5% = Beta * 9.2%
8.2% = Beta * 9.2%
=>Beta=8.2%/9.2%=0.891304348

Step 2:
Beta is now doubled to = 0.891304348*2 =1.782608696
Expected return when the value of beta doubles = 5% +1.782608696*9.2%= 0.214
Current Dividend =54*13.2% = 7.128
New Market Price = Dividend / Expected return if beta doubles
= 7.128 /0.214 = \$33.31