In a previous post, I plotted the returns of 25 portfolios which were formed by sorting stocks on both size and value characteristics. The data, from the Kenneth French website, showed a clear pattern of increasing returns as size decreased and value (measured by book-to-market ratio) increased. In other words, the small-value portfolio had outperformed the broader market over most periods of 20 years or more, and the margin of outperformance was often quite large.
Fama and French, who built the size and value effects into an asset pricing model, believe that the higher returns of small stocks and value stocks are related to the higher risks associated with holding these stocks. This may be true, and there is some persuasive evidence supporting the Fama-French viewpoint. However, another issue with capturing the small-value premium is cost. The returns of the Fama-French 25 portfolios do not include trading costs, fees, or taxes, and these costs are likely to be higher for investors who are trying to implement a small-value tilt in their personal portfolio.
In this post, I will evaluate several ETFs which track popular indexes and calculate how well these funds capture the theoretical returns predicted by the Fama-French model. In addition, I will place the factor loadings of these funds in the context of the Fama-French 25 portfolios. For example, does a fund which is described as a “small-value” fund really behave similarly to the most extreme small-value portfolio from the Fama-French 25 portfolios? If not, which of the portfolios does it approximate most closely?
The Fama-French regression equation is shown here:
I’ve created an R script which downloads 10-years of stock price data from Yahoo! Finance and calculates the monthly return data from the adjusted closing price at the end of each month. The risk free rate is then subtracted from each monthly return, and the Fama-French factors are regressed on this monthly return series.
The Fama-French factor loadings of the ETFs are shown below. The regressions were run using monthly returns from November 2000 thru October 2010. Statistically significant alphas are marked with a “*”.
|Fund Ticker||Description||Monthly Alpha||FF-Beta||FF-s (size)||FF-h (value)||R-squared|
|IVE||Large Cap Value||-0.206%*||0.99||-0.05||0.27||0.960|
|QQQQ||Large Cap Growth||0.053%||1.33||0.29||-0.92||0.920|
|IWN||Small Cap Value||-0.158%||0.88||0.76||0.61||0.959|
|IJS||Small Cap Value||-0.171%||0.91||0.85||0.48||0.951|
For comparison, the table below shows the factor loadings, over the same 10-year period, for four of the Fama-French 25 portfolios: Large-Growth, Large-Value, Small-Growth, and Small-Value.
|Portfolio Description||Monthly Alpha||FF-Beta||FF-s (size)||FF-h (value)||R-squared|
Notice that small-cap and value ETFs do not have as high of a loading on the small and value factors as the most extreme of the 25 Fama-French portfolios. Also, the small-cap (IWM and IJR) and small-value (IWN and IJS) funds seem to have larger negative alphas than the large cap funds. Of the small cap funds, only the alpha for IWM is statistically significant, but the other small cap alphas are negative enough to be economically meaningful if they continue to persist into the future. Finally, it is somewhat surprising that IVE, which is a S&P500 value fund, only has a slightly higher value loading than the regular S&P500 index.
In the plots below, I’ve tried to place each ETF ticker over the return of the portfolio in the Fama-French 25 portfolios with the most similar factor loadings. The marker placement should only be interpreted as a rough approximation of the closest match since the factor weights don’t match up precisely.
The first plot shows the Fama-French 25 portfolio returns over the same date range used for the ETF regressions. The second plot shows the Fama-French 25 portfolio returns over the full date range, but the ETF marker placement is still based on the 10-year regressions.
My conclusion from this analysis is that it is difficult in practice to capture the full small-value premium. The small-value ETFs available to the average investor are not a good approximation of the most extreme small-value fund in the Fama-French portfolios. Also, it appears that there is a somewhat larger implementation shortfall for the small-cap ETFs than there is for the large-cap ETFs. This observation isn’t statisitically significant in this sample, but it seems reasonable that the small cap funds would face some higher costs due to the lower liquidity of these stocks and the higher portfolio turnover for these funds.
Disclosure: At the time of publication, the author owned shares of SPY and IJS.