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Fama-French Factor Loadings for Popular ETFs » The Calculating Investor

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.  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:

 r_{i}-r_{f}=\alpha _{i}+b_{i}\left ( R_{M}-r_{f}^{} \right )+s_{i}SMB+h_{i}HML+\epsilon _{i}

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 TickerDescriptionMonthly AlphaFF-BetaFF-s (size)FF-h (value)R-squared
SPYLarge Cap-0.087%0.96-0.130.0120.986
DIALarge Cap0.098%0.89-
IVELarge Cap Value-0.206%*0.99-
QQQQLarge Cap Growth0.053%1.330.29-0.920.920
IWMSmall Cap-0.199%*0.980.820.190.980
IWNSmall Cap Value-0.158%0.880.760.610.959
IJRSmall Cap-0.138%0.910.800.300.958
IJSSmall Cap Value-0.171%0.910.850.480.951
IYRU.S. REITs0.078%0.930.410.890.663

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 DescriptionMonthly AlphaFF-BetaFF-s (size)FF-h (value)R-squared
Large-Growth (LG)0.036%0.95-0.19-0.280.96
Large-Value (LV)-0.182%1.07-0.230.600.78
Small-Growth (SG)-0.681%1.181.18-0.380.87
Small-Value (SV)0.159%0.981.060.720.94

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.

17 Responses to “Fama-French Factor Loadings for Popular ETFs”

  1. The Fama-French factors are not independent of each other. I believe you will find they have significant correlation with each other. That being the case, It will be difficult to find an ETF that is correlated to only *one* of them…

    • Thanks for stopping by my blog. I agree that it is not possible to find an ETF which only has loading on just one factor in isolation.

      What I’m trying to show in this post is that most “value” or “small-value” ETFs have a modest loading on the SMB and HML factors, so they capture only a portion of the small cap and value premiums. In other words, “small-value” ETFs don’t capture as large of a premium as the Fama-French “SV” portfolio, and “value” ETFs don’t capture as large of a value premium as the Fama-French “LV” portfolio.

      • I see your point. I am not sure how an ETF could replicate e.g. SMB if it only had the ‘S’ part! One would have to short the ‘B’ part as well. Perhaps you could regress the SMB monthly returns against monthly returns of a small cap ETF and a large cap ETF and see if you get regression coefficients like +1 and -1, and an acceptable R^2 coefficient.

        • Yes, to really replicate SMB or HML would require a long-short portfolio…not a long-only ETF.

          After re-reading my post, I think I was not 100% clear in what I’m trying to show. I wrote that the ETFs fail to capture the “full-premium”, which you correctly point out would require a long-short portfolio….but what I am trying to show is that most small-value and value ETFs have lower HML and SMB factor loadings than some of the commonly cited benchmark portfolios constructed by Fama-French which are long-only.

          The FF factor portfolios used in the regression model (HML, SMB) are long-short, but the Fama-French 25 portfolios (the average returns of which I’ve plotted as the 5×5 3d plot) are long-only portfolios formed by sorting stocks on size and value characteristics. So, I’m trying to compare the FF factor loadings of the real ETFs against the factor loadings of the Fama-French 25 portfolios, and I see that the ETFs have significantly lower HML and SMB factor loadings that the most extreme portfolios in the Fama-French 25 (apples to apples comparison, since the FF25 and the ETFs are both long-only).

          My motivation for this analysis is that I often see posts on investment forums touting the high returns of the most extreme Fama-French portfolios within the Fama-French 25 (such as the portfolios I’ve labled as SV and LV in the plots). However, these extreme portfolios contain a lot of thinly traded and illiquid stocks with high bid-ask spreads, and I think it is difficult to replicate the returns of these portfolios in an ETF. So, I’m attempting to show in this post that real, investable small-value ETFs do get you a small-value premium…but it is meaningfully less than the theoretical returns of the most extreme long-only benchmark portfolios.

        • Why would you want to short the B to get the SMB? It’s there, regardless of whether or not you short the B. Similarly, the ERP is there even if you don’t short T-Bills.

