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I stumbled upon this questionn and answer on the forum. Can someone pls explain why the variance is being raised to the power of *2*

28.1 Assume the riskfree rate is 4% and the expected (overall) market return is 12% with 20% volatility. Our portfolio (P) has volatility of 30% and a correlation with the market of 0.4. According to CAPM, what is the portfolio's expected return?

beta = cov(P,M)/variance(M) = (20%*30%*0.4)/20%^2 = 0.6
CAPM says E(P return) = 4% + 0.6*(12%-4%) = 8.8%
 

David Harper CFA FRM

David Harper CFA FRM
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#2
Hi @Jerry Nwoko The volatility of 20% is being squared (notice that we "Assume the riskfree rate is 4% and the expected (overall) market return is 12% with 20% volatility."). For the beta of a portfolio with respect to the Market, β(P,M), the key formula is β(P,M) = cov(P,M)/variance(M) but cov(P,M) = correlation(P,M) * StandardDeviation(P) * StandardDeviation(M) and variance(M) = StandardDeviation(M)^2 where volatility is a synonym for StandardDeviation. So we can also cancel one of the StdDev:
  • β(P,M) = cov(P,M)/variance(M) = [correlation(P,M) * StandardDeviation(P) * StandardDeviation(M)] / StandardDeviation(M)^2, and cancelling:
  • β(P,M) = [correlation(P,M) * StandardDeviation(P) * StandardDeviation(M)] / StandardDeviation(M)^2, so it's also true:
  • β(P,M) = correlation(P,M) * StandardDeviation(P) / StandardDeviation(M); i.e., "beta is correlation multiplied by cross-volatility." You definitely want to know this for the exam. Thanks,
 
Thread starter #3
Thanks for the response Harper.
I want to beleive my challenge with the capm is having to pick pieces of information and putting them all together.

I have a basic understanding of the model that states the return on an efficient portlio as;
Rp = Rf + Beta ( Rm - Rf )

I want to build on this knowlede ground up. Which material puts all this peices together, from basic to more complex ( including calculations). So I can have a more wholistic understanding of the model and its applications.
 
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