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To Improve Active Managers' Returns, Just Change How You Run the Numbers

As I mentioned on Friday, active managers tout their strategies with claims such as:
  • "Active management beats passive management in bear markets."
  • "Active management is better in inefficient markets like small-cap stocks or in emerging markets."
A particularly egregious purveyor of investment pornography is the investment advisory firm FundQuest, a subsidiary of the multinational bank BNP Paribas. The reason I highlight them is not only does it use improper measurements when claiming active investing outperforms passive in certain asset classes, but FundQuest continues using the same improper measurements after its mistake was exposed by my colleague Vladimir Masek.

In the 2006 InvestmentNews article, "Study: Performance Depends on Asset Class," FundQuest presented evidence that, "The average active mutual fund beat benchmarks in 31 of those [63 Morningstar] categories, including bank loan, convertibles and world stock funds." In Vladimir's response, he showed that FundQuest was able to make its claim only because it was guilty of improper measurement.

The CFA Institute, in its Global Investment Performance Standards, 2010 edition, states clearly: "Composite returns must be calculated by asset-weighting the individual portfolio returns using beginning-of-period values or a method that reflects both beginning-of-period values and external cash flows." The reason they have this requirement is, as William Sharpe noted in "The Arithmetic of Active Management," "Third, and possibly most important in practice, the summary statistics for active managers may not truly represent the performance of the average actively managed dollar. To compute the latter, each manager's return should be weighted by the dollars he or she has under management at the beginning of the period." Despite the requirement to use beginning-of-period data, FundQuest used end-of-period data to get its results.

Vladimir provides the following simple example to demonstrate how using the wrong methodology can produce bad results. Consider funds A and B. In 2009, Fund A returns 20 percent, and Fund B loses 10 percent. To calculate the return earned by investors, we need to look at the asset-weighted average return. Assume both funds began the year with $100 million of assets under management and that there were no cash flows into or out of the funds. At the end of 2009, Fund A would have $120 million, and Fund B would have $90 million. If we calculate the asset-weighted return using these figures, we get an asset-weighted return of 7.14 percent.

2009 Beginning Assets (in Millions) 2009 Returns 2009 Ending Assets (in Millions) Asset-Weight
Fund A

$100

20%

$120

.5714

Fund B

$100

10%

$90

.4286

[0.5714 x 20% + 0.4286 x (-10%) = 7.14%]


Now let's look at the proper way to calculate returns. Investors began the year with $200 million and ended the year with $210 million. That's an asset-weighted return of just 5 percent.
2009 Beginning Assets (in Millions) 2009 Returns 2009 Ending Assets (in Millions) Asset-Weight
Fund A

$100

20%

$120

.5

Fund B

$100

10%

$90

.5

[0.5 x 20% + 0.5 x (-10%) = 5%]


In the real world, using end-of-period results would produce even more distorted results. The reason is that cash flows tend follow returns. Thus, a "hot" fund would likely receive cash inflows, and a "cold" fund would experience cash outflows. The result is that using end-of-period data likely overweights the results of the top performers and underweights the results of the underperformers.

To illustrate this point, consider this example. Fund A's strong performance would likely have led to cash inflows, so let's assume it ended the year with, say, $150 million of assets (75 percent of total assets). On the other hand, Fund B's poor performance would likely have caused fund outflows, leaving the fund with, say, just $50 million of assets (25 percent of total assets) at the end of the year. Now, using end-of-period data the asset-weighted return would have magically jumped to 12.5 percent.

[.75 x 20% + .25 x (-10%) = 12.5%]


It was bad enough that FundQuest made such an error. It's worse is that even after Vladimir's exposure of the error, it continues to foist phony data on an unsuspecting public every year. Now a skeptic might say that FundQuest (and anyone else using end-of-period results) would only be doing so because using the correct methodology would produce results that for them would be the equivalent of committing economic suicide. Count me a skeptic.

The mathematics of active investing are quite simple -- in aggregate, active investors must earn the same gross return as passive investors. And since they have higher costs, in aggregate they must earn lower net returns. As Sharpe explained: "Over any specified time period, the market return will be a weighted average of the returns on the securities within the market, using beginning market values as weights. Each passive manager will obtain precisely the market return, before costs. From this, it follows (as the night from the day) that the return on the average actively managed dollar must equal the market return. Why? Because the market return must equal a weighted average of the returns on the passive and active segments of the market. If the first two returns are the same, the third must be also."

As much as they would like to, purveyors of active management as the winning strategy can't suspend the laws of mathematics. In aggregate, active investors must underperform passive investors regardless of the asset class, market direction or market efficiency. It's simply a matter of costs.

However, all is not lost for the active management faithful. The fact that in aggregate active management must lose still leaves the hope that a minority of active managers will outperform. The problem is that not only have the vast majority failed (especially after taxes), but no one yet has found a way to identify ahead of time a reliable way to identify the few winners. This is why active management is the triumph of hope and hype over wisdom and experience. It's also why Charles Ellis called passive investing the winner's game.

Novelist Victor Hugo wisely observed: "There is one thing stronger than all the armies of the world, and that is an idea whose time has come." No matter how much strong the armies Wall Street amasses, the trend toward passive investing marches on.

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How Commodities Affect a Portfolio Stocks Are Dying, Again Are Corporate Bonds a Good Investment? A Simple Way to Beat the Market Are Outperfoming Active Managers Lucky or Skillful?

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