The expanding (alpha) universe

CAPM / Alpha Theory 23 Dec 2007

Apparently, the universe is big.  Really big.  We learned this week that it holds about 10^80 atoms (see previous posting).  But how big is the alpha universe?  How much alpha can possibly be generated by hedge funds (or any active manager)?  Neither universe is easy to get your head around and neither can be measured directly.

We tackled this question about a year ago in relation to a seminal white paper written by Lars Jaeger and Christian Wagner.  But we thought it would be interesting to revisit this given the myriad of new estimates that have recently come out on the size of the hedge fund industry.

To get to the bottom of this, we went right to the expert on the topic, Hilary Till of Chicago-based Premia Capital Management.  Till wrote a paper back in 2004 for both the Journal of Alternative Investments and the AIMA Journal on the theoretical capacity of the hedge fund industry.  The AIMA Journal version of the piece was called “The Capacity Implications of the Search for Alpha” and Jaeger and Wagner actually cite it when establishing a conceptual framework on hedge-fund capacity.

In a summary of 2004 article (available here) Till says:

“If hedge funds are exploiting market inefficiencies, this means that other investors are supplying those inefficiencies. This means that, unfortunately, we can’t all profit from exploiting inefficiencies. Therefore, there is a natural cap on the potential size of the hedge fund industry, assuming that hedge funds are indeed exploiting inefficiencies rather than taking in risk premiums.”

(Since 2004, many have come to realize that hedge funds don’t just exploit inefficiencies.  In fact, much of their aggregate returns can be explained by “taking risk premiums” (a.k.a. “alternative beta”).  We’ll return to this later.)

Till argued that the world’s investors were willing to put up with a certain amount of market inefficiency.  That is, they were willing to offer a small part of their lunch to the alpha-seekers.  She picks 0.50% as investors’ “allowable inefficiency” – its annual free lunch.  Further, she assumes that global equity and bond markets are $55 trillion in size (a 2001 estimate).  Thus, US$275 billion of the world’s capital markets were being offered each year to alpha-seekers who could exploit market inefficiencies.

Assuming that hedge fund investors required a 10% annual excess return in order to invest their capital, Till concluded that the world’s total alpha potential was about $2.75 trillion.

She ran the analysis using different “allowable inefficiencies” (0.75%, 1.0%) and investor return requirements (7.5%, 5.0%).  The results ranged up to $11 trillion (see table).

At the time of Till’s analysis, Putnam Lovell estimated that hedge funds would represent 3% of global high net worth and institutional assets by 2010.  Till pointed out that this was consistent with an “allowable inefficiency” of about 0.3% and a required excess return of 10%.

Till recently told that new estimates for the size of global capital markets will impact these numbers.  She cites a recent McKinsey report (see related posting) that says global financial assets were US$167 trillion in 2006.  This would approximately triple Till’s 2004 estimates.

Assuming the highest possible estimate of hedge fund industry size ($4 trillion – see related posting), Till’s original analysis may still be on the mark. This would make hedge funds about 2.4% of global markets – exploiting 0.25% allowable inefficiencies and delivering investors 10% excess returns.

The gradual realization that hedge fund returns are not “pure alpha” but are laced with various risk premia (“alternative betas”) means that the figure may be even higher, as also pointed out by Géhin and Vaissié of EDHEC-Risk in their 2005 paper, The right place for alternative betas in hedge fund performance. (Till is also a research associate at EDHEC-Risk.)

If hedge fund investors are assumed to require a 10% return, only a portion of that may actually have to be truly excess (i.e., derived from market inefficiencies). This would increase the calculated capacity of the hedge fund industry.

But one could also argue that the inefficiencies apparently not being exploited by hedge funds after all are actually being exploited by the rest of the capital markets.  After all, hedge funds don’t have a monopoly on alpha generation.  (Till cites MIT’s Stephen Ross as one proponent of this idea).

Till cites the US mutual fund market timing scandal as evidence that “allowable inefficiency” may actually be around 0.50%  (increasing the theoretical size of the hedge fund industry ceteris paribus).  In an email to, she writes:

“In one aspect of this scandal, US mutual funds struck the Net Asset Value (NAV) for European mutual funds based on Europe’s close, which is about 12pm US-time. Then the mutual funds would allow anyone to buy or sell these funds at this stale NAV until late afternoon US time. If there were a dramatic market event after 12pm US-time, and say the US equity market rallied, one might expect that European funds would perform similarly well the next morning. A day trader could buy the European fund in the US afternoon at stale, advantageous prices. For years, there had been academic studies pointing out that buy-and-hold investors were losing something like -50 basis points per year from this activity (see related research). But these studies didn’t seem to attract much attention at the time. Later when this effect caused a drag in performance of some international equity mutual funds by over 100 basis points per year, then this effect apparently became too egregious, and the scandal finally hit the mainstream press as well as attracting adverse regulatory attention. (see related research).  This re-confirms the tolerance for inefficiencies at some level since mutual-funds continued having a stale-pricing problem, but at a reduced level compared to when the scandal broke into the headlines.”

Like the size of the physical universe, we may never actually know the total size of the world’s alpha universe.  Neither universe can be measured directly and therefore must be guessed using a series of assumptions that scientists refer to as SCWAGs.  While these assumptions evolve, Till’s methodology provides an enduring framework for analyzing the never-ending flow of SCWAGs.

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