Question

The market price of a security is $26. Its expected rate of return is 13%. The risk-free rate is 5% and the market risk premium is 7.0%. 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.)

Answer 1

According to capital asset pricing model

Expected return on stock = R1 = Risk free rate + Beta x Market risk premium

13% = 5% + Beta x 7%

8% = Beta x 7%

Beta = 8% / 7% = 1.1428

We know that Beta = (Correlation of market and security x Standard deviation of security) / Standard deviation of market

Using the above formula to beta, we can interpret or see that if Correlation of market and security doubles, then Beta of security will also double.

So New Beta = 2 x 1.1428 = 2.2856

Now Using CAPM

New Expected rate of return = R2 = Risk free rate + New Beta x market risk premium = 5% + 2.2856 x 7% = 5% + 15.9992% = 20.9992%

Let D1 = Constant Dividend = Expected dividend next year

As dividends are expected to be constant, hence growth rate of dividends = g = 0

Now Using Constant Growth rate model

Current Price of security = D1 / (R1 - g)

26 = D1 / (13% - 0)

D1 = 26 x 13% = $3.38

Also

New price of security = D1 / (R2 - g)

New Price of Security = (3.38 / 20.9992% - 0) = 3.38 / 20.9992% = 16.0958 = 16.10 (rounded to two decimal places)

Hence New price of Security = $16.10