Is alpha really just a function of manager skill?

In this article we make a?non-technical argument that highlights the often falsely held notion, that outperformance is only a function of a fund manager's skill.

We argue that even if multiple managers foresee a future information state with perfect accuracy, and that the future they predict is different to the current market consensus, there will be constraints such as size and investment mandates that translate to varying degrees of success that managers attain from acting on their informed insights.

Let's build a simple model, let there be N merchants of varying wealth which consists of various combinations of gold coins and cash.

Furthermore let's say that 2 of the N merchants spot a bandit on the horizon making his way towards the group of the merchants, and that the other N-2 merchants are oblivious to the bandits movements; lets also make this bandit a special kind of bandit who steals all gold coins in sight but will not steal cash, he is also an entrepreneurial bandit, who after stealing gold coins will happily sell them back to anyone at market prices in exchange for cash.

The choice here of 2 informed merchants is arbitrary, but we can put some bounds on this number, we know that for any outperformance to occur we cannot have N informed merchants out of N, because if this were the case nobody would buy any more gold from other merchants because they would all know a bandit is on the near horizon who will steal it all from them, in this case the whole market would be in a state of common consensus about the future, and thus nobody can outperform from this information. We can safely say that the more informed merchants we have, the greater downward pressure it would have on the price of gold as there would be more informed merchants looking to sell gold coins and fewer uninformed merchants willing to buy them.

The 2 merchants who have seen this bandit on the horizon and knowing he only steals gold and not cash, simultaneously start to sell their gold coins to the other N-2 unknowing merchants in exchange for cash, the smaller merchant who has fewer gold coins than the larger merchant is able to sell all his gold coins in a shorter time and at a more favorable price per coin than the larger merchant who must take a larger discount to entice other merchants to buy his larger holding of gold coins due to his larger market impact.

Market impact is often modelled, by formula such as Kyles Model

E(π) = x(v ? λx ? μ)

This postulates the expected profit of a trade to be impacted negatively by λx where λ is some constant that represents the price elasticity of demand of the market in question and x is the sixe of the order, ie. less liquid markets will have a higher λ, and a larger order equates to less expected profit due to its greater market impact and μ represents the bid-ask spread. These models always model market impact as a monotonically increasing function of the size of the order relative to the average volume traded of the asset in question, in laymans terms the more of a financial asset you have to sell and the smaller the volume traded of the asset in question, the worst price you will get on average, and vice versa for buy orders. In a world where markets are becoming less elastic to incoming orders, and strategies are becoming increasingly similar (likely due to funds poaching each others quants, and using a function of recent performance to guide their poaching), this equates to orders coming in at similar times for similar assets, and thus markets are becoming less able to digest orders without large price swings, the effect of fund size on performance will become more and more significant as these trends play out.

As the percentage of AUM of quant strategies increase, this will also likely create more similarity in investment strategies employed in the market, quant by its very nature is more objective than fundamental investing, and thus as quant AUM grows, more funds will more often reach similar objective answers from the data on which assets to buy and sell, they may employ different strategies, but all else being equal, given Quant is more objective in nature, there will be less noise in the market to cushion market impact from orders. Put simply, FCFF (a potential quant input) is a lot more objective than whether you like the management team (more a fundamental opinion), therefore the former is much more likely to reach a common consensus than the latter. All quant strategies are not the same, but its likely fair to say they have a greater chance of similarity than fundamental strategies do.

To also touch on the subject of constraints, assume there is a third merchant who also predicted the appearance of the bandit, but he is a merchant who is constrained by his investors never to sell his gold holding, so even though he had the correct foresight, his investment constraints prevented him from acting on it, despite having the same informed information set, constraints are pervasive amongst investment managers. This constrained manager might be able to not buy as soon as he sees the bandit, but he is often constrained not to sell.

Because the larger merchant creates more market impact due to the larger size of his initial holding of gold coins he wants to sell, he ends up with a lower average price for his gold coins than the smaller merchant who was able to sell all of his gold in a quicker time and at a more favorable price, even though they both predicted the bandit on the horizon at exactly the same time.

Shortly after these 2 merchants have disposed of their gold in exchange for cash, the bandit strikes, he predictably leaves the 2 informed merchants alone as they now only have cash and no gold (given this bandit only steals gold and not cash), and proceeds to rob all the gold of the remaining merchants.

After the heist, the 2 merchants who predicted the bandits strike, now being flush with cash and deciding that the future looks safe from the bandit striking again for some time, decide to do a deal with the bandit to purchase back gold coins in exchange for their cash, again the smaller merchant is able to buy back gold faster and at a more favorable price from the bandit than the larger merchant whom the bandit knows will want to purchase a lot more gold (as he has more cash) so increases his prices accordingly, again we have the notion of market impact as the larger purchase causes the average cost per gold coin to increase for the larger merchant.

In both scenarios the smaller merchant who predicted the bandits appearance made a better return on his capital than the larger merchant in both the buying and selling of the gold coins, this was solely due to his smaller market impact in both the buying and selling of his gold bars than the larger merchant, not of any difference in skill in predicting the future.

Now assuming that investors allocate their capital to merchants based on the merchants return on capital which is a (somewhat) realistic assumption for the world we live in, investors will therefore after the heist allocate some more resources to the smaller merchant via some function based on his outperformance (assuming the merchants are equal in every sense other than return on capital).

If the heist scenario repeats again and again and capital is reallocated as a function of outperformance after each heist, the smaller intelligent merchant will become progressively larger and his outperformance will reduce as he grows in size due to his increased market impact.

Assuming also that the larger merchants will now have a smaller allocation as the amount of capital in the world is finite, they will become smaller, allowing them to capitalize more effectively by the above argument when they have superior foresight as they will subsequently create less market impact.

We can also assume without contradicting empirical evidence (that funds alpha's are often not persistent over time) that foresight is randomly and uniformly distributed amongst all the merchants regardless of size, this creates a dynamic system whereby each merchants AUM grows and shrinks based on their outperformance, but also that their outperformance is a function of how much they have grown or shrunk which gives rise to some form of mean reversion.

This dynamical system evolves through time assuming no deaths or births of merchants, then as time passes each merchant will have varying AUM based on his size and thus outperformance. We can also model the bandits appearance as a Poisson process, and we can assign the market impact as a function of AUM using market impact models and what underlying's the fund trades, this model could help us model how quickly AUM changes amongst funds and the impact this has on the market.

Also for a simple takeaway, as an Investor if you are proposed two funds using the same strategy, one large and one smaller, you will often be better off investing in the smaller one (assuming all the other fees and attributes are the same).