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The market price of a security is $70. Its expected rate of return is 14%. The...

The market price of a security is $70. Its expected rate of return is 14%. The risk-free rate is 6% and the market risk premium is 8.5%. 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

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Expert Solution

We have the following given data

Market price of a security (MPS) = $70

Expected rate of return (ERR) = 14%

Risk free rate (RFR) = 6%

Market Risk Premium (MRP) = 8.5%

Ans,

1. As per Capital Asset Pricing Methode (CAPM), we have

Expected Rate of Return =Risk Free Rate + Beta * Market Risk Premium

14% = 6%+Beta * 8.5%

0.14 = 0.06 + Beta * 0.085

(0.14 - 0.06)/0.085 = Beta

0.94 = Beta

If the correlation coefficient with the market portfolio doubles, Beta is also doubles

So

New Beta = 2 * 0.94

New Beta = 1.88

2. Computation Expected Rate of Return with new Beta   

Expected Rate of Return =Risk Free Rate + Beta * Market Risk Premium

= 6 + 1.88 * 8.5

  = 21.98 %

3. Computation of divident  

Market Value of Security = Divident / Expected Rate Of Return

   70 = Divident / 14 %   

Divident = 70 * 14%

Divident = $9.8

4. Computation of Market Value of Security with new Expected Rate of Return

Assume that the stock is expected to pay a constant dividend in perpetuity

Market Value of Security = Divident / Expected Rate Of Return

Market Value of Security = 9.8 / 21.98 %

Market Value of Security = $ 44.585

  

ekkarill92 answered 2 months ago
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