Goodhart’s Law of Active Management

It’s hard to allocate capital across different active fund managers. You need to consider many candidates, interview them, study their materials, and arrive at a final decision about their skill or lack thereof. Trailing returns are not especially helpful, since luck is such a major factor in determining outcomes.

Hence the search for a holy grail, a manager characteristic or portfolio practice that predicts future performance. There must be some variable, call it X, that measures skill. X doesn’t need to be perfect, but if we could use logic to identify an X that is a necessary condition for success, we could at least screen out those managers who lack X.

One such logic-based X is as follows. If you are trying to beat a given benchmark, then you cannot hold the benchmark but rather you have to hold something else. Makes sense. There are various ways that have been proposed to measure deviation from the benchmark:

• Holdings-based methods
  • Active share, as proposed by Cremers and Petajisto (2009)
  • Portfolio concentration
    • measured by number of holdings
    • measured by weight in top-ten holdings
• Return-based measures
  • Trailing active risk or tracking error

• Holdings-based methods
  • Active share, as proposed by Cremers and Petajisto (2009)
  • Portfolio concentration
    • measured by number of holdings
    • measured by weight in top-ten holdings
• Return-based measures
  • Trailing active risk or tracking error

I’ll call all of these measures “conviction.” Managers with very high conviction are so confident of their abilities that they feel no need to diversify; they argue with a straight face that their portfolio of only ten stocks is actually less risky than the market, because they have wisely picked ten sure winners that are uncorrelated with each other.

Some argue that because conviction is a logical pre-condition for success, higher conviction is always better than low conviction. They argue that good managers must be courageous, must move the needle with big bets, and must not be lazy, cowardly, asset-gathering closet indexers.

I have three problems with this argument: logic, evidence, and Goodhart’s Law. Goodhart’s Law is the statement “When a measure becomes a target, it ceases to be a good measure,” and I use this term to refer to a phenomenon reflecting various ideas in economics including incentives, competitive equilibrium, and catering. Goodhart’s Law says that if you could find an X that predicted performance, and you started using X to select fund managers, X would quickly become useless or counterproductive.

If some X is good, more X isn’t necessarily better

Let’s start with logic. It is certainly true that you have to bear some risk to outperform. But I think the logic is often misapplied. While some is necessary, more is not always better.

If you have back pain, you must take a non-zero number of painkillers to get relief. But it is not true that taking 100 pills is better than taking two.

The right level of portfolio risk is the level that reflects the client’s preferences and other holdings, together with the ability of the manager to select securities. Higher is not always better.

The evidence is unclear

Let’s consider the empirical claim that higher conviction predicts higher performance. As I’ve previously explained, this claim is untrue for individual investors, where higher conviction is associated with both lower IQ and lower performance. But for mutual fund managers, Cremers and Petajisto (2009) say that the opposite is true: higher active share managers have higher performance. Here’s Rekenthaler (2021) describing the reaction to their results:

The mutual fund industry was delighted. Its product managers published article after article after article about the benefits of being different--that is, about why potential customers should consider buying higher-cost funds that were actively managed rather than index their investments.

In addition to active share, some researchers claim that other conviction measures predict high performance for professional investors, including portfolio concentration and idiosyncratic return volatility, as discussed by Cremers, Fulkerson, and Riley (2019). Not everyone agrees with these claims. Frazzini, Friedman, and Pomorski (2016) find active share is not a reliable predictor of performance, and Rekenthaler (2021) describes the out-of-sample evidence on active share as a “great disappointment.”

Now, it is not my goal to adjudicate the empirical controversies about the predictive power of portfolio conviction. So let’s just imagine we lived in a world where there was zero controversy and everybody agreed that conviction predicted return. What then?

When a measure becomes a target, it ceases to be a good measure

Suppose that it was scientifically proven that portfolio concentration historically predicted subsequent fund performance. A blue-ribbon committee of Nobel prize winners determined that all funds with ten or fewer holdings indisputably had alpha of +10% during the period 1980 to 2024, but funds with more than ten holdings were wasteful closet indexers with negative alpha. Suppose this pattern was true in large and small cap, domestic and foreign, equities and bonds, everywhere.

Is our quest for the holy grail complete? Can capital allocators just relax and hire fund managers with ten holdings? Mission accomplished?

Sadly, no. Consider what would happen in equilibrium if this rule were universally adopted. If clients only allocated to managers with ten holdings, then all managers would immediately trim their number of holdings to ten. That’s the competitive equilibrium and illustrates Goodhart’s Law, which Goodhart (1984) defines as “any observed statistical regularity will tend to collapse once pressure is placed upon it for control purposes.”

Here’s Goodhart’s Law in action from Bjerksund, Døskeland, Sjuve, and Ørpetveit (2020):

Closet indexers are low-activity mutual funds that are sold and marketed as active. Their investors therefore only receive part of the service they pay for. Supervisory authorities all over the world are now considering how these funds should be regulated. We examine evidence from interventions carried out by Scandinavian regulators. The impact is identified by comparing scrutinized Scandinavian closet index funds with similar unaffected European funds. Given the choice between reducing fees or increasing activity, the scrutinized funds opt for the latter. Although this results in a more actively managed fund, performance deteriorates. Thus, regulation leads to the worst outcome.

