By: Alan D. Crane Ph.D. & Kevin Crotty, Ph.D.
Whether we realize it or not, we constantly face situations where we try to sort people into those that are “skilled” and those that are not. Which doctors are the best? Which job applicant is better? Which contractor should we choose? Which athlete should we put on our fantasy team? This sorting problem is particularly relevant for money management, as we attempt to separate skilled managers from merely lucky ones. Despite the ubiquitous nature of identifying skill, it’s an exercise that proves harder than it might seem for fund managers; simply looking at someone’s track record may lead us to an incorrect decision due the influence of randomness (that is, luck).
Let’s start by considering a (fictional) world in which everyone has the same level of ability. In this world, do we expect all surgeons to have the same success rate for their patients? Will all marathons end in a tie? Would all fund managers earn the same alpha? The answer to all of these questions is almost certainly “no.” Why? Because of luck. Some surgeons will, by chance, see sicker patients. Some marathoners will have bad days while others will have good days. Similarly, some fund managers will pick stocks that perform worse (or better) than expected, just due to the inherent randomness of financial markets.
The thought experiment above highlights the fact that, even if every fund manager is equally skilled, someone is going to be classified as the “best” and someone as the “worst” based on their track record. This intuition about luck has important implications for the real world, even where skill does differ. Some differences in track records will be driven by luck, even if people do actually have different levels of skill. The critical question is, how much of the difference is due to luck and how much is due to skill?
Disentangling how much of a fund manager’s track record is due to good or bad choices and how much is due to good or bad luck is actually quite challenging. Recent academic research suggests that most of the variation in managed fund performance is driven by chance rather than ability. Perhaps more importantly, identifying specific managers that are “good” rather than “lucky” is a nearly impossible task. Let’s see why with a stylized example.
Let’s return to our hypothetical world where all managers are equally skilled. To make it simple, let’s imagine they all have no skill and are merely flipping coins to pick ten stocks. Headsthey win, tails they lose. So, on average, we expect managers to earn nothing – their wins (five heads) will exactly offset their losses (five tails). But there are many managers doing this and if each manager picks ten stocks, someone will flip a lot of heads, just by chance. Based on their track record, we’d think this is our stock picking “genius.” On the other side of the coin, someone will happen to flip a lot of tails. Based on their track record, we’d believe this manager to be an unskilled “charlatan.” And yet, they have the same talent. The difference in performance was completely due to chance.
Below is a simulation of this for 1,000 managers where we plot how often we observe a manager with each number of “winning stock picks,” that is, the number of heads out of ten coin flips. The most likely outcome is that a manager has no abnormal performance (five heads and five tails). But we also observe some lucky managers in the right tail that had mostly winning picks and also unlucky managers in the left tail that had predominantly losing picks.
Imagine instead that we have a set of managers that are truly skilled. Skill here means they pick winners more often than not. That is, they flip heads 55% of the time. If we simulate ten stock picks for these managers, as we expect, the distribution is shifted slightly to the right and the average outcome is no longer exactly five “heads.” Yet, there is still substantial variation in outcomes. We still have “geniuses” and “charlatans” despite all managers being identical and having true skill.
Let’s make this more realistic. It is likely that we have both skilled and unskilled managers. The problem we face as investors is whether we can tell them apart based on their track record. Below we simulate both types of managers and gradually hide the color-coding of which ones are truly skilled (darker shade) and which ones are unskilled (lighter shade). Based on the final distribution of outcomes, would you be able to say with much confidence that a given manager, even if they flipped a lot of heads, was actually skilled? No, because luck drives far more of the differences in performance than ability in this example.
