Tuesday, January 17, 2012

Measuring Whitney Tilson's alpha

Whitney Tilson is a value investor.  He co-manages T2 Partners with Glenn H. Tongue.  He was one of the authors of Poor Charlie’s Almanack, generally the best book on Berkshire Hathaway Vice Chairman and multi-billionaire Charlie Munger.

Tilson’s funds lost 24.9% of their value in 2011.  Despite that, they have returned an annualised 6.0% since inception in January 1999.  This is better than the S&P 500 which has returned 2.0% p.a since January 1999.  The total return is 114.2% (T2 Partners) vs 29.2% (S&P 500).

Given that substantial outperformance, you might think that it was obvious that Whitney Tilson can generate “alpha”.  Alpha is a financial term for the risk-adjusted return of an active manager.  Basically, if a manager generates alpha, the manager can achieve the same return as the market with lower risk, or higher returns than the market without a corresponding increase in risk.

I personally think it is very likely that Whitney Tilson can outperform the market.  His letters to investors seem well thought out and he usually has very good justifications for his stock positions.  This, coupled with his performance, suggest to me, a prima facie case for outperformance.  So I decided to test whether a regression shows that Whitney Tilson can generate alpha, or whether he is simply exposing his funds to more risk and achieving a corresponding return.

First, I found and inputted his monthly returns from his later letter from January 1999 to December 2011 into a spreadsheet.  I matched that to the market return minus the risk free rate for all those dates.  I then performed a regression to calculate the 3-factor (Fama-French) and 1-factor (capital asset pricing model) alpha.

I find the story of the 3-factor Fama-French story interesting.  Fama notes in a recent paper that one reason that “value” (as measured by low price-to-book ratios) might outperform growth is that people get some non-financial utility from owning growth stocks.  This makes sense to me.  Some people must like being able to say they own an “up-and-coming” stock rather than an old skeleton they’re just trying to squeeze the last bit of value from.  Think of the film (or book) Moneyball.  It must be exciting to pick young up and comers in your ball team rather than David Justice, a 37 year old who is clearly past his prime.  Despite that, there is more value (as measured by price for performance) in picking David Justice over young glamour players (or at least there was until the Oakland Athletics popularised the strategy). 

Anyway, the 3-factor Fama-French measurement came about because people started to notice that there was a persistent outperformance by “value” stocks (low price to book) and small capitalisation stocks.  One theory was that these stocks were inherently more risky.  But by all conventional measures of risk, they’re not more risky.  The next theory is that it’s “unmeasured risk”.  Effectively the argument is that because they outperform, they must be more risky.  This seems like a triumph of theory over evidence.  It presupposes that the market is perfectly efficient, then explains evidence of its inefficiency (the outperformance of value and small cap stocks) by referring back to the theory and insisting it must be true.  In the face of the question – where is the excess risk? The response is that it can’t be measured yet. 

If the risk can’t be measured, I find it implausible (although not impossible) that market participants are factoring in this unmeasured risk to cause the pricing discrepancy and outperformance.  I find Fama’s proposition of non-financial utility in growth and big cap stocks more convincing.

Now, whether there is more alpha in value and small cap stocks or whether there is more risk is largely irrelevant for our purposes of measuring manager performance.  The key is that you can cheaply access this higher return (be it alpha or risk) through an index fund devoted to value stocks (as measured by low price to book ratios) or small cap stocks (or even both).  Given that ability, you shouldn’t pay a manager high fees to just get you that.

So what does the regression show?

The regression shows that using the 1-factor capital asset pricing model, Whitney Tilson generates 0.305% of alpha per month.  That’s significant, but unfortunately we don’t have enough data points to make it statistically significant.  The null hypothesis is that Tilson has no alpha.  It’s been too long since I did any statistics, but from what I gather, the p-value suggests that if we assume the null hypothesis, there is a 33% chance of obtaining his results just by luck.  The t-stat is 0.977.

Using the 3-factor Fama-French data (ie, controlling for the value effect and the small cap effect), Whitney Tilson generates 0.216% of alpha per month.  That’s not bad either, but the p-value is 0.496 – ie, assuming that Tilson has no alpha, there’s a 49.6% chance of obtaining his results just by luck (assuming my interpretation of a p-value is correct).  The t-stat is 0.683.


Unfortunately, 154 months just isn’t enough to give us statistically significant results.  My own personal null hypothesis is that Tilson can generate alpha, but we won’t know for many many years.  By that time, we’re very unlikely to be able to invest money in his fund.  He’ll either be shown to have no alpha and have closed down, or be some alpha generating machine with too much money clogging up his alpha machine and anchoring his performance.

UPDATE: I realised I rudely forgot to thank Turnkey Analyst for the lesson in how to run this regression. He runs through the method and includes a video here.

No comments:

Post a Comment