In this example, using active share as a target doesn’t just render it useless; it incurs actual harm. That’s a standard result. A classic example of Goodhart’s law is in education. Suppose we adopt a new system to evaluate school quality by student scores on standardized tests. Schools will respond not by raising general quality, but by teaching students how to do well on standardized tests. Goodhart’s law holds also for evaluating elite MBA programs, who when judged by admissions selectivity, respond by seeking applications from obviously unqualified applicants who will be rejected.

In these examples, logical and empirically validated metrics become not just useless, but actively harmful. The same is true for portfolio concentration: in equilibrium, you get higher risk without the accompanying high reward. Perverse.

Sadly, portfolio conviction is especially apt to be gamed by managers because conviction makes it harder to use past returns to infer skill. The central task of manager selection is to differentiate between luck and skill. Conviction turns up the dial on luck, making this task harder.

Suppose you are an unskilled portfolio manager who wants to shirk, that is, to pretend to skillfully pick stocks while actually just picking random stocks and then spending the rest of your day watching reality TV. How long will it take before your clients realize you have zero skill? If they are using classic statistical inference, it will take them a lot longer to detect your shirking with ten holdings than with a hundred holdings. Here’s Brown and Davies (2017):

Intuitively, shirking managers inject noise into their holdings and returns in order to cloud investors’ inferences. Noise injection and shirking are complements; as the moral hazard problem becomes more severe, faux-active managers inject more noise, attenuating investors’ abilities to identify skilled managers. Our result suggests that signals of moral hazard based on holdings or tracking error may be less effective in the future as shirking managers adapt their strategies to avoid detection … popular holdings-based measures may not be effective as funds can engage in signal-jamming to appear truly active.

If clients demand funds of type X, funds of type X will arise. That’s the beauty of markets: supply and demand. If tomato demand is high, farmers will produce tomatoes; if turnip demand is high, farmers will produce turnips. A related idea in corporate finance is “catering:” if investors prefer stocks with characteristic X, then firms will adopt X in order to appeal to investors. Examples of X are dividend policy, corporate names, or leverage; see Baker and Wurgler (2013).

According to the catering view, if investors overvalue dividend-paying stocks, companies will cater to this demand by paying more dividends. Thus, catering is a symptom of overpricing; if you see companies start to pay dividends, that is a clue that all dividend-paying companies are overpriced.

Does this logic translate to concentration? That is, if concentrated funds become popular, does that imply that the stocks they hold are overvalued? That depends on whether the funds purchase similar stocks. Sometimes, they do. Consider the tech stock bubble. Then, as now, technology euphoria was in the air and concentrated funds were all the rage, including the Janus 20 Fund (the second-best-selling mutual fund of 1999) and the Merrill Lynch Focus 20, with both funds holding around 20 stocks. Unfortunately, both funds held Enron.[1] Concentrated portfolios can be correlated with each other, and concentration can backfire.

Something similar happened in ETFs in the past twenty years. The original wave of ETFs were highly diversified, passive instruments. Subsequent ETFs included more concentrated specialty funds targeting specific sectors. As with Enron, it turns out that concentration and overvaluation went hand-in-hand. The new concentrated ETFs were introduced when their sectors were in high demand and thus overvalued. Here’s Ben-David, Franzoni, Kim, and Moussawi (2023):

… issuers of specialized ETFs identify the popular trends in the market and respond to that demand by issuing products that track these investment themes. However, by the time new ETFs enter the market, the securities in which they invest have already reached their valuation peak. Thus, specialized ETFs underperform after launch. According to this hypothesis, specialized ETFs are chosen as a speculative vehicle by investors who extrapolate past performance into the future.

In their data, ETFs with high conviction (high active share or low number of holdings) have significantly worse alpha. So for ETFs, at least, conviction is a bad thing that brings both high risk and low reward.

Another reason to expect concentrated funds to be overvalued is survivorship bias. I’ve previously discussed the connection between survivorship bias and concentrated portfolios. Since concentrated portfolios are riskier, they’re more likely to have very high or very low returns. The losing funds die, and the winning funds attract inflows. Thus if we look at living concentrated funds, they will tend to own stocks with prices that have gone up and might have been pushed up further by inflows.

Moving now beyond portfolio construction, scholars have proposed many other predictors of performance, including the personal characteristics of the manager:

• Vehicle ownership: Owning a minivan is better than owning a sports car according to Brown, Lu, Ray, and Teo (2018)
• Birth month: being born in October and thus being the oldest kid in your class is better according to Bai, Ma, Mullally, and Solomon (2019)
• Masculine appearance: lower testosterone is better according to Lu and Teo (2022)

Unfortunately, here too we must consider Goodhart’s Law. If only minivan-driving managers are hired, then all managers will drive minivans. If only October-born managers are hired, we will suddenly see an influx of portfolio managers claiming to be born in October. If only low testosterone managers are hired, well, I’m not sure what will happen, but I doubt it will be good.

As we say in this business, "Past performance is no guarantee of future results." Unfortunately, neither is active share, portfolio concentration, minivan ownership, or anything else. I have only two pieces of advice. First, don’t pick one easily gameable characteristic to judge portfolio managers. Second, if everyone else is rushing to invest in funds with characteristic X, think twice before following their lead.