By Samuel Lee
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.
click to enlarge
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
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
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
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 (
) 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 (
) 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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including Barclays Global Investors ((BGI)), First Trust, and
ELEMENTS, for use in exchange-traded funds and notes. These ETFs
and ETNs are not sponsored, issued, or sold by Morningstar.
Morningstar does not make any representation regarding the
advisability of investing in ETFs or ETNs that are based on
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