Alpha’s Razor

alphasrazorLet’s say your active equity manager beats the index one month or one quarter.  Fluke?  Maybe so.  How about a few months in a row or a few quarters in a row?  The chance of them having horseshoes in their pockets becomes less likely as the number of months and quarters grows.  But how many months does it take for you to know if your manager’s alleged “alpha” is truly alpha (i.e. skill) and how much is dumb luck.  Furthermore, does this time horizon depend on the volatility of the fund itself?

These questions and others are addresses by a newly released paper by Sassan Zaker of Julius Bear.  Zaker describes investor’s willingness to accept (and reward) out performance of any kind as a “free put option” given to the manager.

Zaker is the co-author of some interesting papers that raise questions about the alpha credentials of many hedge funds (see related AllAboutAlpha.com post).  His recent solo work titled “Alpha Uncertainty Principle,” begins with a noteworthy description of alpha (our emphasis):

“Alpha is the metric, goal, and justification of the active asset management industry, yet there is little agreement on whether and how to integrate alpha in asset allocation. Despite multiple academic studies showing that, as a whole and after cost, the industry has little or negative alpha, as in Gruber [1996], alpha remains what investors demand and what the industry aspires to. Alpha divides the investment community into believers and skeptics. Its business significance stems from the fact that it is often equated with active management skill and as a differentiator justifies higher management fees.”

He goes on to argue that the uncertainty over what is real vs. perceived alpha can be thought of as the “implied cost of assuming alpha’s existence.”   In other words, if you have only a few data points and you believe the manager’s line that they represent true alpha, you are taking a risk that they may also represent simple luck.

Zaker writes that a fund’s information ratio determines the number of data points required before a manager can declare the existence of true alpha.  As intuition would suggest, the higher the information ratio, the fewer data points required before this declaration can be made (with 95% confidence) .

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He also illustrates that higher volatility funds require more data points in order to determine if their returns are truly alpha (with 95% confidence).

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The special challenge when measuring alpha in hedge funds, as Zaker points out, is that returns may be driven by any number of alternative beta factors – many of which might look like alpha.  His “Alpha Uncertainty Principle (AUP)” cautions against too many complex and “overlapping” sources of apparent alpha.  Since each alpha source may not actually be alpha, the more alleged alphas, the greater the chance that they are all an ex poste way of describing one thing: .

Drawing on the axiom first posited by 14-th century smart guy William of Ockham, he writes that this is akin to “Ockham’s Razor” – that, given two possible theories, “the one with the simplest explanation is to be preferred.”

He defines “Alpha’s Razor” in the following way:

“For any given level of alpha produced by different comparable active managers, the one with the least complexity should be regarded as the one with higher quality.”

Broadly speaking, the concept of the Alpha Uncertainty Principle  can be applied to several problems according to Zaker:

  • Delineating alpha from beta: As a portfolio analysis technique, it can help identify true alpha.
  • Setting fees: As a management technique, it can identify alpha-returns that are worthy of higher management or performance fees.
  • Establishing monetary policy: Zaker even suggests that central banks’ controls of short term interest rates “unintentionally disrupt the supply-demand constellation for alpha, causing excessive alpha demand in the short term.”

While statistically-speaking, one prescient market call can look like alpha when a fund is regressed against its benchmark, intuition suggests that successive winning calls are required before an investor can begin to feel comfortable that the manager actually has any skill.

That intuition now has a new name: The Alpha Uncertainty Principle.

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