We Have Expected Goals, What About Expected Alpha?

The football (soccer) team you support has just lost another game. You watch an interview with the manager (coach) and they lament their bad fortune. They dominated the match, had countless chances to score, but were just unlucky. Is this true or are they just trying to mask another bad performance? To answer that question, there is a metric that can help. Expected Goals (xG) has become widely used in football and hockey in recent years. xG tells us the number of goals a team should have scored based on the quality of opportunities created. As with all metrics it is imperfect, but it does provide invaluable help in disentangling skill from luck. Fund management is another area where we have severe difficulties in seeing beyond randomness and chance. Could a metric like xG help, and how might it work?

xG models are complex, but what they are trying to achieve is simple. For every chance created in a game a likelihood of scoring will be ascribed to it, creating an ‘expected goal’ between 0-1.  These probabilities are derived from analysis of historic scenarios. For example, the long-run conversion success rate of a penalty kick is 80%, so, if your team is awarded a penalty, that will result in an xG of 0.8 (whether or not they go on to score).

Why is this information useful? There are three main benefits:

– It provides an insight as to whether a team is underachieving or overachieving (or are perhaps experiencing good or bad luck).

– It may highlight if a team is unusually strong or weak in the most important aspect of the game – do they persistently overshoot their xG, scoring more goals than the model suggests they should?

– It can highlight where a team is going right or wrong. Maybe it is not that they cannot shoot, they don’t even create any good chances to score. 

There is still a great deal of judgement required here – is my team unlucky or terrible at shooting? But just because a metric doesn’t give us a finite answer, doesn’t mean it is not useful.

Investors in active funds are wrestling with many of the issues that the xG metric seeks to address in sport. Are results more a consequence of luck or skill? What are reasonable expectations for performance?

The problem of using a similar idea in investing is that it is a far noisier activity than football. A complex adaptive system, compared to a discrete game with fixed rules and a vast evidence base of similar situations. This distinction, however, does not mean that employing such a concept for active fund investing is without merit. The underlying problem statement is very similar:

xG in football:  Given the opportunity, what was a reasonable expectation for a goal to have been scored?

‘Expected alpha’ in investing: Given the opportunity set, what was a reasonable expectation for a fund manager’s performance?

How do we go about estimating how much alpha a manager should have delivered over a period? There are two possible methods:

Top-down / factor based: In this approach, we can use historic returns to describe a fund manager’s results as sensitivities to various factors (value, quality, momentum, size etc…). We can then compare the performance of their fund to a simplified version of their strategy based on the returns to those factor exposures.

The advantage of this technique is that it is reasonably simple to build a model that is consistent with the historic factor sensitivities of a fund. The downside is that a performance track record of some length is required, and, for some managers, it may be difficult to capture their results through factor exposures. This might be because they carry lots of idiosyncratic risk, or their style shifts through time. Such situations will, however, be in the minority.  

Bottom-up / fundamental:  A more robust approach is to create a systematic replica of the manager’s approach (all fund managers should do this anyway). To do this we would need to understand the investment process in detail – characteristics of the securities purchased, positions sizing etc… In essence we are attempting to build a rules-based, systematic imitation against which we can compare the actual decisions made by the fund manager. This could be as granular or simple as we wished.

The benefit of this more nuanced system is that it is not reliant on historic returns, but the philosophy and process of the manager. It can also provide a clear contrast between what a manager is doing in their fund, and what is happening in our model. The downside is that it requires the bespoke development of a stock picking / portfolio construction model, and is very reliant on how we might interpret the process adopted by a given fund manager.

Both of these approaches are imperfect and noisy, and provide nowhere near the confidence that we might take from an xG metric in football. We are, however, in an industry where discussions of skill are sorely lacking, and there is a heavy reliance on simple past performance with little attempt to separate luck and skill.

Creating some form of ‘expected alpha’ model for funds would have two primary benefits.

First, it would help form sensible expectations for a fund manager’s performance and allow us to focus on the divergence between that and reality. If our expected alpha model is struggling it is reasonable to expect the manager to be performing poorly. This moves us away from constantly obsessing over underperformance and outperformance versus a standard benchmark

Second, highlighting disparities between a fund manager’s results and a simple approximation of their approach could help to identify some form of skill or edge. Is there something happening that is distinct from what can be easily, systematically replicated? Is it worth paying for?

There is no magic bullet in assessing fund manager skill or edge, but the idea behind xG in football points towards a more nuanced means of looking beyond the luck and noise that dominates investing. Assessing fund managers through the lens of ‘expected alpha’ could help investors not only set reasonable performance expectations but better understand if value is being added and, if so, where it is coming from.

My first book has just been published! The Intelligent Fund Investor explores the beliefs and behaviours that lead investors astray, and shows how we can make better decisions. You can get a copy here (UK) or here (US).

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