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).

The Four Questions Investors Must Ask

When we make an active investment decision, we obsess over the particulars of a given opportunity, whether it be a security, fund or asset class. This, however, distracts us from a far more important issue, which is so often ignored – should we be participating in the activity at all? This must always be our starting point. To make it so, we need to ask ourselves these questions:

– What are the odds of the game?

The critical first step is establishing the odds of the game we are playing. We want to engage in an investment activity where the odds are in our favour, or at least more in our favour than in other games. The major mistake we tend to make is grossly overstating our chances of success due to overconfidence in our abilities. To paraphrase Charlie Munger, who cares that 90% fail when I am in the 10% that succeeds?

The best means of guarding against such biased thinking is to assume that we are average. Rather than ask how likely is it that I will be successful, ask how likely is it that any given person will be (you never know, we might even be average ourselves). This approach gives us a reasonable base rate or starting point.

– Do I have an edge?

Once we have established a satisfactory estimate of the odds of success in an activity, we need to gauge whether we have an advantage relative to the average participant. If we are going to engage in a game with terrible odds, we are either ignorant of them, playing for fun (like a trip to Las Vegas) or believe there is something about our approach that puts us in the 10%. 

For professional investors, there is one additional reason that we might play a game with a low probability of success – because the cost of participating is borne by somebody else. The chance of positive (lucrative) outcomes for a fund manager are often significantly greater than it is for their clients.

The worse the odds, the more conviction we must have that we have some form of advantage. 

– What is the edge?

It is not enough to believe we have an edge; we must be clear about what it is and why it might exist. For most active investors, an advantage can be categorised as informational (we have better information than others), analytical (we use that information in a superior way to others) or behavioural (we exploit the decision-making shortcomings of others).

It is often argued that financial markets are more informationally efficient than ever before. There is more data, greater transparency and less friction. Making a case for an information-based advantage (in most major asset classes) seems a somewhat heroic assumption. Analytical edges are possible but incredibly difficult to substantiate. Where an analytical advantage arises, it is probably not from the ability to synthesise information better but to use it for a different purpose. Are we trying to predict next quarter’s EPS for a business or its long-run value?

Most market inefficiencies stem from the vagaries of human behaviour. It is difficult to argue that investor behaviour is becoming more rational, and certainly possible that things are getting worse. There is a problem with a purported behavioural edge, however. Not only do we have to contend that other investors are irrational, but that we are not. We are somehow free from the psychological and institutional burdens that lead to poor decisions. This is far easier to say than do.

– Who am I playing against?

In zero-sum games, the ability of the other participants matters a great deal. My chances of winning at poker heavily depend on who else is sitting at the table. Investing is similar but different.

It is undoubtedly true to say that having sophisticated, well-resourced investors facing off against each other is not a great environment to find an edge. Yet there is a major difference between poker and investing. In poker, everyone is playing with the same objective; in investing, this is not the case. Even though it feels like it. If I have a twenty-year investment horizon (if only) and other participants take a one-year view, we are barely playing the same game. At best, we are playing the same game with very different rules. So, the question becomes not – who am I playing against? But – what is it they are playing, and why am I able to do something different?

A painful confluence of compelling stories and inescapable overconfidence means that we are prone to participate in investment activities where the chances of positive results are very poor. To guard against this, we need to better understand the odds and justify why we might be an exception.  

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).

New Behavioural Investing Podcast – Decision Nerds

I am delighted to announce the launch of a new podcast, Decision Nerds. Paul Richards and I will be discussing a range of behavioural and decision-making problems with some fascinating guests. 

We know that there are a lot of podcasts out there, but there is nowhere near enough focus in the investment industry on how we can make better decisions in highly uncertain environments.

Our behaviour is the most important thing, yet we don’t talk about it anywhere near enough (apart from on this blog!)

We will be exploring a range of decision-making and behavioural issues with innovators, academics and industry specialists. 

In addition to these in-depth discussions, we will also be creating short episodes where we tackle listener questions and problems, and discuss the latest behavioural research. If you have an issue you would like us to cover, let me know!

