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A Value and Size Tilter's Guide

Style indexes under the microscope.

Samuel Lee, 09/21/2011

Eugene Fama and Kenneth French's work popularized the value and size effects, the puzzlingly high returns that value and small-cap stocks have earned in almost every market studied. Their research has resonated with indexers, many who overweight value and small-cap stocks in their portfolios. Despite style tilting's popularity, the popular discussion is short on specific numbers. Some tilters point out that small-value stocks as defined by Fama and French have earned 14.2% annualized from 1928 to 2010, 4 percentage points above the U.S. market's return. But that doesn't mean any value index, small-cap or large-cap, will earn a similar value premium--some indexes are more size- or value-laden than others. The style map is a beautiful way to represent value and size tilts, but it doesn't quantify value and size tilts as readily observable numbers. For that, we have to go back to the size and value premiums' academic roots, to the Fama-French model.

Models and Models
In simple terms, the Fama-French model estimates how sensitive a stock strategy's returns are to three risk factors: the total stock market's returns, value stocks' returns, and small-cap stocks' returns. Value is defined as low price/book; the other factors are self-explanatory. However, since value stocks have both market and size risk mixed into their returns, Fama and French isolate the value-return factor with a strategy that owns a portfolio of low price/book stocks and short-sells a dollar-equivalent portfolio of high price/book stocks, earning the spread between value and growth stocks. The size factor is isolated in a similar manner. An extended version of the Fama-French model, called the Carhart model, adds a momentum factor, which captures the return of a strategy that every month buys the best-performing stocks and short-sells the worst-performing stocks. We'll wield this model from now on.

The Carhart model estimates "betas," numbers that represent a stock strategy's sensitivity to each factor. For example, a value beta of 0.80 means that for each percentage point the value factor rises, the strategy rises by 0.80 percentage points, holding all other factors constant. I've reproduced the annualized returns of the various factors in the table below. The table links betas to actual returns. For example, a strategy with a size beta of 0.50 and a value beta of 1.00 would have earned about 5.17% annualized (0.50*2.50% + 3.92*1.00) from its value and size loadings for the period 1927 to 2011.

Let's look at an actual index. The S&P SmallCap 600 Value had a value beta of 0.61, implying that if it had existed since 1927 and maintained its value loading, it would have earned from its value exposure about 2.39% annualized (0.61*3.92%). The bigger the value loading, the deeper or purer its value tilt.

Fama-French and Carhart Factor Returns (August 1927-June 2011)

Source: French Data Library, Author's Calculations. Market represents the U.S. stock market's returns, minus the T-bill rate. Size, value, and momentum factor annualized returns represent strategies that hold small-cap, value, or high-momentum stocks and short-sell large-cap, growth, and low-momentum stocks.

We can't take this model literally. It doesn't say the S&P SmallCap 600 Value will earn 2.39% annualized from the value premium in the future. All it produces are backward-looking estimates. The true value and size premiums will always be obscured to us. But the model gives us another perspective on the relative style purity of various indexes.

Size, Value, and Momentum
It's worth exploring how the size, value, and momentum factors have behaved over the past century. As the chart below shows, the factors' excess returns can disappear or turn negative for painfully long periods. Witness how the size factor lost money for decades-long periods--from 1983 to 1999 and from 1946 to 1965. Value was more consistent, but even it had decade-long droughts, most recently during the 1990s. The momentum strategy's returns were both greed-inspiring and puzzlingly consistent, but punctuated by horrendous losses during the two great stock market crashes. Besides, its returns were unobtainable for much of the century because of high frictional costs. Value and size tilters need to be committed to their strategies for the long haul and ready to endure years--maybe decades--of underperformance.


Popular Indexes Dissected
I calculated factor loadings for popular style indexes with at least a decade of returns. Again, these figures give us a decent idea of the kind of factor exposure we can expect from such strategies over the long haul. I looked at large-value, small-value, and dividend indexes, and threw in a couple of DFA funds, the gold standard of value- and size-tilted funds.

The DFA funds lived up to their reputation for style purity, with extremely deep-value and size tilts. This isn't surprising; DFA has built its funds around the Fama-French model. The large-cap value indexes are all very much alike, with modest value tilts ranging from 0.31 to 0.38, suggesting that they earned only a modest value premium. The small-cap value indexes are more varied, and their value tilts are much deeper. Dividend indexes seem to offer an unusual combination of deep-value exposure and a large-cap bias.

Carhart Model Factor Loadings


Source: Morningstar Direct, Author's calculations. All values are statistically significant at the 1% level, except for size loadings close to 0. Mergent Dividend Achievers 50 was used as a proxy for VIG's index.

Portfolio Considerations
What does it all mean? Well, the large-value indexes offer similar exposures, and their value loadings are modest. If the value premium continues to be positive, it's doubtful that an investor would earn more than a percentage point or so than the market. Small-value indexes offer more value exposure, but the size premium's inconsistent performance can wash out the value premium for years on end. Tilters concerned about maximizing risk-adjusted returns should emphasize value over size, unless they have a compelling, valuation-based reason to load up on small caps.

On the other hand, dividend strategies are a value tilter's dream. They soft-pedal market exposure, have no size exposure, and have value tilts competitive with small-value funds. Contrary to what some have said, dividend strategies aren't simply inefficient value tilts--if anything, they seem to offer purer exposure. One caveat is that dividend strategies tend to have dynamic value tilts, sometimes offering little exposure and other times offering extremely deep exposure. However, small-value indexes have volatile value tilts, too. More important, dividend strategies' dynamic tilts seem to add a bit of excess return, a point made by Rob Arnott.

The data suggest that most investors, even deep-style tilters, will not earn much of a value and size premium over the long run. An investor holding only a small-value index fund could reasonably expect (but shouldn't rely on) a 3% annualized excess return over several decades. However, the benefit of a small-value slug to a well-diversified portfolio with bonds may well be less than half a percentage point per year; the tilt has to be large to make a dent. For example, an investor devoting a big 20% stake of his portfolio to an S&P SmallCap 600 Value fund such as iShares S&P SmallCap 600 Value Index IJS would only have enjoyed over the past couple of decades about a percentage point increase to annualized returns from his size and value tilts. Tilting with a large-cap value fund such as Vanguard Mega Cap 300 Value Index ETF MGV produces even smaller benefits. In the end, tax optimization, disciplined rebalancing, and avoiding high costs may be much more important to an investor's overall results.

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