Monday, October 13, 2014

capm - learning notes

capm is a "baby model". capm is the simplest of linear models. I guess capm popularity is partly due to this simplicity. 2 big assumptions --
Ass1a: Over 1 period, every individual security has a return that's normal i.e. from a Gaussian noisegen with a time-invariant mean and variance.

Ass1b: there's a unique correlation between every pair of security's noisegen. Joint normal. Therefore any portfolio (2 assets or more) return is normal.

Ass2: over a 2-period horizon, the 2 serial returns are iid.

In the above idealized world, capm holds. (All assumptions challenged by real data.) In real stock markets, these assumptions could hold reasonably well in some contexts.

capm tries to forecast expected return of a stock (say google). Other models like ARCH (not capm) would forecast variance of the return.

Expected return is important in the industry. Investors compare expected return. Mark said the expected return will provide risk neutral probability values and enable us to price a security i.e. determine a fair value.

Personally, i don't have faith in any forecast over the next 5 years because I have seen many forecasts failing to anticipate crashes. However, the 100Y stock market history does give me comfort that over 20 years stock mkt is likely to provide a positive return that's higher than the risk-free rate.

Suppose Team AA comes up with a forecast mkt return of 10% over the next 12 months. Team BB uses capm to infer a beta of 1.5 (often using past 5 years of historical returns). Then using capm model, Team CC forecasts the google 12M expected return to be 1.5 * 10%.

In the idealized world, beta_google is a constant. In practice, practitioners assume beta could be slow-changing. Over 12M, we could say 1.5 is the average or aggregate beta_google.

Personally I always feel expected return of 15% is misleading if I suspect variance is large. However, I do want to compare expected returns. High uncertainty doesn't discredit the reasonable estimate of expected return.

"Market portfolio" is defined as the combined portfolio of all investor's portfolios. In practice, practitioners use a stock index. The index return is used as mkt return. Capm claims that under strict conditions, 12M expected return on google is proportional to 12M expected mkt return and the scaling factor is beta_google. Capm assumes the mkt return and google return are random (noisegen) but if you repeat the experiment 99 million times the average returns would follow capm.

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