Montroid Capital Management LLC, with a track record promising the moon, struts into a pension fund, graces their prospective investor with stingy peeks under the hood, and walks out with a $100m allocation with healthy fees that are of course justified by their investment magic. Fast forward a few confusing years of underperformance, MCM insists that the investment thesis is intact but [something about market conditions], that it is reworking the process, and that a return of alpha is on the horizon. Feeling pressure from the board, the pension fund holds a series of meetings to assess the manager's justifications and decide if the story of an imminent return to glory is credible. Curiously, nowhere in this familiar, story-based process is a rigorous questioning of an alternative, and tragically plausible, truth, which is that MCM had just gotten lucky in the past.

There’s a fascinating cognitive dissonance among academics and practitioners regarding the role of luck in active management. On the one hand, everyone recognizes on an intuitive level that investment outcomes are subject to significant randomness, yet most seem content to all but ignore this fact when analyzing performance. Even generations of technically-proficient academics seem to have collectively missed the mark. This phenomenon has many harmful implications, which I plan to write about in due time, but alpha is a particularly revealing example.

## Evolution of alpha

Let’s first consider how alpha became what it is today. Alpha was not originally postulated as a measure of skill or active management performance, but as a measure of market inefficiency based on the elegant works of asset pricing theorists such Sharpe and Lintner of CAPM fame, and Ross who derived the APT. According to these theories, non-zero alpha should not exist if, very roughly speaking, markets are efficient. This gave rise to a large body of empirical academic research that tested these hypotheses and also led to what is now widely known as factor investing. As various forms of non-zero alpha was discovered in real data, this became interpreted by many as evidence of market inefficiency. So far so good.

It was at this point that a harmful mutation befell the evolution of alpha. If markets are inefficient, the argument went, then some investors must have the ability to predict returns and generate positive alpha, and therefore alpha is a measure of skill. There are many logical fallacies plaguing this chain of reasoning, but suffice it to say that while positive alpha may be a necessary condition for the presence of skill under very specific conditions (more on that later), it is far from a sufficient one. Nonetheless, alpha is now widely used as a measure of a manager’s skill and value-add.

## Positive alpha does not imply skill

No fancy math is required to prove that positive alpha does not imply skill. A manager can beat the S&P 500 by throwing darts and generate positive alpha. Find any number of dart throwing managers, and about half are expected to generate positive alpha over any time horizon, and many will even do so every single year. It’s as simple as that, and this is true of any common variant of alpha.

Researchers have tried to address this issue by calculating p-values, adjusting thresholds for multiple testing, correcting for non-normality of empirical alpha distributions, and so forth. Unfortunately, all of these approaches suffer from the common flaw of misappropriating concepts from equilibrium-based asset pricing theories and performing statistical tests regarding skill based on a framework that has no explicit role for active decisions or even a definition of skill.

## It gets worse

The problem with alpha goes deeper than being achievable by luck. Let’s start with the observation by Cremers, Petajisto, and Zitzewitz (2012) that the S&P 500 has an alpha of 82 bps per annum between 1980 and 2005 with respect to the four Carhart-Fama-French factors. With a p-value close to zero, the de facto interpretation of alpha would suggest that the most famous passive benchmark exhibits skill. The authors go on to propose ways to eliminate this non-zero alpha, but I bring this up to make a different point.

The extraordinary skill of the S&P 500 relates to a more acute contradiction that even unskilled managers can have positive expected alpha depending on their mandates. In fact, we see this all the time in long-only equity mandates for both simple and factor regression-based alpha. What’s more, some mandates have such positively-skewed factor-based alpha distributions such that it would take a tremendous amount of bad luck to achieve negative alpha! Any statistical work that pools alphas across time periods and managers with different mandates is like taking apples-and-oranges and raising it to the power of fruit basket.

## It gets even worse

Factor regression-based alpha makes no sense to me even as a measure of a manager’s value-add. First, factor exposures are estimated after the fact, not to mention time-varying, so it’s not as if the investor can fire the manager and replicate her future performance. This also explains why factor-based manager replication seldom works out of sample. In this sense, it's inferior to simple alpha as an actionable utility metric.

The usual argument is that managers "shouldn't be given credit for taking on known factor exposures." Such a belief leads to many nonsensical implications, such as dismissing as unskilled a manager who can predict factor returns but has zero factor alpha. Factor alphas are also highly sensitive to what one considers "known factors," and that is a controversial issue bordering on the arbitrary. Not only does factor alpha not make sense as a skill metric, but it doesn’t even make sense as a utility metric.

## A silver lining

There is one use case for alpha that is sensible. If the manager’s explicit, ex ante objective is to beat a pre-specified benchmark, then simple alpha is a useful measure of the manager’s value-add from the investor’s utility perspective, and one can argue that positive alpha is a necessary, but still far from sufficient, condition for the existence of skill. It measures the extent to which the investor was better off than allocating to the benchmark. Even in this scenario, however, alpha doesn’t say anything about skill vs. luck or future performance, and allocators can still end up paying unjustified performance fees if they choose the wrong benchmark, which is another dreadful can of worms.

If not an outbreak of skill-eating parasites, what do I think explains the dearth of persistent alpha in the data? Lots of dart-throwing managers on a lucky streak, until it inevitably ends. This was the case for MCM as their investment skill is unfortunately limited by my imagination.

*The views and opinions expressed in this article are those of the author(s) and do not necessarily reflect the views of Applied Academics LLC or any of its affiliates. *

Photograph by Mikihiko Obayashi