Evaluating Investment Performance
The Law of Large Numbers
When More is Less
One of the most widely accepted—but often unexamined—themes in performance measurement is the belief that a long performance history is better than a short performance history. Fund rating services generally won’t offer a rating for new funds that have less than three years of history. Many investment advisors limit their holdings to funds at least 10 years old.
The more-is-better logic is straightforward. A fund manager who has produced, say, 8% a year for 10 years is seen as having stronger evidence of success than another manager who has produced 8% a year for five years.
That conclusion seems obvious enough … but it’s also useful to ask Why? Why do we intuitively consider a longer history more reliable than a shorter history?
The answer is rooted in a core tenet of statistics, “the law of large numbers.” That law says that the larger a sample, the more reliable the findings. In particular, a large sample average (average return, for example) will be closer to the “true” universal average … which is to say, closer to what we can expect going forward.
Thinking of investment performance as a sampling problem is unconventional, but really important. In effect, a manager has some innate return-generating capability—some outcome that will emerge over time, if only there are enough stocks and enough holdings and enough market trends to average out. The investor or analyst wants know what is that manager’s “true” long-term expected value, and a key element is past performance, which is in effect a sample of the manager’s entire universe of possibility. And (back to the law of large numbers) the longer the history, the larger the sample; and the larger the sample, the more faith we can have in the result.
But there are problems.
Most critically, the investment process being sampled is not constant. The market today is never quite like the market yesterday. And the manager today is never quite the same as he or she was yesterday. So the market-and-manager dynamic has endless possible combinations. With everything constantly changing, it’s always possible that the most recent year gives a better indication of a manager’s current capability than a multi-year or decades-long record.
Consider the case of Bill Gross, founder of Pacific Investment Management Company and lead manager of the giant PIMCO Total Return Fund. Bill Gross has built a stellar performance record over decades. But the fund has lost money in recent months (down 2.8% in June, and down 3.4% year to date). Some investors are losing confidence, and the fund had withdrawals of nearly $10 billion last month.
While some of that outflow reflects fears about pending Fed policy changes (affecting all bond funds), it may also reflect seeds of doubt about whether Bill Gross is his same old self in today’s conditions.
That’s a size-of-sample issue. Should we consider the long-long term success of the so-called “King of Bonds,” or should we worry that the game has changed and focus on a more recent sample for current relevance?
There is no definitive answer, but here’s the way I look at it.
Recent performance is more relevant—but not too recent. My own experience is that the most recent three-to-five year history is far more relevant than a 10-year or longer history, and more robust than a one-or-two year sample. I’ve found that mid-range efficacy has been true for a long time, but it’s even truer in recent years as the investing environment evolves more quickly. (New products come to market at a furious pace these days. And technological changes like “big data” analysis and High Frequency Trading affect the texture and behavior of the markets.)
As for Bill Gross and the Total Return Fund, I find he’s broken stride occasionally in the past, and managed to recover quite nicely. But his range of performance variability has increased quite notably in recent years, and I do not expect a return to the modest-but-persistent outperformance that dominated the fund’s history up to about 2008.
If you’re interested, I have a “moving alpha” chart that illustrates the point. Send me an email if you’d like to receive a copy.
Editor of ETF Investing Systems
Editor’s Note: Robin Carpenter is the analyst and editor of Cabot ETF Investing System, which combines market timing and sector selection to beat the market over the long term. Over the past 10 years, Cabot ETF Investing System has earned 133.08%. Over the same period, the S&P 500 earned just 91.82%. Which means that if you’d put $100,000 into this system 10 years ago, you’d now have $233,080 having gained $40,000 more than the S&P 500.
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