Pop Quiz for Long/Short Equity Investors: When does a high “up-capture” not cost you a commensurately high “down-capture”?

CAPM / Alpha Theory 07 Dec 2010

A couple of weeks ago, we lamented the lack of any “tail wind” for hedge funds.  From the low dispersion of security returns, hedge fund returns, and even the hedge fund strategy returns, it appeared that there simply wasn’t a lot for active managers (e.g. hedge funds) to work with.  An interesting research paper published this week by asset manager Commonfund takes a slightly different angle on this phenomenon.  But unfortunately for those waiting for the wind to pick up, the forecast isn’t that much different: expect dead calm.

Author Kristofer Kwait and John Delano use principal component analysis (PCA) to examine what drives the returns of the HFRI Equity Hedge Index.  First, they turn their focus to the S&P 500.

Below is a chart from the paper that shows the “eigenvalue” of the broad market advance/decline variable over a trailing 36 month period.  The eigenvalue is a measure of the share of total volatility explained by changes in the broad market advance/decline variable and is shown in blue (left hand scale).  Kwait and Delano also show the VIX in grey (right hand scale).  (Click to enlarge.)

Notice how the eigenvalue (proportion of S&P 500 volatility explained by the broad market advance/decline) rose when the VIX was low between 2002 and 2008.   As Kwait and Delano put it, “[A]s correlations build among subsets within the market, this eigenvalue would climb as a proportion of the total.”

Regular readers may remember this post about how the period around the turn of the century was marked by a high average stock volatility, but also by a very low security cross-correlation; see chart below from a slide deck by Analytic Investors’ Steve Sapra.  The low average stock by stock correlation around the year 2000 in this chart is congruent with the low eigenvalue for the advance/decline above.

As you can see, this chart ends in 2008.  The eigenvalue chart above from Kwait and Delano shows what happened after that.  Oddly, the eigenvalue stayed high even as the VIX fell.  This is happening in today’s weird combination of high correlations and simultaneous (relatively) low volatility.  You might have also seen in this chart from Credit Suisse’s recent industry overview – see this post for details.

So what does that mean for hedge funds, long/short equity hedge funds in particular?  According to Kwait and Delano, when stocks become correlated, i.e. the eigenvalue for the broad advance/decline factor, it gets harder for long/short managers to retain their asymmetric return profile.  In other words, their up-capture ratio drops while their down-capture ratio rises (see this recent post for more on up-capture and down-capture ratios).  Eventually, if things get really ugly, their up-capture and down-capture ratios converge, meaning they perform no better than the market itself.

Unfortunately for equity hedge fund managers, things have gotten really ugly this year.  The chart below from the Kwait and Delano paper show how the 36 month down-capture ratio of the HFRI Equity Hedge Index is actually higher than its up-capture ratio right now.

The duo then plotted the up-capture and down-capture ratio data on a chart.  Naturally, you’d expect the relationship to be upward sloping – that a higher up-capture ratio would come with the “cost” of a higher down-capture.  They did this across 6 periods.  Here’s the June 2004 – May2007 chart (ignore the grey line for now):

If you look closely, you can see that the intercept of the black regression line is very positive, meaning that investors could, on average, get a healthy up-capture percentage with zero down-capture, i.e. a free lunch.  Kwait and Delano found 3 such 3-year periods when this free lunch was significant – and they all happened when the eigenvalues were falling.  By contrast, periods when the eigenvalues were rising yielded relatively small free lunches:

They go on to adjust these constants (or intercepts) for the “risk neutral fair value of up-capture for each period” using options pricing theory, but the conclusion is the same: periods of rising broad advance/decline eigenvalues are also those where long/short equity managers have trouble generating a high up-capture without paying for it in higher down-capture.

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