Alpha as a Statistical Outlier

Alpha, which attempts to measure the risk-adjusted ability of portfolio managers against a benchmark, has become a moniker for manager and portfolio “performance.” However, we wouldn’t be wrong to consider that “performance” may be more of a misnomer than moniker.  Alpha’s link to outperformance, (when alpha is positive) debatably services what some might claim to be hyperbolic promotion from the finance industry, something I neither defend nor refute. However, given this, alpha may be misleading.

Numerically-expressed measures wrapped inside Greek symbols enjoy an almost empirical mystique. Alpha is no exception, providing a crucible in which the latest portfolio management stars are forged to be later celebrated by finance media and pundits. What bears repeating, because of this “star manager” phenomenon, is that positive “alpha” is deemed synonymous with “outperformance.”  This synonymy hides a consideration, a loose thread in a poorly tailored seam used to tie manager performance to alpha.

Bill Miller, former manager of the Legg Mason Value Trust enjoyed an incredible 15 year streak in beating the S&P 500.  To put this extraordinary feat in perspective, SPIVA, which measures the performance persistence of portfolios like that of Mr. Miller, found that within a four-year period (2008-2012) there was a 99.82% chance that a manager’s top quartile portfolio would eventually fall, landing between the fissures of the bottom three performance quartiles.  Using data from 1955 -1964, Michael Jensen, the designer of alpha, found dire results as well.  Out of 115 managed portfolios, alpha averaged a negative 1.1%

Given SPIVA’s findings, it is not unreasonable to entertain whether Mr. Miller’s streak, and other’s like his, in which positive alpha persists beyond a few years, is from skill (which “alpha” as “performance” staunchly implies) or is in part or whole from luck (which “alpha” as “performance” does not entertain).  In the latter instance “superior performance” might be a statistical outlier, no more than an aberration brought about by some degree of chance.

The alpha formula: αp= rp – [rf p(rm-rt)], simply compares a portfolio’s return with a risk-adjusted market return and, as a quantitative and results-based measure, does nothing to suggest the hand of chance in the results. Nonetheless, chance invites a clustering phenomenon. When the clustering is valuable to us, we call it a “lucky streak.”  If we flipped a coin 200 times, we would expect to see consecutive heads or tails.  In fact, if we did not see these streaks, we’d be justified in questioning if the flips were truly random.  If we kept flipping, we’d eventually have rare streaks of 10 or even 20 consecutive heads or tails, perhaps similar to a 15-year outperformance streak of a managed portfolio.

Streaks and statistics can notoriously go against our intuition. Consider entering a classroom of fifty-six kids and considering the likelihood that two of them share the same birthday.  Remarkably, the probability is 99%. Had we paid attention to the media and invested with Bill Miller’s portfolio two years before its peak, we would have basked in his “alpha,” enjoying a latitude north of the S&P 500.  Ultimately, however, we would have witnessed a drop, winding up with a ten year return of 1.55% versus the S&P’s 7.08%.

3 Responses to "Alpha as a Statistical Outlier"

  1. D. Chadwick   August 6, 2013 at 12:27 pm

    David, I found you and had a good read. Like your language, it makes interesting and fun to read..

  2. xw3t   August 7, 2013 at 2:55 am

    this is a similar thesis to Taleb's "Fooled by Randomness"

  3. David Stackpole   August 7, 2013 at 8:20 am

    Yes Indeed. Xw3t. Thank you for bringing up Taleb, who discusses our ability to find meaning and structure in randomness.

    What is particularly interesting to me is the *semantic implications* of alpha as performance. I say this because this implied relationship doesn’t entertain accident or fortunate deliberatoin in the mix.

    Since varied degrees of accident could be responsible for manager success, and since we don’t know the degree in the mix for any manager, such measures (and the media that supports them) should be considered cautiously.