A “small-cap bias” in hedge funds themselves?

If you’re in the hedge fund industry, you know the name Pertrac.  These are the guys who make the ubiquitous software platform that many hedge funds use to analyse and report performance to their investors.  Last March, the firm compared the performance of large ($500 million+), medium ($100 million-$500 million) and small (under $100 million) hedge funds to see if size determined success in Hedgistan.  They also compared the performance of young (under 2 years old), middle aged (2-4 years old) and seasoned (4 years old +) hedge funds.

Earlier this week, the company announced the updated results of the same study.  It came as no surprise to researchers that last year’s findings were reinforced.  Young funds and small funds did better than their larger and older cousins.  The chart below appears in the firm’s press release:

You don’t need to be a finance Ph.D. to see the parallels between this research and the work of Eugene Fama and Kenneth French on the “small-cap bias”.  Apparently, small cap stocks aren’t the only small things that tend to outperform.

But what is also striking about this chart is that – despite all the talk about declining hedge fund returns – large hedge funds are producing returns in keeping with historical averages for the group.  (Of course, 2008 may be a different story.)  Declining hedge fund returns are particularly pronounced amongst small hedge funds.

Still, small hedge funds seem to beat large ones every year.  But as the chart clearly illustrates, small hedge funds are also more volatile than larger hedge funds.  Students of the CAPM would be excused for wondering why an investor wouldn’t simply allocate 100% to small funds.  Apparently, investors in large hedge funds are indifferent to the apparent out performance of the small fry.  So are small funds just (effectively) levered versions of the big guys?

With the caveats that this is only a sample of hedge funds, a very unscientific back-of-the-envelope analysis suggests the answer may be “no”.  Volatility does not seem to rise in proportion with returns and therefore the smaller funds tend to have a higher Sharpe ratio than the large ones.

But return volatility may not be the only measure of risk for small hedge funds.  Since the majority of hedge fund blow-ups occur as a result of operational inadequacies, investors just might be implicitly pricing in a form of risk not captured by return volatility.  We’re not suggesting that any investors make such an explicit comparison between large and small funds, but the aggregate effect of their decisions does seem to lead to a CAPM-like outcome.

How much is that hidden risk worth?  Apparently about 3%.  In aggregate investors in the Pertrac sample seem to demand about 3% greater return from small funds for some extra-economic reason (blow-up risk?).  Conversely, they view these risks as the equivalent of about 2.8% of increased return volatility.

The chart below was reproduced from the back of a napkin found lying around the lunchroom at AllAboutAlpha.com.  We plotted the standard deviation of annual returns against the average annual return of the three fund-size categories (note: we used arithmetic average returns, not compounded returns by backing them out of the Sharpe ratios reported by Pertrac in their press release – table at right).

We then drew a capital market line from the risk free rate used in the reported Sharpe ratios (5%) through the large fund data point and made the heroic assumption that an investor could simply lever her holdings of large hedge funds up or down by borrowing or lending at 5% per annum.

As you can see, both the medium sized funds and the large funds produced returns that go beyond what the investor could get if she were to simply lever up or down the (low risk) large funds.  Since investors apparently know about this small fund outperformance, they must be actively electing not to dump all their large funds in favour of small ones.  That small fund outperformance, could be viewed as just enough to make investors indifferent between the battle-test larger funds and the (operationally risky?) smaller funds.  (Medium sized funds seem to have outperformed to the tune of 1.2% vs. the return that would have been achieved by a large fund investor who simply put a small portion of his portfolio in cash.)

Put another way, matching the return of the small funds would have taken a significant amount of leverage for the large fund investor – leverage that would have generated a standard deviation of 9%.  This is nearly 3% above what the small funds actually produced and suggests that investors who are indifferent between large and small funds have implicitly priced the hidden risks of small funds at about 3 percentage points of annual standard deviation.

What’s also striking about the chart provided by Pertrac is that the returns of small, medium and large funds seem to be converging.  Is the advantage enjoyed by small funds already being arbitraged into oblivion?  Small fund bias, we hardly know ya’!

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  1. Walt French
    May 21, 2008 at 11:00 pm

    Another possibility is that it’s easier to slip a small fund into a database after a successful development phase in the nursery, while unsuccessful small funds get merged into other strategies or not reported at all. Ergo, smaller funds — especially, younger ones, which, since I didn’t RTFA, may or not have been corrected for in the work.

    $2 billion funds, of course, don’t just appear out of nowhere and few of them disappear without some parting shot.

    Also, managers of small funds may feel they have almost nothing to risk and take higher bets: a small fund is either dramatically more successful than its peers or is condemned to eternal unprofitability on any asset-based fee schedule. Ergo, higher risks taken (with clients’ money).

    Just speculation, in case it’s not obvious from a close read.

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