The current market price of a security is $40, the security\'s expected return i

Question

The current market price of a security is $40, the security's expected return is 13%, the riskless rate of interest is 7%, and the market risk premium is 8%.

Part A: According to CAPM, what is the current beta of this security?

Part B: What will be the beta of this security if the covariance of its rate of return with the market portfolio doubles?

Part C: According to CAPM, what is the new expected return on this security?

Part D: What is the new price of this security?

Part E: How is your result consistent with our understanding that assets with higher systematic risks must pay higher returns on average?

PLEASE SHOW ALL CALCULATIONS AND FORMULAS. THANK YOU.

Explanation / Answer

As per CAPM,

Expected return Ke = Rf+(Rm-Rf)*beta

13 = 7+ beta*8

Beta = 0.75

If the rate of return covarience doubles with the market portfolio then beta also doubles = new beta = 1.5

New expected return = 7+(1.5*16)=31%

New price of security = 40*13%/31% = $16.77

The same can be identified by the reduced market price of the security to provide higher rate of return.

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