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{"id":620,"date":"2011-01-16T18:07:22","date_gmt":"2011-01-17T00:07:22","guid":{"rendered":"http:\/\/www.calculatinginvestor.com\/?p=620"},"modified":"2011-01-19T09:45:55","modified_gmt":"2011-01-19T15:45:55","slug":"fama-french-etfs","status":"publish","type":"post","link":"http:\/\/www.calculatinginvestor.com\/2011\/01\/16\/fama-french-etfs\/","title":{"rendered":"Fama-French Factor Loadings for Popular ETFs"},"content":{"rendered":"

<\/a>How well can the small-value premium be captured using ETFs?<\/strong><\/p>\n

In a previous post<\/a>, I plotted the returns of 25 portfolios which were formed by sorting stocks on both size and value characteristics.\u00a0 The data, from the Kenneth French website<\/a>, showed a clear pattern of increasing returns as size decreased and value (measured by book-to-market ratio) increased.\u00a0 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.\u00a0<\/p>\n

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.\u00a0 This may be true, and there is some persuasive evidence supporting the Fama-French viewpoint.\u00a0 However, another issue with capturing the small-value premium is cost.\u00a0 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.\u00a0 \u00a0<\/p>\n

In this post, I\u00a0will evaluate several ETFs which track popular indexes and calculate how well these funds capture the theoretical returns predicted by the Fama-French model.\u00a0 In addition, I will place the factor loadings of these funds in the context of the Fama-French 25 portfolios.\u00a0 For example, does a fund which is described\u00a0as a \u201csmall-value\u201d fund really behave similarly to the most extreme small-value portfolio\u00a0from the Fama-French 25 portfolios?\u00a0 If not, which of the portfolios does it approximate most closely?\u00a0<\/p>\n

The Fama-French regression equation is shown here:<\/p>\n

\"<\/p>\n

I\u2019ve created an R script <\/a>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.\u00a0 The risk free rate is then subtracted from\u00a0each monthly return, and the\u00a0Fama-French factors are regressed on this monthly return series.\u00a0<\/p>\n

The Fama-French\u00a0factor loadings of the ETFs are shown below.\u00a0\u00a0The regressions were run\u00a0using monthly returns from November 2000 thru October 2010.\u00a0 Statistically significant alphas are marked with a\u00a0“*”.<\/p>\n\n\n\n\t\n\t\t\n\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t\n\t\t
Fund Ticker<\/th>Description<\/th>Monthly Alpha<\/th>FF-Beta<\/th>FF-s (size)<\/th>FF-h (value)<\/th>R-squared<\/th>\n\t<\/tr>\n<\/thead>\n
SPY<\/td>Large Cap<\/td>-0.087%<\/td>0.96<\/td>-0.13<\/td>0.012<\/td>0.986<\/td>\n\t<\/tr>\n\t
DIA<\/td>Large Cap<\/td>0.098%<\/td>0.89<\/td>-0.22<\/td>0.11<\/td>0.907<\/td>\n\t<\/tr>\n\t
IVE<\/td>Large Cap Value<\/td>-0.206%*<\/td>0.99<\/td>-0.05<\/td>0.27<\/td>0.960<\/td>\n\t<\/tr>\n\t
QQQQ<\/td>Large Cap Growth<\/td>0.053%<\/td>1.33<\/td>0.29<\/td>-0.92<\/td>0.920<\/td>\n\t<\/tr>\n\t
IWM<\/td>Small Cap<\/td>-0.199%*<\/td>0.98<\/td>0.82<\/td>0.19<\/td>0.980<\/td>\n\t<\/tr>\n\t
IWN<\/td>Small Cap Value<\/td>-0.158%<\/td>0.88<\/td>0.76<\/td>0.61<\/td>0.959<\/td>\n\t<\/tr>\n\t
IJR<\/td>Small Cap<\/td>-0.138%<\/td>0.91<\/td>0.80<\/td>0.30<\/td>0.958<\/td>\n\t<\/tr>\n\t
IJS<\/td>Small Cap Value<\/td>-0.171%<\/td>0.91<\/td>0.85<\/td>0.48<\/td>0.951<\/td>\n\t<\/tr>\n\t
IYR<\/td>U.S. REITs<\/td>0.078%<\/td>0.93<\/td>0.41<\/td>0.89<\/td>0.663<\/td>\n\t<\/tr>\n\t
MDY<\/td>Mid-Cap<\/td>0.092%<\/td>0.97<\/td>0.37<\/td>0.16<\/td>0.950<\/td>\n\t<\/tr>\n<\/tbody>\n<\/table>\n\n

