Mommy, Where do alphas come from?

Ah, the question every parent dreads.  Where do alphas come from? How can you possibly explain such a complex and miraculous process that has given life to asset managers since time began?

Thankfully, MIT’s Andrew Lo just released a new paper entitled “Where Do Alphas Come from?: A New Measure of the Value of Active Investment Management”. In it, Lo proposes a new way of measuring alpha that addresses this age-old question (hat-tip to The Beta Brief for calling the AllAboutAlpha tip line with this one).

(Lo, by the way, scored his own chapter in Peter Bernstein’s new book Capital Ideas Evolving.  Much more on this book in the coming days as we wade through it here at world headquarters.)

Traditional (CAPM) measures of active management have relied on the extent to which a fund is correlated to its benchmark.  Then in 1992, William Sharpe took this notion a step further by regressing mutual fund returns against not just a fund’s own benchmark, but against several passive indices.

More recently, Martijn Cremers & Antti Petajisto proposed a hybrid measure that integrates both a returns-based regression analysis and an analysis of the deviation between fund weights and index weights.  Ross Miller of the State University of New York also recently examined holding-level data in his dissection of Fidelity’s Magellan Fund. And Marcin Kacperczyk & Amit Seru compared portfolio weightings to sell-side recommendations to identify true alpha.

While an examination of position-weightings can certainly provide a definitive view of active management, a nagging question seems to always remain.  How much of what appears to be “active” management is actually noise.  For example, a dart-throwing monkey could assemble a portfolio with weightings that also differed from the benchmark.  But this doesn’t really signify active management.  Lo’s argument suggests that such a fund would be a passive fund, not an active one because the monkey’s active picks aren’t correlated with stocks that actually went up.

The true measure of active management, argues Lo, is the extent to which security weightings are correlated with the individual returns of those securities (the assumption being that an active manager should be overweight stocks that end up appreciating and underweight stocks that end up depreciating).  A high correlation between weights and returns would therefore suggest good forecasting ability.  No correlation, on the other hand, would suggest no forecasting ability and therefore no alpha.

In Lo’s words:

“This is a novel definition of passive and active investing, and has little to do with the standard definitions involving deviations from a benchmark portfolio. I show that a more natural definition for a passive portfolio is one where the portfolio weights are uncorrelated with returns. If weights have no forecast power, then active management is adding no value and the only source of expected return is risk premia, which can usually be generated by a buy-and-hold portfolio.”

Lo says his new method provides additional insight into the nature of returns.  For example, it allows a return to be decomposed into risk premia (passive), security selection (active), and factor timing (also active).  Compared to hedge funds, long-only funds are relatively constrained with regard to factor timing.  As a result, Lo suggests that the isolation of the factor timing element in returns helps explain why hedge funds seem to produce alpha more easily than do long-only funds.

“This decomposition provides one explanation for the seemingly persistent differences between long-only and alternative investments – the long-only constraint imposes a limit to the amount of factor timing that can be accomplished, and this limit may be a severe handicap in environments where factor risk premia change sign…”

This method also helps identify when beta can actually be alpha.  In other words, it identifies when a manager’s market (“factor”) timing ability is actually producing alpha – even in the absence of security-selection skills.

His idea is remarkably accessible to those of us who don’t teach at MIT.  You really just need to know the definition of covariance.

In plain English (using two funds as an example), covariance can be defined as the amount that the product of the average returns of two funds is exceeded by the average product of each month’s returns. Try it in Excel if you’d like.  Create two columns of numbers and multiply their averages.  Now multiply together each pair of numbers from top to bottom to create a third column of data.  The average value of that third column less the number we just calculated is the covariance.

Now imagine that the two columns of data were the portfolio weightings and the monthly returns of two securities.  Lo shows that it’s a simple matter of manipulating this definition of covariance to split the portfolio’s overall return into two components:

He calls the left term the “active component” and the right term the “passive component”.  And he refers to the ratio of the active component to total returns “the active ratio”.  While acknowledging the simplicity of this manipulation, he says it is surprisingly useful.

Lo explains:

“…if a manager has positive weights when security returns are positive and negative weights when security returns are negative on average, this implies positive covariances between portfolio weights and returns, and will have a positive impact on the portfolio’s expected return. In effect, the covariance term captures the manager’s timing ability, asset by asset…”

Revisiting the equation above, we can see that in the absence of any market timing (i.e. any deviation to individual security weightings – where the left term becomes zero), returns come solely from the passive returns of each underlying security (the right term).  This, as Lo points out, is analogous to a simple a buy-and-hold strategy.

“…a portfolio is passive if its weights do not contain any information related to future returns. Whether or not the portfolio is benchmarked is irrelevant. For example, consider a portfolio with a market beta of 1.00, achieved through S&P 500 futures contracts, that also happens to include a diversified buy-and-hold basket of commodities.  The expected return of such a portfolio is likely to exceed the S&P 500 because of the positive risk premium associated with the commodities component, but should the excess return be attributed to active management? Using traditional performance measures, this portfolio is likely to exhibit positive ‘alpha’, but the AP decomposition will yield a very different conclusion. The crucial characteristic of an active portfolio is the deliberate and successful use of information for forecasting returns – this is usually what we have in mind when we speak of ‘investment skill’.”

Lo proposes the following integrated formula as a way “to assess the value-added of hedge funds that make directional bets”:

He continue: “If hedge funds possess factor-timing ability or ‘allocation alpha’, this should be viewed as ‘alpha’ or active management. But if the beta exposures are being generated passively, i.e., not with covariances but with relatively stable weights, then there are cheaper alternatives such as the ‘beta grazers’…or the futures-based hedge-fund beta replication strategies…”

This is actually a pretty easy paper to read.  Just skip the scary parts (like, “…each security i forms a stationary and ergodic stochastic process with finite moments up to order 4…”) and you should be fine.

In the end, Lo has essentially redefined “active management” to include only successful active management.  He assumes that active management of the type doled out by the dart-throwing monkey is not, in fact, active management – but is passive.  On the other hand, one might also argue that it’s “bad” active management, but active nonetheless.  Sure, its result may be tantamount to passive investing, but its activities are active.  (There’s no doubt that such superficially active investing is a necessarily precursor to Lo’s (successful) active management).  So, faced with evidence that a fund’s holdings differ from those of the index, the salient question therefore remains: does the investor buy the active manager’s story?

Next time your kids ask you where alphas come from, refer them to this paper and tell them to get back to you if they have any questions.  That should keep them busy for a while – and allow you to avoid answering some tough questions.

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