Dimensional Fund Advisors

Small Cap Growth Indexing and the Multifactor Three Step

Dimensional Fund Advisors

Unless you've just spent the last decade looking for Elvis, you know that indexing most asset classes will beat most active managers. From time to time a majority of active managers in a given asset class will beat indexing, but this usually doesn't last very long. Not true with small cap growth stocks, which is one of active management's few persistently bright spots. Were the Wilshire small cap growth index a fund with no expenses, then it would have ranked 121st out of 173 SCG funds for the past 3 years, 50th out of 86 over 5 years, 25th out of 30 over 10 years, and 5th out of 10 for 15 years. Recall Dunn's Law, from the article, "When Indexing Fails:"


When an asset class does relatively well, an index fund in that class does even better.

It follows that if you've invested in a bad asset class, it's better to be in an actively managed fund. The trouble with SCG is that it just hasn't had a bad 3, 5, 10, and 15 years. It's had a bad seventy years, as you can see from data by a study by Fama and French, alluded to in the article "Investment Entertainment Value:"


In contrast, over the past several years large growth stocks have been the place to be. It's thus no accident that the Vanguard Index Growth Fund placed 4th of 185 funds in the Morningstar large growth category over the past 5 years. John Bogle covers this territory well in his famous "Tic Tac Toe" speech. Below is a figure from that piece which displays the added return of indexing over the average fund in the 9 Morningstar style categories:


Note the superiority of indexing almost everywhere except the lower right corner of the figure, where indexing cost 2.8 percent pa. This is where small growth lives. The farther away you get from this corner of the diagram, the better indexing looks.

Clearly, this entire corner of the equity market is a swamp, and to fully expose it it's worth a long but meaty digression into the Heart of Darkness of finance academia: the dreaded 3 Factor Model.

In June of 1992 academicians Eugene Fama and Kenneth French ("F/F") rocked the investing world with a study published in the Journal of Finance, innocuously entitled "The Cross-Section of Expected Stock Returns." The piece is the cognitive equivalent of an enormous hunk of marzipan cake which sits in your freezer for months there's no way you'll get through it in one whack, and is properly consumed only in small sittings. In fact, unless you've gotten considerably beyond Stat 101, it's probably best avoided. So, here's the short course:


  • "Beta," the measure of market exposure of a given stock or portfolio, which was previously thought to be the be-all/end-all measurement of stock risk/return, is of only limited use. F/F convincingly showed that this parameter did not predict the returns of all equity portfolios, although it is still useful in predicting the return of stock/bond and stock/cash mixes.


  • The return of any stock portfolio can be explained almost entirely by two factors: Market cap ("size") and book/market ratio ("value"). The smaller the median market cap of your portfolio, and the doggier the stocks, the higher its expected return. F/F viewed both size and value as risk factors, for which one is rewarded with extra return. The term "book/market ratio" generates some confusion. This bit of Famafrenchspeak is the inverse of the more familiar "price/book ratio." Thus, a high book/market ratio means the same thing as a low price/book ratio-value. In Famafrenchspeak, high book/market is acronymed "HBM."

Using the above formulation, F/F created a powerful 3 Factor Model ("3FM") for predicting the returns of any given stock portfolio.

The 3 factors are as follows:

  1. "Market Factor." This is the return for for being exposed to stocks and is calculated as the return of a broad basket of stocks, the CRSP 1-10 Decile portfolio (roughly equivalent to the Wilshire 5000), minus the T-Bill return.


  2. "Size." This is the return of small stocks minus that of large stocks. When small stocks do well relative to large stocks this will be positive, and when they do worse than large stocks, negative.


  3. "Value." This is the return of value stocks minus growth stocks, which can likewise be positive or negative.

Let's say you have a money manager whose performance you want to evaluate. Traditionally, you'd pick a benchmark appropriate to their investment style - the Russell 1000 Value Index, say, for a large cap value manager, and compare returns. The problem is that maybe the manager owns some growth stocks, or perhaps some small stocks. Except in very rare instances, it is impossible to pick a precise benchmark against which to meaningfully measure his/her performance.

The 3FM trumps this problem. Remember that each of the 3 factors has a return, just like a security. One simply matches the manager's series of monthly returns against the returns for the 3 factors and performs a multiple regression analysis. (This sounds formidable, but in the microprocessor era can be accomplished by a secretary with a spreadsheet.) The salient outputs from this analysis are as follows:

  1. "Loading values" for each of the 3 factors-i.e., how much the manager is exposed to the market, small size, and value. The "market loading" typically will be the same as a fund's equity exposure-1.0 for an all equity fund, 0.5 for a fund with 50 percent stock. The "size loading" reflects the median market cap. In the convoluted logic of academic finance, a high size loading signifies small stocks, a low one large stocks. The S&P 500 has a size loading of about -0.16, whereas the CRSP 9-10 decile (very small stocks) has a size loading of 1.18. Lastly, the "value loading" reflects whether the fund behaves more like a value or growth fund. A high value signifies a value orientation, a low value a growth orientation. Values range from about 0.5 for value portfolios down to -0.15 for growth portfolios.


