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接下来的两篇paper就不用多说了，金融学的绝对经典之作，欢迎大家讨论，下周我总结一下自己的感受
1、Fama, E. F. and J. D. MacBeth (1973). "Risk, return, and equilibrium: Empirical tests." The Journal of Political Economy: 607-636.
2、Fama, E. F. and K. R. French (1992). "The cross-section of expected stock returns." Journal of finance: 427-465.
Hi, everybody! From today on, I’d like to write the paper summary in English due to the following two reasons. First, it is more convenient for me since the paper that we are talking about is written in English so I do not need to translate it before I summarize it, which I believe, will improve the efficiency so that I could have time to cover more papers in the future. Second, I think it is also a good opportunity for all of us to practice English writing,coinciding with the purpose of “Follow us” section.

Today, I’d like to summarize the first seminal paper Fama&Macbeth1973. This paper, as a whole, is an empirical work for some hypotheses derived from CAPM model. However, this paper provides a very subtle method to test those hypotheses, cited as Fama-Macbeth Method, making the paper well known in the field of finance. Therefore, I will only focus on the method per se.

Whenever we read an empirical paper, the following two questions should always be kept in mind. First, how can we duplicate this paper? Second, why did the authors do like this? So, I will summarize this paper following the above logic.

How can we duplicate this paper?

To duplicate a paper, we should clarify the procedure of the original empirical work: how the data were manipulated? Why to select those independent variables and control variables? , and so on so forth.In FM1973, we will illustrate the portfolio formation by taking portfolio 2 on P618 as an example.

Step 1: Get monthly percentage returns from January1926 through June 1968 at NYSE;

Step 2: keep the non-missing data during Portfolio formation period and Initial estimation period, in this case from 1927 through1938;

Step 3: run regression between individual returnsand market returns by individual using data from 1927 through 1933 (portfolioformation period) and then keep betas;

Step 4: divide data into 20 groups according to theorder of betas;

Step 5: merge the above data with original monthly return data and then keep data from 1934 through 1938 (initial estimationperiod);

Step 6: recalculate beta as step 3 and predict the standarderror. At the same time, generate beta square;

Step 7: merge the above data with original monthly return data and then keep data from 1939 through 1942 (testing period);

Step 8: sort data by group, year and month and then get the mean of individual returns, beta, beta square and standard error by each group at the same month, so we can get 12 pairs of individual returns,beta, beta square and standard error within each group;

Step 9: sort by year and month and then run regression between individual returns and beta, beta square, standard error by year and month, so in every month, there are 20 observations, one from one group. We call this dataset as “input”; the result is one estimate in one month. We call thisdataset as “output”;

Step 10: for input data, we sort it by different group and then take average of beta within each group so we get table 2. If we test output data, we will get table 3.

Note that, the above shows how to duplicate thispaper. However, the Fama-Macbeth Method derived from this paper is not that complicated. It refers two step procedure.In the first step, for each single time period, a cross-sectional regression is performed. Then, in the second step, the final coefficient estimates are obtained as the average of the first step coefficient estimates. STATA xtfmb module could help you fulfill it. That is not a big deal!

Whydid the authors do like this?


1. why use portfolio beta?
The reason is that the “error in variable” problem occurs when we estimate betas. However,Blume (1970) argues that beta of portfolio can be much more precise than beta for individual securities.

2. why form 20 groups?
Comparing to using individual securities, using portfolios could lose some information inthe risk-return tests. To conquer this problem, a wide range of portfolio betasis obtained by forming portfolios on the basis of ranked values of betas for individual securities.

2. why recalculate portfolio betas at step 6?
The group formation could result in a serious regression problem. In a cross section of individual betas, high observed betas tend to be above the corresponding true betas and low observed betas tend to be below the true betas. Forming portfolios on the basis of ranked individual betas thus causes bunching of positive and negative sampling errors within portfolios. The resultis that a large portfolio betas would tend to overestimate the true betas,while a low portfolio betas would tend to be an underestimate. So, this paperrecalculate portfolio betas at step 6. With fresh data, within a portfolioerrors in the individual security betas are to be a large extent random across securities, so that in a portfolio betas the effects of the regression problemare minimized.
2011年12月5日更新
关于FF1992这篇文章的笔记可以参看附件

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