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Andrew Allentuck

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Reversion to the mean

Andrew Allentuck

 

WINNIPEG (GlobeinvestorGOLD) — If you own units in a science and technology fund, take heart.

For the five-years ended Sept. 30, 2004, the science and tech funds sector produced a dismal, 13.7-per-cent average annual decline. But help is on the way. The statistical principle of reversion to the mean should pull funds filled with shares of companies that make chips and cell phones back to the long term returns of both the industry and the market. And those returns are hardly mean at all.

Reversion to the mean is the process that draws outliers back to the centre of the pack where the unweighted average of performance numbers lies. It works with the sizes of peas, heights of people, values of stocks and prices of mutual funds.

In capital markets, it reflects the process of asset arbitrage in which investors buy and sell assets over time until companies' stock prices merge into the long-term, risk-adjusted return for their industries and industries' returns merge into the long-term, risk-adjusted return for their markets. In a globalized world, it pulls returns of markets to a central, risk-adjusted world return for capital.

Consider how the process appears to work in mutual funds sold in Canada. The following table shows returns to several groups of funds tracked by the Globe and Mail.

Mutual Fund Sector Average Annual Compound
Sector Return 5 yrs
to Sept. 04
Return 5 yrs
to Sept. 99
A. Today's also-rans
Global equity -1.6% +10.7%
North American equity +1.6% +11.5%
Science and technology -13.7% +23.0%
European equity -3.2% +15.2%
B. Today's leaders
Natural resources +14.2% -2.6%
Precious metals +16.8% -5.9%
Real estate +9.3% +3.6%
Latin American equity +6.9% -8.7%

Reversion to the mean is the dark force of capital markets. The late Saturday Night Live actress Gilda Radner had a phrase for it: "It's always something."

It is a powerful force in capital markets, but making trading decisions on it requires an understanding of what drives the reversion process. After all, to be able to look back from one five-year period to another is just hindsight. Turning reversion to the mean into foresight is quite a different process.

Sal Pellettieri, a quantitative analyst at IG Investment Management in Winnipeg, said that there is a good deal of pencil work required to identify the mean to which asset prices may revert.

"You need a series of prices with a long history so that you can determine that there is a stable average," he explained. "If there is a secular trend in one direction that moves the mean, then you can't find mean reversion."

There are other problems, Mr. Pelletieri noted. "If managers change, or there is style drift, then there is no true reversion. If a portfolio is constructed so that it contains assets that are not covariant, that is, do not rise and fall together, then they may cancel out much of each other's movements and leave the fund or asset uncharacteristic of any sector."

Statistical quibbles aside, investors in various markets make use of reversion to the mean in trading. Commodity traders and some stock traders use Bollinger Bands, a technical trading tool, to find assets that are trading above or below a measured deviation from their mean. An investor can buy when an asset price is below the band and sell when their price is above the band.

Securities analyst Karen Bleasby, head of investments for Spectrum United Mutual Funds, authored a classic study of reversion to the mean operating in foreign equity markets. She showed that buying the index of the top three national emerging stock markets at the end of each year, holding for a year, then selling and buying the next top three winners, and keeping the process going for a decade would produce an average annual return of 4-per-cent.

Buying the bottom three losers of a preceding year and rolling this process forward every year at Dec. 31 would have yielded an average annual return of 61-per-cent.

The process is conceptual, for, as she warned, not every emerging market has an index. Her study ignored tax consequences of trading and trading costs. Her conclusion, nevertheless, was forceful: "it often pays to ignore the crowd and invest in those markets that have suffered poor performance."

One must be careful in using reversion to the mean as a trading strategy for stocks or mutual funds. It is as blunt a tool as its antithesis, the momentum investor's belief that what has gone up will continue to go up.

"I don't subscribe to reversion to the mean as a basis for valuing a security," said Michael McHugh, vice president for fixed income at Dynamic Mutual Funds in Toronto. He warned that many companies whose stocks decline are headed to bankruptcy and cannot recover on a statistical principle.

Mutual fund analyst Dan Hallett said that reversion to the mean is too powerful a force to ignore. President of fund research firm Dan Hallett & Associates Inc. in Windsor, Ont., he explained that "reversion to the mean cancels out volatility and brings markets and stocks back to the core return for their tier of capital," he said. "The caveat is that it works only with coherent divisions of capital, that is, meaningful sectors or industrial groups."

In the end, reversion to the mean is the cure for hubris. Take winning fund managers' preening with a grain of salt. It's as well to have compassion for those that wind up at the back of the pack. Reversion to the mean shows that, on average, outperformance isn't likely to last forever and that tough times tend to come to an end.

Andrew Allentuck writes about investments for The Globe and Mail, and reviews books on finance for globefund.com and globeinvestor.com. He is also the author of several books.

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