Research Affiliates approach to equity investment management is based upon the
insight that stock prices are “noisy” and “mean-reverting.”
- Noisy. Calling prices “noisy”
means acknowledging that they contain errors. The market overvalues some stocks
and undervalues others. Investors who buy and sell stocks irrationally or
erratically are known as “noise traders.”
- - Mean-reverting. “Mean reversion” means that
stocks whose prices have been trending upward or downward will, at some point,
reverse direction and head back toward their average values.
there’s much more to it than that. After presenting an intuitive explanation of
mean reversion and reviewing the empirical evidence for it, I will consider why
mispricing isn’t quickly arbitraged away and discuss how long-term investors
can structure portfolios to benefit from mean reversion.
What is Mean Reversion?
us use the analogy of a pendulum—a real one, not a mathematical model—to
illustrate the basic concepts of mean reversion. The pendulum consists of a
weight, or bob, suspended from a pivot. In Figure 1, the bob is
moved from point A to point B and released. It will swing back past point A to
point C, and it will continue swinging back and forth until it eventually slows
down and comes to rest again at the equilibrium point A. While the bob has
speed, its momentum is the best indicator of where it will be moving in the
immediate future. Because A represents the bob’s average position, it is the
place where we are most likely to find the bob in the long run. The shorter and
shorter swings of the bob constitute the process of reverting to the mean.
pendulum is, of course, governed by Newtonian mechanics and has few
irregularities. In contrast, the process of mean reversion in financial markets
is neither deterministic nor smooth. Nonetheless, the pendulum analogy
expresses key characteristics of stock price movements.
the short run the most recent price movements are predictive of where the price
will continue in the immediate future—this is known as momentum in prices. Long
run mean reversion implies that high or low prices are temporary; over time,
prices tend to return to their more average levels. It also means that if
prices were moving in one direction in the past, they are likely to move in the
opposite direction in the future. Moreover, the greater the swing in one
direction, the stronger is the reverse movement.
Both Individual Stocks and the Stock Market
in General Exhibit Mean Reversion
studies show that stock returns are not completely random. In a classic study
of overreaction in financial markets, Werner De Bondt and Richard Thaler (1985)
assigned stocks to “winner” portfolios and “loser” portfolios on the basis of
their cumulative excess returns over the previous three years (i.e., the
difference between the cumulative 36-month return of the individual stock and
that of the market as a whole). They then traced the performance of the winner
and loser portfolios for the subsequent three years. Using CRSP prices for the
period between January 1926 and December 1982, De Bondt and Thaler employed
this procedure to construct winner and loser portfolios for 16 non-overlapping
measurement periods. On average, 36 months after portfolio formation, the loser
portfolios outperformed the market by 19.6%, while the winner portfolios
underperformed the market by about 5.0%. The difference in cumulative average
residual was 24.6%. Figure 2 shows the
portfolios’ paths to these striking results.
shape of the curve on Figure 2 gives us a rich description of the data. In the
first month after the portfolio formation there is a very strong mean
reversion. This is known as short term mean reversion. Then for a horizon up to
a year the winner stocks actually tend to slightly outperform the loser stocks.
Just as there is momentum in a pendulum, there is intermediate term momentum in
prices. Beyond the horizon of one year the winner stocks tend to underperform,
while the loser stocks tend to outperform. This is known as long-term mean
reversion. Even though the De Bondt and Thaler chart stops three years after
portfolio formation, long term mean reversion can be detected for as many as 10
years from the starting point.
potential explanation for the superior performance of extreme loser stocks is
that they are riskier. However, De Bondt and Thaler report that the average
market betas of the securities in the winner portfolios (1.369) are
significantly larger than the betas of the loser portfolios (1.026). “Thus,”
the authors write, “the loser portfolios not only outperform the winner
portfolios; if the CAPM is correct, they are also significantly less risky.”
The traditional risk-based model does not explain the difference in return
between “winner” and “loser” portfolios.
Bondt and Thaler suggested an alternative, non-risk based explanation. Market
participants might have overreacted to several years of subpar performance by
the loser stocks, and underpriced them. Market participants also overreacted to
several years of extraordinary performance on the part of the winner stocks,
and overpriced them. Eventually the market discovers this mispricing, and the
undervalued “losers” surprise their holders with superior performance. The
overvalued “winners,” of course, produce disappointing results as their prices
addition, numerous articles demonstrate that not only individual stocks but the
stock market in general is subject to mean reversion. Among others Fama and
French (1988) and Poterba and Summer (1988) present evidence that stocks
mean-revert on the horizon up to five years. Furthermore, high valuation
multiples such as aggregate book-to-market or earnings-to-price ratios, which
signal low current prices, have been found to forecast high subsequent stock
market returns. (See Campbell and Shiller , among others).
