Most investors believe all passively managed funds within the same asset class should have the same, or at least very similar, returns. However, while all index funds and passive structured asset class funds are similar in the way that rectangles and squares are similar, they are also very different. All squares are rectangles, but not all rectangles are squares.
Similarly, while all index funds are passively managed, not all passively managed structured asset class funds attempt to replicate the returns of popular retail indexes like the S&P 500 or the Russell 2000.
Instead, they tend to use academic definitions of asset classes and structure portfolios to minimize the inherent weaknesses of pure indexing. Those weaknesses, which result from the desire to minimize what is called “tracking error” (returns that deviate from the return of the benchmark index), include:
The Price Of Tracking Error
Another advantage that structured funds can bring, in return for an investor accepting tracking error risk, is that they can gain greater exposure to certain factors for which there is persistent and pervasive evidence of a return premium (such as market beta, size, value, momentum and profitability/quality).
For example, a small value fund could be structured to own smaller and more “valuey” stocks than a small-cap value index fund might include. It can also be structured to have more exposure to highly profitable companies. And it can screen for the momentum effect (avoiding the purchase of stocks that are exhibiting negative momentum and that delay the sale of stocks with positive momentum).
While all these attributes are benefits, they come with a “price” in the form of the aforementioned tracking error. Investors seeking the advantages of structured funds must accept the fact that it’s a virtual certainty there will be periods (even very long ones) during which they underperform an index fund in the same asset class.
Investors enjoy it when the tracking error is positive—their passively managed structured fund outperforms an index fund in the same asset class—but when the tracking error is negative, they unfortunately exhibit a tendency to make the dual mistakes of confusing strategy with outcome and losing discipline (they become impatient).
Confusing Strategy With Outcome
“Fooled by Randomness” author Nassim Nicholas Taleb had the following to say on confusing strategy and outcome: “One cannot judge a performance in any given field by the results, but by the costs of the alternative (that is, if history played out in a different way). Such substitute courses of events are called alternative histories. Clearly the quality of a decision cannot be solely judged based on its outcome, but such a point seems to be voiced only by people who fail (those who succeed attribute their success to the quality of their decision).”
In investing, there are no clear crystal balls. Thus, a strategy should be judged in terms of its quality and prudence before—not after—its outcome is known.
Compounding the problem of confusing strategy with outcome is impatience. I have learned that when contemplating investment returns, the typical individual investor considers three to five years a long time, and 10 years an eternity. When it comes to the returns of risky asset classes, however, periods as short as three or five years should be seen as nothing more than noise. Even 10 years is a relatively brief period.
To demonstrate the potential problem posed by tracking error regret, I will compare the performance of several of Vanguard’s index funds with structured, passively managed funds in the same asset class from Dimensional Fund Advisors (DFA). (In the interest of full disclosure, my firm, Buckingham, recommends DFA funds in constructing client portfolios.) However, before doing so, a brief history of capital asset pricing models will prove helpful.
Building on the work of Harry Markowitz, the trio of John Lintner, William Sharpe and Jack Treynor are generally given most of the credit for introducing the first formal asset pricing model, the capital asset pricing model (CAPM). It was developed in the early 1960s. The CAPM provided the first precise definition of risk and how it drives expected returns.
CAPM: A One-Factor Model
The CAPM looks at risk and return through a “one-factor” lens—the risk and return of a portfolio are determined only by its exposure to market beta. This beta is the measure of the equity-type risk of a stock, mutual fund or portfolio relative to the risk of the overall market.
The CAPM became the financial world’s operating model for about 30 years. But like all models, it was, by definition, flawed, or wrong. If such models were perfectly correct, they would be laws, like we have in physics. Over time, anomalies that violated the CAPM began to surface.
In 1981, Rolf Banz’s “The Relationship Between Return and Market Value of Common Stocks” found that market beta doesn’t fully explain the higher average return of small stocks. That same year, Sanjoy Basu’s “The Relationship Between Earnings’ Yield, Market Value and Return for NYSE Common Stocks” found that the positive relationship between the earnings yield (E/P) and average return is left unexplained by market beta.
