Evaluating Investment Performance


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.


Robin Carpenter
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.

Click here for more details.

Headline News

Stock Picks

Tesla Motors

If Tesla ever begins to cut back on development and innovation costs, earnings will soar.


China seems to be raising up its very own version of Amazon in Alibaba (BABA.


Roy Ward uses the PEG ratio to determine if the stock is undervalued or overvalued.

Cabot Wealth Advisory

What Fed Speeches Mean for the Stock Market Today

By Chloe Lutts Jensen on September 29, 2016

Four Fed presidents gave speeches yesterday, and every word was digested by the stock market in an attempt to better predict the Fed’s next move. With odds of a December rate hike now about even, how should stock investors prepare?Read More >

The Emerging Market Stock You Ought to Own

By Paul Goodwin on September 27, 2016

The company I’m talking about (the one that you probably don’t own) is the largest Chinese instant messaging company. It is a giant in its own right, with a market cap of $262 billion and annual sales of over $19 billion. The company grew revenue by 28% in 2015 and routinely boasts after-tax profit margins over 30%.Read More >

Tesla Model 3 vs. Chevy Bolt: Which Affordable Electric Car Is Better?

By Timothy Lutts on September 26, 2016

The Tesla Model 3 and Chevy Bolt are the first two affordable electric cars with a driving range of more than 200 miles. Let’s see how they stack up - and what they could mean to Tesla Motors (TSLA) and General Motors (GM) stock. Read More >