Mean Reversion is Related to the Value and
Small Size Effects
mean reversion effect stands in an interesting relationship with the value and
small size premia. All three reflect the fact that low-price stocks tend to
outperform high-price stocks. Value stocks have relatively low
price-to-fundamentals ratios. For example, as of July 31, the price-to-earnings
multiple of the Russell 1000®
Value Index (15.02) was 26% lower than that of the Russell 1000 Growth Index
(20.3). And small stocks have lower market capitalizations. (Market
capitalization is also a measure that reflects a company’s stock price.) At the
end of July 2013, the median market capitalization of the Russell 1000 was U.S.
$6.762 billion, while the median market capitalization of stocks held in the
Russell 3000® Index
was U.S. $0.642 billion.1 Some companies are in the Russell 1000
because they are large companies; some companies are in Russell 1000 because
they are high price companies. In the case of mean reversion, the “losers,” the
stocks which recently went down in price, are the outperforming stocks. A study
by Arnott, Hsu, Liu, and Markowitz (2011) shows that a mispricing component in
prices which the market eventually corrects can fully account for the mean
reversion, value, and size effects observed in the data.2
is similar to a pendulum’s weight moving away from the resting position. The
farther the distance, the stronger the gravitational pull. The degree to which
stocks are mispriced can vary over time, and when there is more mispricing
there are greater opportunities for generating profits. Asness, Friedman,
Krail, and Liew (2000) demonstrated that an estimate of the degree of aggregate
mispricing can be used to forecast the value premium. The measures they chose
were the spread in valuation multiples between a value portfolio and a growth
portfolio (the value spread) and the spread in expected earnings growth between
a growth portfolio and a value portfolio (the earnings growth spread). The
authors found that both measures are significant determinants of the difference
in expected returns between value and growth strategies.
plots the forecasted and realized differences between value and growth returns
as reported in Asness et al. (2000). The pale blue line shows the forecast
implied by the relative cheapness of stocks with low valuations. It operates on
something like the pendulum principle: the higher it goes, the higher will be
the value strategy’s subsequent outperformance (the dark blue line).
Interestingly, the paper appeared at the height of the tech bubble, and the
last point on the chart was forecasting a very high value premium. This
prediction came true when the tech bubble burst in 2001.
Why Doesn’t Arbitrage Eliminate the Profit
to textbook finance, if noise traders introduce mispricing, then arbitrageurs
can be expected to enter profitable trades that will soon drive prices close to
fundamental values. However, in a 1997 study called “Limits to Arbitrage,”
Shleifer and Vishny (1997) explain why asset managers may be unable to exploit
mispricing. There is a quote attributed to John Maynard Keynes: “Markets can
remain irrational a lot longer than you and I can remain solvent.” Shleifer and
Vishny formalized this idea in their paper.
financial theory, arbitrageurs require no capital and bear no risk. Shleifer
and Vishny assume, much more realistically, that arbitrageurs operate with
investors’ capital. “The fundamental feature of such arbitrage,” they write,
“is that brains and resources are separated by an agency relationship.”3
to the essentials, engaging in arbitrage means buying cheap (i.e., undervalued)
assets and selling similar assets that are expensive (overvalued). However, the
market may continue to misprice the cheap asset that the arbitrageur holds.
Indeed, the gap between the asset’s market price and its fundamental value may
proceed to widen. In this case, the expected value of the trade is rising but,
in the interim, the arbitrageur is sustaining losses. The investors, who may or
may not understand what the arbitrageur is doing, will surely see that he or
she is losing their money. They may then engage in what Shleifer and Vishny
call “performance-based arbitrage,” withdrawing their capital from the losing
manager and placing it with someone who appears to be more competent.
institutional arrangements in the asset management industry make it possible
for mispricing to persist for prolonged periods. The long-term mean reversion
that we observe is the consequence of this tenacious mispricing. Shleifer and
Vishny help us understand the paradox, if not relish the irony: as the
opportunities to profit from mispricing increase, traditional asset managers
become more constrained and less capable of taking advantage of them.
outcome described by Asness and his co-authors constitutes an empirical
validation of this paradoxical conclusion. The dot-com bubble is a prime
example of persistent and increasing mispricing. As tech stocks continued to
outperform the market for years on end, it became harder and harder for
managers to adopt a contrarian stance and trade against them. The fear of
losing clients (and the assets under management on which investment advisory
fees are based) prevents managers from taking advantage of mispricing. Although
long-term portfolio returns are bound to suffer, the managers’ behavior is
Reversion Matter to Long-Term Investors?