And in 1985, Barr Rosenberg, Kenneth Reid and Ronald Lanstein found a positive relationship between average stock returns and book-to-market (B/M) ratio in their paper, “Persuasive Evidence of Market Inefficiency.” The last two studies provided evidence that, in addition to a size premium, there also is a value premium.
Fama-French Three-Factor Model
The 1992 paper “The Cross-Section of Expected Stock Returns,” by Eugene Fama and Kenneth French, summarized and explained these anomalies in one place. The essential conclusion from the paper was that the CAPM explained only roughly two-thirds of the differences in returns of diversified portfolios, and that a better model could be built using more than just the one factor. Fama and French proposed that, along with the market factor of beta, exposure to the factors of size and value explain the cross section of expected stock returns.
The new Fama-French model greatly improved on the explanatory power of the CAPM, accounting for more than 90% of the differences in returns between diversified portfolios. And the Fama-French three-factor model replaced the CAPM as the workhorse model in finance.
Since then, financial economists have uncovered a number of other factors (including momentum, profitability and investment) that have been shown to provide premiums that have been persistent (across time) and pervasive (across industries, countries and regions) while also improving the explanatory power of asset pricing models.
However, given that the Fama-French three-factor model does explain more than 90% of the differences in returns of diversified portfolios, to keep our analysis simple, we’ll use it to explain the differences in returns of the similar Vanguard and DFA funds.
The table below shows the 5-, 10- and 15-year annualized returns, as well as the recent weighted average market capitalizations (the size metric) and weighted average price-to-book (P/B) ratio (the value metric) for domestic Vanguard and DFA funds covering the broad market (large-cap, midcap and small-cap stocks in addition to value, core and growth stocks) plus the large value, small and small value asset classes. It also shows the factor premiums. We’ll then show how the factor models and factor returns explain the differences in performance.
As you review the data, keep in mind that while the factor models have good explanatory power, they are not perfect representations of the world. Since we are using a three-factor model, differences in returns may also be explained by exposure to other factors (such as momentum or profitability). In addition, differences in returns may be explained by a fund’s exposure to other asset classes. This is especially true in the case of the small value funds.
While the Vanguard small value fund includes exposure (currently about 11%) to REITs because REITs are included in the benchmark index, the DFA fund specifically excludes REITs, treating them as a separate asset class (if you want to own REITs, then you should own a REIT index fund). REITs have lower historical returns than small value stocks. The critical point to keep in mind is that if REITs outperform (underperform), the Vanguard small value fund will benefit (be negatively impacted).
US Broad Market
Vanguard’s Total Stock Market Index Fund (VTSMX) replicates the performance of the Center for Research in Security Prices (CRSP) U.S. Total Market Index. To do that, it basically owns all the equities in the index weighted by market capitalization. DFA’s Core Equity 2 fund (DFQTX) basically owns all the stocks in the index as well.
However, because the DFA fund is designed to provide exposure to the size and value factors, using a proprietary formula, it overweights (or has more exposure to) small and value stocks.
Note the “2” in its name reflects the fact that the fund is designed to have approximately 0.2 (20%) exposure to each of the factors. By using the regression factor tool from Portfolio Visualizer, we can see the differences in what is referred to as factor loading (how much exposure a fund has to a certain factor).
Because it is a total market fund, by definition, we should expect to see that VTSMX has no exposure to the size and value factors. That’s precisely what we find. The loadings were both 0.0. And the R-squared figure (a measure of how well the model explains the performance of the fund) was 99.9%. Given its design, we should expect DFQTX to have exposure to the two factors.
We can observe this by looking at the above table. DFQTX’s weighted average market capitalization is much smaller (only about 40% of the weighted average capitalization of VTSMX) and it is more “valuey” (its P/B ratio is about 15% lower).
