Review of CAPM

**Risk return graph to position any security**

- abscissa axis : s
_{S} - ordinate axis : r
_{S}

**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, b
_{S}= covariance(R_{S}, R_{M}) / Var(R_{M}) - It is approximated by the slope of the straight
line fitted, with the appropriate method, through a scattergram of past
outcomes of (R
_{M}, R_{S}) - R
_{S}= r_{TB}+ b_{S}(R_{M}- r_{TB}) + e_{S} - We say that S moves "like the market" with a
"reactivity factor" b
_{S}, plus an extra random term e_{S}the mean of which is zero. - Let's look at the expectation of R
_{S }(denoted r_{S}) - r
_{S}= r_{TB}+ b_{S}(r_{M}- r_{TB}) - Let's look at the variance of R
_{S }(denoted s^{2}_{S}) - s
^{2}_{S}= b^{2}_{S }*_{ }s^{2}_{M}+ Var(e_{S}) - The part b
^{2}_{S }* s^{2}_{M}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.