In our first episode, we look at why investors can often be reticent to receive feedback on their decision making, with Clare Flynn Levy of Essentia Analytics. Clare founded a company with the express intention of helping investors become aware of their behaviour and improve it.

Put simply the quandary is this – to improve our decision-making, we need to clearly understand where we need to develop, admit that and then engage with a process that can help us. This sounds simple, but there are obvious risks as well as rewards. What if we find out we are not as good as we think we are, even worse, what if other people find out!?

Clare has been helping fund managers engage with these issues for many years, and shares some fascinating insights on the challenges around improvement and how they can be solved. There are some great thoughts and stories for anyone who wants to improve their investment decision making.

The pod is available on all your usual podcast platforms and also: here

Please leave a review and do let me know if there are topics you would like us to discuss in the future.

Why Don’t Fund Managers Talk About Skill?

In my career, I have spent hundreds of hours with fund managers attempting to assess their investment approach. When I look back at this, aside from questioning my life choices, the one thing that strikes me is how little fund managers discuss skill. Of course, they talk about past performance (if it is good), but the randomness and chance in financial markets render this a terrible proxy. This is a puzzling situation, investors in active funds are seeking to identify and pay for skill, but the people managing them seem reticent to mention it. 

It has always struck me as odd that in active fund selection, the onus falls heavily upon the allocator to strive to prove that the thing they are buying (skill) exists. Surely the seller of the product should be making that case?

Before exploring the reasons why investment skill is such a rarely discussed topic, it is worth defining terms. What exactly is skill?

Skill exists where we can see a repeatable link between process and outcomes (what we intend to do and the result of our action). We are often guilty of focusing on the second part of this equation – if the result is good, then some skill must be involved. This can be an effective shorthand if the activity is simple (shooting free throws in basketball) or heavily structured with limited randomness in the outcomes (playing chess). It is when things get noisy that the trouble starts.

In activities where the results combine luck and skill, focusing on outcomes alone can lead us astray. The greater the involvement of chance, the greater the need to understand the process that led to the outcome.

This is easier said than done. Focusing on process as much, if not more, than outcomes means retaining conviction and confidence even when headline performance is disappointing. Two things are critical here – time and belief. Extending our time horizon should tilt the balance in favour of skill over luck, but in order to have the required patience we must (continue to) believe that skill exists.

Imagine we have a biased coin that is likely to come up heads on 52% of flips. We should have more confidence in this edge becoming apparent the greater the sample size. To prove this advantage, we would rather see 10,000 flips than 10. We can think of this as akin to lengthening our time horizon. The problem is that if after 50 flips the coin has landed showing tails more often than heads, we might start to doubt that the coin is weighted at all.

Even if we possess an edge, we must often sit through periods when results make it look like we do not.

In investing, if skill exists, then it is difficult to identify and, if we do discover it, tough to benefit from. That does not mean we should ignore it. Asset managers are not only selling skill; they are paying people a great deal of money on the basis that they possess it. They should probably think about it more than they seem to.

Why don’t they?

Past performance is everything: The industry is obsessed with past performance, and it is so ingrained in how it functions that trying to have nuanced conversations about skill might be deemed to be pointless. Strategies with strong past performance sell; trying to evidence skill does not.  

Stories sell better: Evidence of skill, which might be about the consistency of decision-making through time, is far less compelling and persuasive than captivating stories about an investment theme or star fund manager.   

Time horizons are just too short: As time horizons in asset management seem to become ever-shorter, the relevance of skill diminishes. Nobody operates with a time horizon long enough to even attempt to prove they are skilful.

Too much complexity: Looking at past performance is easy, trying to define and evidence skill is complex and messy.

Don’t want to know: Let’s assume some active fund managers – but not many – have skill, 20%, perhaps. If I am one of the majority, it is in my interest to actively avoid the question of skill. My odds of a lucrative career are much better relying on random performance fluctuations and trends.

There are many reasons why the notion of skill is rarely discussed in the asset management industry, and all parties are complicit in its neglect. The existence and persistence of skill, however, is the foundation of active fund management and it needs to be talked about more.

If it is being sold, it helps to know what it is.

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).