In addition, the regression analysis shows that loading on both the size and value factors was about 0.2 (the R-squared was 99.5%). This means that when small and value stocks outperform (the premiums are positive), we should expect to see DFQTX outperform, and vice versa. And that’s exactly what we find.
Broad Market Results
During the most recent five-year period, in which the size premium was -2.5% and the value premium was -2.8%, VTSMX managed to outperform DFQTX by 1.1 percentage points, mainly because the DFA fund has more exposure to the underperforming small and value stocks (the fund also has a higher expense ratio, 0.22% versus 0.16%). In the 10-year period, the size premium was 0.0% and the value premium was -1.4%.
We should once again expect VTSMX to have outperformed, although by a smaller margin. And that’s what we find, as it outperformed by 0.5%. Unfortunately, DFQTX is only about 10 years old, so we don’t have returns data for the full 15-year period. However, given that the size premium was 3.1% and the value premium was 1.6% over that period, we should expect DFQTX to have outperformed.
Investors shouldn’t view DFQTX’s underperformance relative to VTSMX as “bad” nor any outperformance as “good.” Both funds did what they were designed to do. A problem arises when investors make the aforementioned mistake of confusing strategy with outcome, becoming impatient because they fail to understand that even 10 years is noise when it comes to returns of risky investments.
No more proof is required than the -1% per year return to the S&P 500 Index during the first decade of this century. Investors in stocks shouldn’t have lost faith in their belief that stocks should outperform safe Treasury bills due to the experience of that period. If they did, they missed out on one of the greatest bull markets in history.
US Large Value
Vanguard’s Value Index Fund (VIVAX) is designed to track the performance of the CRSP U.S. Large Cap Value Index. DFA’s large value fund (DFLVX) is designed to provide more exposure to the value factor, thus it has different construction rules. As you can see in the table, DFLVX’s market capitalization is about one-third smaller than that of VIVAX, and its P/B ratio is about 20% lower.
We see this in the regression as well. VIVAX has loadings on the size of -0.2 (it holds larger stocks) and 0.3 on value. The R-squared figure was 97% (demonstrating that the model explains the returns well). DFLVX’s loadings are 0.1 and 0.5, respectively (it has more exposure to both premiums). The R-squared was also 97%.
Turning to the performance analysis, we find that DFLVX underperformed by 0.4 percentage points in the most recent five-year period when both premiums were negative. It did, however, manage to outperform slightly (by 0.1 percentage point) during the most recent 10-year period when the size premium was zero and the value premium was slightly negative. But over the longer 15-year period, when both premiums were positive, DFLVX outperformed by 1.8 percentage points, just as you should have expected.
US Small Cap
Vanguard’s Small Cap Index Fund (NAESX) is designed to track the performance of the CRSP U.S. Small Cap Index. Both the DFA small-cap fund (DFSTX) and its microcap fund (DFSCX) are designed to provide greater exposure to the size factor, thus they have different construction rules.
As you can see in the table, DFSTX’s market capitalization is not much more than half that of NAESX, and DFSCX’s market capitalization is more than 70% smaller. Their P/B ratios are similar, although smaller in both cases (DFSTX by 3% and DFSCX by 7%).
We see this in the regressions as well. NAESX has a loading on the size of 0.7 and 0.2 on value. The R-squared in this case was 99%. DFSTX and DFSCX have loadings on the size of 0.8 and 0.9, respectively. The loadings on value are 0.2 and 0.3, respectively. The R-squared figures were 97% and 99%, respectively.
Turning to the performance analysis, over the most recent five-year period, both DFSTX and DFSCX were able to outperform NAESX (by 0.7 percentage points and by 0.8 percentage points, respectively) despite having somewhat higher exposures to the size factor, which was negative during the period.
