In an earlier post we examined the covariance between the
Poor Man's Hedge Fund and the SPY ETF. Using a
cross-validation method, we demonstrated an apparently stable linear
relationship between the total montly returns of the Poor Man's Hedge Fund
and those of the
SPY ETF. Given this relationship, it is natural to ask whether it can
be exploited to remove systematic risk factors that are not idiosyncratic to
the hedge fund trading style — which is a long winded way to say that we
can hedge out market risk, for example by taking a long position in the
SDS ultra-short inverse tracking ETF.
The chart above is visually dense (perhaps violating the suggestions of
Edward Tufte's The Visual Display of Quantitative Information)
but has a lot of information to convey, so please forgive me. Most strikingly,
the vertical bars indicate which dates were in the training set (shaded
grey) or validation set (left white). These set memberships were
chosen at random with a 50:50 chance of a given date being in each set. I
seeded the random number generator with a known seed (in this case the number
12345), so that I could reproduce the chart made and importantly
to prevent selection bias that I might engage in by picking a chart
that looks good.
The four lines are a value added monthly index which represents the
cumulative total return of investing in each vehicle. Individually, they are:
-
the total return, including dividends, of the SPY ETF;
-
the cumulative return of the dynamic trading risk factor;
-
the total return, including dividends, of the Poor Man's Hedge Fund tracking
portfolio;
-
the cumulative residual return of the Poor Man's Hedge Fund, using the
β to SPY estimated with the training set data.
The stories of each time-series are interesting. The total return of the SPY,
which is designed to track the S&P 500 share index, for the entire
decade to the and of May, 2009 is a loss of 23%. This is a terrible return for
a decade. Conventional wisdom is that a ten year horizon for an equity
investment to pay off is ten years. (Even
Warren Buffett suggests this horizon in interviews.) Over the same
period, investment in the dynamic trading risk factor, which should
represent the performance of a typical hedge fund, has delivered a
return of 65%. On its own, the Poor Man's Hedge Fund delivered 27%
— not as good as a pure hedge fund factor play, but impressive versus the
benchmark. On a residual basis, this series is an outstanding performer, giving
a total return of 111% over the period. However, one should not write off the
hedge funds — as we have not presented an analysis of that series with
its market risk exposure hedged out.
As a final datum, we can look at the simple sharpe ratio (the ratio of the
annualized average monthly return to the annualized standard deviation) of the
residual returns series; this is 1.1 for the training set and 0.6 for the validation
set.