What about in the real world? Recent academic work using equity mutual funds shows results that are consistent with this simple coin flipping intuition. Luck makes up most of the differences we observe in investment performance. Over the last 20 years, around 50% of active equity mutual fund managers earn a positive “alpha” after adjusting for market risk exposure (authors’ calculations). Most of this is due to chance. In fact, estimates of the fraction of funds that earn a positive alpha due to skill rather than luck range from close to 0% to 10%.[1]
“Well, that’s ok, right? We just need to figure out how to pick one of the 0% to 10% of managers that outperform the market.” Unfortunately, it’s not so easy. If you pick among the best-performing managers, there’s still a reasonably high chance that you’re picking someone that did well because they were lucky, and in the worst case, you may get someone that’s actually bad but had some good luck in the past. In the end, you’re likely to pay “genius” level fees for the privilege of investing with a lucky manager.
Professional fund rankings and rating systems are not immune from these issues. Most commonly used ratings are just putting managers and funds into categories based on track records. Funds are still likely end up as a highly-rated fund due to chance.
The academic literature has tackled the question by trying to predict fund performance. In other words, luck shouldn’t be persistent, so if I can use something from the past that forecasts which funds will do better, then I can perhaps sort funds reliably based on true skill. This research has produced a number of fund characteristics (based on things like size of holdings, frequency of trading, etc.) that correlate with differences in performance. Unfortunately, these proxies for skilled management have performed relatively poorly when used to predict “out-of-sample” performance (Jones and Mo, RFS 2021) and funds that rank highly based on these proxies have undesirable levels of downside risk (Back, Crane, and Crotty, RFS 2018).
So, should an investor try to sift through the set of managers in an attempt to find the best active manager? The literature on skill and luck implies this is an almost impossible task. The fraction of “good” managers is small, and the chance of picking them correctly is low. Instead, their performance is likely to be driven by luck. And while there are those of us happy to take a gamble in the hopes of a lucky outcome, remember that an unlucky bad outcome is also possible. So, take luck out of the equation. By owning everything, you’re taking luck out of play and earning a fair return on your investment. This is the argument for holding a diversified, low fee portfolio that invests in as many asset classes as possible. If you have a higher risk tolerance, then you may consider either tilting this diversified portfolio to hold more riskier asset classes or use leverage and keep intact the original fully diversified portfolio. It doesn’t sound as exciting as finding the stock-picking “genius” out there. But when you realize that those fees for active management may be compensation for lucky outcomes, it’s clear that the boring choice is the better strategy.
[1] Using a false discovery approach, Barras, Scaillet, and Wermers (JF 2010) find that only 0.6% of funds appear to be skilled while the rest are either zero-alpha funds or value-destroying negative alpha funds. Using bootstrap techniques, Fama and French (JF 2010) also find that very few funds outperform the performance distribution we’d expect to observe due to change. Using a mixture model, Harvey and Liu (RFS 2018) estimate that about 10% of mutual funds have positive ability.
Disclosures:
Inscription Capital, LLC (“Inscription”) is a registered investment advisor. Advisory services are only offered to clients or prospective clients where Inscription and its representatives are properly licensed or exempt from licensure.
The information provided is for educational and informational purposes only and does not constitute investment advice and it should not be relied on as such. It should not be considered a solicitation to buy or an offer to sell a security. It does not take into account any investor's particular investment objectives, strategies, tax status or investment horizon. You should consult your attorney or tax advisor.
The views expressed in this commentary are subject to change based on market and other conditions. These documents may contain certain statements that may be deemed forward‐looking statements. Please note that any such statements are not guarantees of any future performance and actual results or developments may differ materially from those projected. Any projections, market outlooks, or estimates are based upon certain assumptions and should not be construed as indicative of actual events that will occur.
All information has been obtained from sources believed to be reliable, but its accuracy is not guaranteed. There is no representation or warranty as to the current accuracy, reliability or completeness of, nor liability for, decisions based on such information and it should not be relied on as such.
Past performance shown is not indicative of future results, which could differ substantially. No investment strategy or risk management technique can guarantee returns or eliminate risk in any market environment. All investments include a risk of loss that clients should be prepared to bear.