For comparison,\u00a0the table below shows the factor loadings, over the same 10-year period,\u00a0for four of the Fama-French 25 portfolios:\u00a0Large-Growth, Large-Value, Small-Growth, and Small-Value.<\/p>\n\n\n\n\t\n\t\t\n\t\n\t\t\n\t\t\n\t\t\n\t\t
Portfolio Description<\/th>Monthly Alpha<\/th>FF-Beta<\/th>FF-s (size)<\/th>FF-h (value)<\/th>R-squared<\/th>\n\t<\/tr>\n<\/thead>\n
Large-Growth (LG)<\/td>0.036%<\/td>0.95<\/td>-0.19<\/td>-0.28<\/td>0.96<\/td>\n\t<\/tr>\n\t
Large-Value (LV)<\/td>-0.182%<\/td>1.07<\/td>-0.23<\/td>0.60<\/td>0.78<\/td>\n\t<\/tr>\n\t
Small-Growth (SG)<\/td>-0.681%<\/td>1.18<\/td>1.18<\/td>-0.38<\/td>0.87<\/td>\n\t<\/tr>\n\t
Small-Value (SV)<\/td>0.159%<\/td>0.98<\/td>1.06<\/td>0.72<\/td>0.94<\/td>\n\t<\/tr>\n<\/tbody>\n<\/table>\n\n

Notice that\u00a0small-cap and value ETFs\u00a0do not have as high of a loading on the small and value factors as the most extreme of the 25 Fama-French portfolios.\u00a0 Also, the small-cap (IWM and IJR)\u00a0and small-value (IWN and IJS)\u00a0\u00a0funds seem to have\u00a0larger negative alphas than the large cap funds.\u00a0 Of the small cap funds, only\u00a0the alpha for IWM\u00a0is statistically significant, but\u00a0the other small cap alphas\u00a0are\u00a0negative enough to be economically\u00a0meaningful if they\u00a0continue to persist into the future.\u00a0\u00a0Finally, it\u00a0is somewhat surprising that IVE, which is a\u00a0S&P500\u00a0value fund, only has a\u00a0slightly higher value loading than the regular S&P500 index.\u00a0 \u00a0<\/p>\n

In the plots below, I’ve tried to place each\u00a0ETF ticker\u00a0over the return of\u00a0the\u00a0portfolio in the Fama-French 25 portfolios with the most similar factor loadings.\u00a0 The marker\u00a0placement\u00a0should only be interpreted as a rough approximation of the closest match since the\u00a0factor weights\u00a0don’t match up precisely.\u00a0\u00a0\u00a0<\/p>\n

The first plot shows the Fama-French 25 portfolio returns over the same date range used for the ETF regressions.\u00a0 The second plot shows the Fama-French 25 portfolio returns over the full date\u00a0range, but the ETF marker placement is still based on the 10-year regressions.<\/p>\n

\"\"<\/a><\/p>\n

\"\"<\/a><\/p>\n

<\/a><\/a><\/p>\n

<\/a><\/p>\n

Conclusions<\/strong><\/p>\n

My conclusion from this analysis\u00a0is that it is difficult in practice to capture the full small-value premium.\u00a0 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.\u00a0 Also,\u00a0it appears\u00a0that there is\u00a0a somewhat larger implementation shortfall\u00a0for the small-cap ETFs than there is for the large-cap ETFs.\u00a0 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\u00a0these funds.<\/p>\n

Disclosure:\u00a0 At the time of\u00a0 publication, the author owned shares of SPY and IJS.<\/em><\/p>\n","protected":false},"excerpt":{"rendered":"

How well can the small-value premium be captured using ETFs? In a previous post, I plotted the returns of 25 portfolios which were formed by sorting stocks on both size and value characteristics.\u00a0 The data, from the Kenneth French website, showed a clear pattern of increasing returns as size decreased and value (measured by book-to-market […]<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[1],"tags":[],"_links":{"self":[{"href":"http:\/\/www.calculatinginvestor.com\/wp-json\/wp\/v2\/posts\/620"}],"collection":[{"href":"http:\/\/www.calculatinginvestor.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.calculatinginvestor.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.calculatinginvestor.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/www.calculatinginvestor.com\/wp-json\/wp\/v2\/comments?post=620"}],"version-history":[{"count":211,"href":"http:\/\/www.calculatinginvestor.com\/wp-json\/wp\/v2\/posts\/620\/revisions"}],"predecessor-version":[{"id":1076,"href":"http:\/\/www.calculatinginvestor.com\/wp-json\/wp\/v2\/posts\/620\/revisions\/1076"}],"wp:attachment":[{"href":"http:\/\/www.calculatinginvestor.com\/wp-json\/wp\/v2\/media?parent=620"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.calculatinginvestor.com\/wp-json\/wp\/v2\/categories?post=620"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.calculatinginvestor.com\/wp-json\/wp\/v2\/tags?post=620"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}