We saw above that, due to
the process of mean reversion, winner stocks become losers, and losers,
winners. Contrarian investment strategies create opportunities for investors
who have the courage to sustain interim losses and the discipline to rebalance
even—or especially—when mispricing increases.
is exceedingly difficult for investors and managers alike to hold fast when the
market continues to move against them. One potential solution is to strip
contrarian investing of its emotional component by committing long-term assets
to a transparent algorithmic rebalancing strategy. Smart Beta strategies—a
recent innovation in financial management—are transparent, non-price weighted
solutions. Transparency and dispassionate rebalancing rules help significantly
mitigate the agency problems facing regular managers.
Hsu, Kalesnik, and Little (2011) and Arnott, Hsu, Kalesnik, and Tindall (2013)
showed that Smart Beta strategies consistently trade against price movements.
This contra-trading allows them to capture the opportunities presented by
mispricing. The authors demonstrate that long term mean reversion in the form
of value and size premia explains the majority of the Smart Beta value added.
intent of Smart Beta investing is to profit from mean reversion; accordingly,
the best strategies would be the ones which have high capacity and do not trade
too frequently. (Recall that rebalancing too often raises turnover costs and
risks trading against momentum.) If stock prices are noisy and mean-reverting,
as we firmly maintain, then fundamentals-weighted indexing—a rules-based Smart
Beta strategy which sells winners and buys losers—seems very sensible. Tying
weights to accounting measures of company size creates capacity; choosing to
rebalance annually, rather than more often, controls turnover; and “buy
low/sell high” is truly a sound investment principle.
1. Russell Investments is the source of the P/E and
median market cap figures cited here.
2. See also Arnott and Hsu (2008).
3. Shleifer and Vishny (1997), 36.
4. The managers’ failure to buy losers and sell winners
may be described as rational because the fear of losing clients before
portfolio gains materialize is, itself, entirely reasonable. For recent
evidence that mutual fund investors withdraw funds from underperforming
managers, see Cashman, Deli, Nardari, and Villupuram (2012).
Arnott, Robert D.,
Jason C. Hsu, Jun Liu, and Harry Markowitz. 2011. “Can Noise Create the Size
and Value Effects?” Working Paper, University of California at San Diego and
Arnott, Robert D.,
Jason Hsu, Vitali Kalesnik, and Phil Tindall. 2013. “The Surprising Alpha from Malkiel’s Monkey and Upside-Down Strategies.” Journal of Portfolio Management, vol. 39, no. 4
Arnott, Robert D., and
Jason C. Hsu. 2008. “Noise, CAPM and the Size and Value Effects.” Journal of Investment Management,
vol. 6, no. 1 (First Quarter):1–11.
Asness, Clifford S.,
Jacques A. Friedman, Robert J. Krail, and John M. Liew. 2000. “Style Timing:
Value versus Growth.” Journal
of Portfolio Management, vol. 26, no. 3 (Spring):50–60.
Berk, Jonathan B. 1997.
“Does Size Really Matter?” Financial Analysts Journal, vol. 53, no. 5
Campbell, John Y., and
Robert J. Shiller. 1988. “Stock Prices, Earnings, and Expected Dividends.” Journal of Finance,
vol. 43, no. 3 (July):661–676.
Cashman, George D.,
Daniel N. Deli, Federico Nardari, and Sriram V. Villupuram. 2012. “Investors Do
Respond to Poor Mutual Fund Performance: Evidence from Inflows and Outflows.” Financial Review,
vol. 47, no. 4 (November):719–739.
Chow, Tzee-man, Jason
Hsu, Vitali Kalesnik and Bryce Little. 2011. “A Survey of Alternative Equity Index Strategies.” Financial
Analysts Journal, vol. 67, no. 5 (September/October):37–57.
De Bondt, Werner F. M.,
and Richard Thaler. 1985. “Does the Stock Market Overreact?” Journal of Finance,
vol. 40, no. 3 (1985):793–805.
Fama, Eugene F., and
Kenneth R. French. 1988. “Dividend Yields and Expected Stock Returns.” Journal of Financial Economics,
vol. 22, no. 1 (October):3–25.
Poterba, James M., and
Lawrence Summers. 1988. “Mean Reversion in Stock Prices: Evidence and
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Shleifer, Andrei, and Robert W. Vishny. 1997. “The
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