Problem: Suppose there is a risk free asset in the economy that gives a return o

Question

Problem: Suppose there is a risk free asset in the economy that gives a return of 0.02 (i.e. 2 percent), and that the returns of Security A, B and the market portfolio are given by the following table State of the world Market Portfolio Security A Security B Bear Market Normal Market Bull Market 0.10 0.08 0.25 0.20 0.10 0.20 0.30 0.05 0.30 Bear markets happen with a 20 percent chance, normal markets with a 50 percent chance and bull markets with a 30 percent chance A: Find each security's beta implied by the CAPM B: Draw the Security Market Line and plot each security. Does each security fall on the security market line? What can be inferred about each security's alpha?

Explanation / Answer

Expected return on

Market: 0.2*-0.1+0.5*0.08+0.3*0.25=0.095

Security A: 0.2*-0.2+0.5*0.10+0.3*0.20=0.07

Security B: 0.2*-0.3+0.5*0.05+0.3*0.30=0.055

Now, as per CAPM

return=riskfree+beta*market risk premium

As beta of market=1,

so market return=0.02+market risk premium

=>0.095=0.02+market risk premium

hence, market risk premium=0.075

So, return on security A=0.02+beta*0.075

=>0.07=0.02+beta*0.075

hence, beta of A= 0.6666

Similarly, return on security B=0.02+beta*0.075

=>0.055=0.02+beta*0.075

hence, beta of B= 0.4666

Slope of SML=rm-rf=0.075

Equation of SML: return=0.02+beta*0.075

As each stock is following this equation, each security falls on SML

Hence, alpha=0

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