  2. An "R squared," which measures how well the portfolio's returns are explained by the model.


  3. Most importantly, an "alpha," or the amount by which the manager has led or lagged the custom benchmark provided by the 3FM.

Let's look at a typical example. I regressed the monthly returns of the highly regarded Tweedy Browne American Value (TWEBX) fund for the period 1/94-9/98 against the 3 factor return series, and came up with these outputs: The "market loading" was 0.92, about what one would expect for a fund which typically carries about 8-10 percent cash. The "size loading" was 0.12, again, reflecting that this is a mid-large cap fund. Lastly, the "value loading" was 0.37, indicating that this fund is true to its value orientation. The R-squared of the regression fit was 0.92. In other words, the 3FM explains 92 percent of the monthly returns. This is a bit lower than the 0.95 usually seen with domestic funds and is due to the fact that TWEBX carries about 15 percent foreign equity. So, a pretty good fit, but not perfect. Disappointingly, the fund's alpha was -0.08 percent per month. In other words, you'd have been better off indexing by 1.0 percent pa. This fund actually did beat the model before expenses, but the 1.4 percent expense ratio gobbled it up, and then some.

In fact, viewed on the pathologist's slab of the 3FM, precious few managers earn significantly positive alphas over the long term. And, needless to say, a past positive alpha does not predict a future one.

Which gets us back to F/F's original data. The June 1992 study aroused cries of anguish from the owners of a wide variety of gored oxen, the most salient of which was that F/F were "data mining," i.e., their results were an artifact of the 1963-90 study period. Fair enough, F/F said, so they dug up a pile of stock manuals from the 1929-63 period, and redid their study. The 1929-63 data was almost identical to the later data (which they extended to 1997). If you're a glutton for punishment, this paper is available online. (Strangely enough, I've not been able to find the original '92 paper on the web.)

Fama and French calculate loading factors, R squareds, and alphas for portfolios formed on size and book/market ratio, and as might be expected found very high R squareds and near zero alphas in almost all areas. (It is a bit of a tautology to calculate these parameters from portfolios from which the regression data is itself drawn, but no matter.) One bit of data sticks out from both periods like a sore thumb-small growth (or, in F/F lexicon, "S/L") stocks. There the alphas were -0.53 percent per month for the earlier period and -0.22 percent per month for the later period, or about -6.5 percent and -2.5 percent per annum, respectively.

So, we're dealing with a very bad actor here-an asset with low returns and ferocious risk. (I did mention that the standard deviation of small growth stocks is over 50 percent higher than the market as a whole, didn't I?)

Back to Dunn's Law and small growth investing. These stocks are characterized by poor returns. Period. The active manager, who is free to sneak into his/her portfolio a little bit of Caterpillar or Merck, will benefit, but for the indexer there is no escape. In other words, active small growth managers succeed to the extent that they are free to invest elsewhere.

There is a certain irony here. The key to becoming a successful small growth manager is to first get yourself classified as one, and then avoid the real item. This happens automatically through asset bloat. Successful SG funds rapidly attract large inflows, and must of necessity invest in larger companies, slowly extricating themselves from Investing's Bermuda Triangle.

There's also another factor involved, and that's momentum. If you're running a small cap growth index fund you are going to sell your fastest growers as soon as they increase beyond a certain market capitalization, whereas the active manager is more likely to hold onto such a stock. This shows up rather nicely in F/F's data. For all four of their "style corners" they examine two different strategies. The first is involves selling a stock as soon as it moves beyond strict size and valuation parameters. Because this requires relatively high turnover, a second strategy is also examined, in which a "hold range" (in their terminology, "RGE") is established. This is a sort of buffer zone beyond the index's usual borders within which the stock is not sold.

For SCG for 1963-98, the strict portfolio strategy return was 10.46 percent, versus 11.93 percent for the RGE strategy. In other words, 1.47 percent of extra return was obtained by holding onto the winners a bit longer. In contradistinction, the returns for SCV were 17.82 percent for the "strict" strategy and 17.21 percent for the RGE strategy. In this case, you were 0.61% better off selling SCV stocks as soon as they got out of range, at least theoretically. F/F believe that the RGE disadvantage in this category is outweighed by the reduced trading costs.

But the big picture is that with small stocks value beats growth by a wide margin. Whether your approach is active or passive, the best advice about small growth investing is to just say no. ~

copyright ©1999, William J. Bernstein
Reprinted by permission. All rights reserved.

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©1999 IndexFunds.com