  2. Is the return for the area where IWM and IJR is located higher than for the section classified as large value on the second chart? It looks like that is so, but I am not totally certain.

    • Yes, it is a little higher. That area is 1.092% per month, and the FF portfolios shown as LV averaged 1.012% per month.

      Here is the data that is shown in that plot. The top row shows the averages from the SG portfolio to the SV portfolio, and bottom row is the LG thru LV row of the plot.

      SG thru SV
      0.33221 0.81468 1.15359 1.33243 1.47968
      0.72099 1.09213 1.23825 1.27523 1.32885
      0.82865 1.07341 1.14953 1.21787 1.27593
      0.86264 0.93549 1.09020 1.14952 1.14648
      0.79833 0.81480 0.93165 0.91065 1.01211
      LG thru LV

  3. Another question, where would a fund tracking the MSCI U.S. Small Cap Value Index be placed on the size section of the graphs? The average weighted market cap for that index is 1.7 billion. The size is larger than IWN, IWM, IJS, and IJR but smaller than MDY.

    I wonder if it would be in the middle, but leaning more towards the second smallest section.

    • Here is a comparison of IJS, MDY, and VBR over a recent 5-year period.

      VBR is only slightly more tilted towards small stocks than MDY, but it has quite a bit more value tilt than MDY.


      Estimate Std. Error t value Pr(>|t|)
      (Intercept) -0.002252 0.001588 -1.418 0.162
      rmrf 0.892569 0.032434 27.520 < 2e-16 *** smb 0.903898 0.072353 12.493 < 2e-16 *** hml 0.393902 0.059197 6.654 2.09e-08 *** --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 Residual standard error: 0.01151 on 50 degrees of freedom (6 observations deleted due to missingness) Multiple R-squared: 0.9744, Adjusted R-squared: 0.9729 F-statistic: 635.4 on 3 and 50 DF, p-value: < 2.2e-16


      Estimate Std. Error t value Pr(>|t|)
      (Intercept) 0.0001175 0.0016186 0.073 0.942
      rmrf 1.0094366 0.0330607 30.533 < 2e-16 ***
      smb 0.4871640 0.0737520 6.605 2.49e-08 ***
      hml -0.0622261 0.0603411 -1.031 0.307
      Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

      Residual standard error: 0.01174 on 50 degrees of freedom
      (6 observations deleted due to missingness)
      Multiple R-squared: 0.9672, Adjusted R-squared: 0.9653
      F-statistic: 491.9 on 3 and 50 DF, p-value: < 2.2e-16

      Estimate Std. Error t value Pr(>|t|)
      (Intercept) -0.000903 0.001672 -0.540 0.592
      rmrf 0.961907 0.034158 28.160 < 2e-16 ***
      smb 0.584734 0.076200 7.674 5.33e-10 ***
      hml 0.489201 0.062344 7.847 2.87e-10 ***
      Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

      Residual standard error: 0.01213 on 50 degrees of freedom
      (6 observations deleted due to missingness)
      Multiple R-squared: 0.9724, Adjusted R-squared: 0.9707
      F-statistic: 587.3 on 3 and 50 DF, p-value: < 2.2e-16

  4. VBR is one fund that tracks that index.

  5. Please contact me when you can. I am a professor of Finance at Seattle University. Good work. Not sure Yahoo gives reliable dividend information, may be it does, or not. CRSP is a good audited source. I can tell you more. 206 236 6309

  6. deat Vinay Datar please share your point with all of us

  7. i want to check the tilt toward value or growth factor in almost 30 mutual funds. please guide me how should i proceed it. should i perform separate analysis for each fund, and then compare its alphas and coefficients of SML and HML. or is there any method which can be used to find out the tilting effect here…

  8. Can you actually short Small Cap ETF and Long Large CAP ETFs to create a long-short portfolio that is similar to SMB for example?

  9. There is very little difference in performance of IJS, IWN and VBR. However, the first two have ridiculous expense ratios of 0.25%, while VBR – only 0.09%.

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