Updated: 4/4/2004; 10:48:31 AM.
Tahsin Alam's Radio Weblog
        

Tuesday, March 30, 2004

Sayee's blogs!

Hey - there are fellow bloggers amongst my friends that I was unaware of. Here are two of Sayee's blogs: Baiju and Reluctant Messiah.

8:27:45 AM    comment []

[Copied over from my previous blog at http://blogs.law.harvard.edu/tahsin ] 

Finance - Tests of EMH and CAPM

Reading BKM Chap 13 and about tests of EMH/CAPM. Wanted to outline what I am reading for future reference.

Testing 1-factor CAPM/APT

Typical tests of CAPM involve
(i) gathering return data for a large number of stocks
(ii) constructing a security characteristic line for each stock - basically use time series returns to estimate the beta for each stock
(iii) now do a cross-sectional regression using the beta of each stock to see if it predicts the stocks average return

CAPM rejected: First tested in this manner by Lintner, Miller and Scholes in 1965, 1972; result of the test - the CML is too "flat" compared to CAPM prediction. Alpha is positive, and idiosyncratic returns are statistically significant.

But market proxy was bad: "Roll's critique" to these tests is basically that the market proxy used (S&P 500) is invalid. There is a more detail to this that I don't understand. What I think Roll is saying is that if the "market" portfolio is constructed using stocks in the study, then the beta's of the stocks measured against this "market" portfolio will perfectly predict the ex-post returns of the stocks, i.e. CAPM will hold perfectly. However, this says nothing about the ex-ante betas measured against the true market portfolio.

Roll & Ross's arbitrary beta-return relationship: Roll & Ross showed that it's possible to construct universes of stocks with reasonable characteristics where there are large numbers of market proxies that are "pathological". They are "pathological" in the sense that the stock betas measures against them have no relationship to the stock returns. These market proxies can be very close to the efficient frontier.
    In short - betas approximated using OLS on a market proxy are extremely sensitive to the choice of the market proxy. Others showed later that using GLS helps, but doesn't solve the problem.

Bad estimates of beta lead to other problems: So if the beta estimates are "bad" in the sense that they are measured with errors, then the 2nd stage regression has an independent variable that is measured with an error. OLS, in this case, will lead to biased coefficients that will make SML appear "flat" just as was found in the early Lintner study.

Back to square one: So, the earlier disappointing results can be explained away, but we have no positive proof of CAPM.

Correcting estimates of beta: Using portfolios of stocks, rather than individual stocks, corrects the beta measurement (somehow). Fama and MacBeth grouped stocks into portfolios by the stock beta, and reran the 2 stage regression. Their results: idiosyncratic returns are insignificant, but the SML is still too flat with a positive alpha. But the flatness is not statistically significant. So, maybe we are ok, but it's not fully satisfying still.CAPM seems qualititatively correct, but maybe not quantitatively.

Testing multifactor CAPM/APT

This is tough to do since we don't know what the factors are! Anyway, Chen, Roll & Ross (1986) tried to use a few proxies. The results are promising but not conclusive.

Anomalies Literature

Size and Value: Fama, French's "Cross Section of Expected Stock Returns" shows that size and book-to-market are factors that matter. Their original claim, that beta doesn't matter once you control for size, was later questioned by other papers that use different statistical techniques. But, at least, size and "value" are established as important factors in addition to market beta.

C-CAPM: Two observations: human capital is a large non-traded asset, and asset betas are related to business cycles. C-CAPM incoporates these two factors. Tests using change in aggregate labor income, and corporate bond risk premium (hi-grade minus lo-grade) show that these are significant factors. Also, significance of the size factor disappears.

Short-term momentum: Lo, Mackinlay (1988), "Stock Market Prices Do No Follow Random Walks" and Conrad, Kaul (1988) show that weekly NYSE returns show positive serial correlation. The correlation is, however, weak.

Medium-term momentum: Jegadeesh, Titman (1993), "Returns to Buying Winners and Selling Losers" show that there is momentum in 3-12 month returns. This time the pattern is strong enough to generate abnormal trading profits.

Long-term reversal: Fama, French (1988), "Permanent and Temporary Components of Stock Prices" and Poterba, Summers (1988), "Mean Reversion in Stock Prices" show long-term negative serial correlation. There are statistical issues with these studies.

Post-earnings announcement price drift: Foster, Olsen and Sheflin (1984).


8:26:24 AM    comment []

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