This outperformance could be explained by the DFA funds’ greater exposure to the profitability factor (which, as I mentioned earlier, might result from a construction methodology that excludes certain stocks). The profitability premium was more than 3% in the five-year period, more than 3.5% in the 10-year period and 4% in the 15-year period. It might also be explained by patient trading, securities-lending activities and other factors discussed previously.
Over the most recent 10-year period, when the size premium was 0, DFSTX produced the same return as NAESX, and DFSCX underperformed by 0.9 percentage points. During the most recent 15-year period, when the size premium was 3.1%, as we should expect, we find that DFSTX outperformed NAESX by 0.6 percentage points and DFSCX, with its greater exposure to both the size factor and the value factor (which was 1.6%), outperformed by 1.2 percentage points.
US Small Value
Vanguard’s Small Cap Value Index Fund (VISVX) is designed to track the performance of the CRSP U.S. Small Cap Value Index. Both the DFA small-cap value fund (DFSVX) and the firm’s U.S. targeted value fund (DFFVX) are designed to provide greater exposure to the size and value factors. Again, they thus have different construction rules.
As you can see in the table, DFSVX’s market capitalization comes in at under half that of VISVX, and DFFVX’s market capitalization is about 20% smaller. In addition, the P/B ratios of the funds are lower, by 28% and 20%, respectively.
We see this in the regressions as well. VISVX has a loading on the size of 0.7 and 0.4 on value. The R-squared was 97%. DFSVX and DFFVX have loadings on the size of 0.9 and 0.8, respectively. The loadings on value are 0.6 and 0.5, respectively. The R-squared figures were 98% and 97%, respectively.
Turning to the performance analysis, over the most recent five-year period, when the size and value premiums were both negative, as you should expect, DFSVX underperformed VISVX by 1.9 percentage points. And DFFVX, with a lesser loading on size and value than DFSVX but a higher loading than VISVX, also underperformed (as should be expected), but by a lesser amount (1.4 percentage points).
Over the most recent 10-year period, when the size premium was 0 and the value premium was -1.4%, DFSVX underperformed VISVX by 1.2 percentage points (less than its underperformance over the five-year period, when returns to both factors were more negative) and DFFVX underperformed by a lesser amount as well, 0.5 percentage points (due to a smaller difference in exposure to the two factors).
During the most recent 15-year period, when the size premium was 3.1% and the value premium was 1.6%, as we should expect, we find that DFSVX outperformed VISVX by 1.2 percentage points. DFFVX outperformed by 1.3 percentage points.
The lesson I hope you take away is that you don’t want to be like investors in actively managed funds, chasing returns. Instead, the choice of the fund you use should be based on other criteria, including what factors you want exposure to, how much exposure you want to those factors, the fund construction rules, for taxable accounts whether the fund is managed for tax efficiency and, of course, a fund’s expense ratio.
And remember that just because two passively managed funds have similar names and/or are in the same asset class, it doesn’t guarantee that they’re following similar fund strategies. Thus, when making a fund decision, you want to be sure to weigh all of the criteria.
It just might be that the fund with a higher expense ratio is the better choice because it provides more exposure to the factors that determine returns and carry premiums. In other words, it’s not only cost, but cost per unit of expected return (and risk) that matters.
For example, while VISVX has an expense ratio of 0.20% (the Admiral shares version of the fund, VSMAX, costs just 0.09%), and DFSVX has an expense ratio of 0.52%, the higher costs of the DFA fund have been more than offset by greater exposure to the desired factors and a focus on adding value by minimizing the negatives of pure indexing.
Bridgeway’s Omni Small-Cap Value Fund (BOSVX)—which, in full disclosure, my firm also recommends in the construction of client portfolios—has an even higher expense ratio, but is much smaller and more “valuey” than DFSVX. Morningstar reports that the fund’s year-end 2015 weighted average market capitalization was just $627 million (about half the market capitalization of DFSVX) and its P/B was just 1.05. Thus, its expected returns are higher.
This commentary originally appeared April 13 on ETF.com
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