Review of CAPM

Risk return graph to position any security

• abscissa axis : sS
• ordinate axis : rS

CAPM theory identifies, for any security, a fundamental risk and a specific risk (akin to an extra roulette wheel generated randomness)

• fundamental risk (= market risk, = undiversifiable risk, = systematic risk, = risk which cannot be eliminated) vs...
• ...specific risk (which can be eliminated by averaging out in a portfolio of "similar" securities).
• It is a mathematical result in linear algebra of RVs
• TB have zero risk, zero variability. Their return is the minimum (average) return one can get in the market. And it is sure.

CAPM main results

• One central portfolio is the "market portfolio", denoted M
• M is well approximated by any well diversified portfolio of 20 to 40 securities (eg : S&P portfolio, DJ portfolio)
• Define, for any security S sold in the market, bS = covariance(RS, RM) / Var(RM)
• It is approximated by the slope of the straight line fitted, with the appropriate method, through a scattergram of past outcomes of (RM, RS)
• RS = rTB + bS (RM - rTB) + eS
• We say that S moves "like the market" with a "reactivity factor" bS, plus an extra random term eS the mean of which is zero.
• Let's look at the expectation of RS (denoted rS)
• rS = rTB + bS (rM - rTB)
• Let's look at the variance of RS (denoted s2S)
• s2S = b2S * s2M + Var(eS)
• The part b2S * s2M is called the undiversifiable risk of the security S
• A portfolio made of a few securities is also, itself, a security
• A central idea of CAPM is to "average out" the diversifiable part of the risk of securities of same b by pooling them into portfolios
• Remember, if you throw one die, you will get a random result with mean 3,5 and std dev 1,7. If you throw several dice, the average result won't change but the std dev of the average result will be reduced.
• beta of any security S is estimated from past history of S and M, and published by agencies like Merrill Lynch.