The debate about whether the size and value premiums have existed on paper was settled many years ago. The long-term historical data clearly shows robust size and value premiums. The average annual U.S. size and value premiums have been 3.6 and 4.8 percent, respectively, from 1927-2012. What has been more hotly debated, however, is whether these premiums could actually be captured in the real world net of transactions costs and fund expense ratios. In my opinion, even this debate is a bit silly at this point. If you examine the returns of intelligently built, low-cost mutual funds that have been designed specifically to capture these premiums, it’s clear they’ve been successful.

To examine this question, I’m going to compare the returns of DFA Small Value, which started in April 1993, with the returns of the Russell 3000 Index and see whether the difference in returns between these two series can be attributed to the size and value premiums. The Russell 3000 is a great benchmark for this exercise because it has virtually no tilt toward small cap or value. My data covers April 1993–June 2013, and the size and value premiums were about 2.6 and 3.1 percent per year over this period. Because the premiums were both positive over this period, we should see that DFA Small Value substantially outperformed the Russell 3000. That, in fact, is exactly what the table below shows.

The results show that DFA Small Value had a compound annual return that was 3.6 percent per year higher than the Russell 3000 and that the growth of $1 was almost twice the size of the Russell 3000. These results clearly show that these two premiums can be captured in practice net of fund expense ratio and transaction costs.

**Answering the Skeptics**

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A skeptic, though, might still argue whether the difference in returns can be directly attributed to the size and value premiums. It turns out it can be, and you can examine this by regressing the difference in returns of DFA Small Value and the Russell 3000 on the returns of the premiums themselves.

If these two premiums explain the return results, the R-squared ratio (which can be as low as 0 percent and as high as 100 percent) should be on the high side of this range. If you run this analysis, you get an R-squared ratio of 90 percent. This indicates that the large positive return gap is almost certainly because DFA Small Value effectively captured the size and value premiums.

**Random Links and Commentary of the Week**

The NFL season is here and what better way to kick it off than with three B.S. Report podcasts:

## Comments

## Re: Can the Size and Value Premiums Be Captured?

## Volatility

## Re: Can the Size and Value Premiums Be Captured?

Were the market factor or a constant included?

## Study details

Dependent Variable: DFSVX returns – Russell 3000 returns

Independent variables: SMB & HML

Period: 4/1993 – 6/2013

Constant: -0.01 (in percent)

SMB Coefficient: 0.89

t-stat: 43.6

HML Coefficient: 0.59

t-stat: 27.8

Adjusted R2: 90%

SMB and HML above are the Fama and French research factors from French’s site. Note my adjusted R2 of 90% instead of 93% (must’ve taken down the wrong number when I was writing the piece...corrected now in the body of the blog)…still a very high value.

This basically shows that the variance in the return difference above is strongly linked (i.e., attributable to) to the size and value premiums.

JK

## Re: Can the Size and Value Premiums Be Captured?

I agree that the results suggest that the deviations of the fund from the Russell 3000 were strongly associated with small and value factors.

I was wondering why you did not use the market factor and risk free rate from the French data? The Russell 3000 excludes much of the small universe, and has an unpredictable amount of value. Doing the regression without a constant can inflate the apparent strength of association.

Interesting work. If one wanted to know the extent to which the fund captured the size and value premiums one would have to predict what the returns to the premiums would be and compare that to the returns of the fund. This might work if one wanted to independently assess capture of the value premium for a value fund or the size premium for a small fund. When you want to capture two premiums it would seem to depend in part on the correlations between the returns of stocks that meet the value criteria and stocks that meet the size criteria.

Thanks again

## Constant, RFR and Market Factor

I didn't include the RFR because you aren't supposed to when your LH variable is one total returns series minus another total returns series and your RH variables are long-short portfolios.

I didn't use the market factor b/c it's basically irrelevant when your LH variable is one portfolio w/ a market beta close to 1 minus another portfolio w/ a market beta close to 1...meaning your LH variable is basically completely neutral w/ respect to equity market exposure. If you include a market factor, consequently, the results basically don't change.

JK