Research Doesn’t Tell Us
June 14, 2011
This exercise is also called “running a regression.” The line is called the regression line – it represents an inferred underlying linear dependency of the vertical-axis variable upon the horizontal-axis variable.
You could visualize these points in three dimensions instead, with a plane drawn through them using the same method. Then the plane would express a dependence of one of the variables on the other two. The same thing can be done in higher dimensions with more variables, but you can’t visualize it.
The method gets dicier if the underlying dependency isn’t linear. For example a graph of the growth of an asset at compound interest over time looks like this:
Obviously, the line on the right isn’t a good fit to the points on the left. Since this is well known, time-series regressions for asset growth generally modify the asset values by taking their logarithms. But if you get the underlying relationship wrong – if there even is one – you can get wacky results.
Fortunately, statistics derived from the sum of the squared distances tell you whether your fit is good or not. They do not, however, tell you why.
The 1992-1993 Fama-French studies
The CAPM says that a portion of a stock’s return is a linear function of the return on the whole market – specifically, the stock’s beta times the market return. Hence, part of the stock’s variability is due to its correlation with the market. The “systematic” risk of this market-related portion is compensated with an expected return.
The remainder of the stock’s return variability is “idiosyncratic.” The risk of this residual non-market-correlated variability is not rewarded, because in theory it can be eliminated through diversification.
However, the classic Fama-French study found evidence of return variability in value stocks and small stocks that was not correlated with the market, but was nevertheless richly rewarded over a long period. They posited that stock returns should depend on these two new fundamental factors as well as beta.
When they added “smallness” and “value-ness” to “marketness” as stock characteristics, they got a better regression line fit. This introduced the idea that you should regress a portfolio’s returns against three variables: the whole market, the small stock market portfolio, and the value stock portfolio, to see how much of its performance is “explained” by its statistical dependency on each of these factors.
It should be noted that Fama and French ended both papers with similar caveats, saying in the 1992 paper that their results “are not economically satisfying” and asking, “What is the economic explanation for the roles of size and book-to-market equity in average returns?”
Would you like to send this article to a friend?Remember, if you have a question or comment, send it to .