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Download PDF, Issue 26 - Swiss Futures and Options Association

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“These results seriously<br />

question the diversification<br />

rationale for engaging<br />

in Alternative Investments.”<br />

Hedge Funds<br />

Chart 2: Correlation of Returns between Hedge Fund Indices, Equities <strong>and</strong><br />

Bonds, 1999–2004.<br />

Comparing Strategies A <strong>and</strong> B, one<br />

would likely be tempted to infer that a<br />

probability of positive return of about<br />

50 bp., for instance, is higher for<br />

Strategy A than for Strategy B. Based on<br />

the frequency of returns, it is hard to dispute<br />

that point, since the returns on<br />

Strategy A have a mean of 48 bp. <strong>and</strong> a<br />

st<strong>and</strong>ard deviation of only 45 bp. The<br />

returns on Strategy B, on the other h<strong>and</strong>,<br />

display a st<strong>and</strong>ard deviation of 179 bp.,<br />

or about 4 times greater.<br />

According to the transitive principle<br />

<strong>and</strong> taking this logic further, the probability<br />

of a positive return above +0.5%,<br />

say 2%, for Portfolio A should always<br />

exceed the corresponding probability for<br />

Portfolio B.<br />

35<br />

Again, the clustering of Hedge Fund<br />

returns in the top right quadrant does<br />

not differ much from the previous picture.<br />

Outliers are still the same as before.<br />

Similar plots emerge for returns during<br />

shorter periods between May 1999 <strong>and</strong><br />

May 2004.<br />

What does this mean? For all the<br />

diversification benefits that hedge fund<br />

managers are supposed to bring to<br />

investors, it is simply too risky – <strong>and</strong><br />

politically incorrect – to underperform<br />

traditional asset classes when these<br />

exhibit positive returns. Simply put, two<br />

different risk frames are at play to make<br />

investors’ perspective lop-sided in their<br />

Hedge Fund performance assessments:<br />

• during downturns, investors are biased<br />

to focus on the relative performance,<br />

i.e. they lose less than long-only strategies;<br />

any positive absolute return that<br />

they can produce is icing on the cake;<br />

• during uptrends, investors praise hedge<br />

funds’ lower risk relative to long-only<br />

strategies – which makes up for the<br />

underperformance bias of the former<br />

category vis-à-vis the latter.<br />

As risk-adjustment in Alternative<br />

Investments relies overwhelmingly on<br />

historical simulation alone (see the next<br />

point), there is no way to include in the<br />

process the significant correlations<br />

shown earlier.<br />

Frequency <strong>and</strong> probability of<br />

returns,<br />

Consider the following chart:<br />

P A(0.5%) > P B(0.5%)<br />

P A(2%) > P B(2%)<br />

<strong>and</strong>, in addition,<br />

P A(2%) < P A(0.5%)<br />

This way of thinking assumes implicitly<br />

that underlying prices may follow a continuous<br />

function. Market prices, however,<br />

can <strong>and</strong> do experience discontinuities,<br />

Chart 3: Using Frequency in Drawing Probability Assessments for Trading<br />

Strategies.<br />

SWISS DERIVATIVES REVIEW <strong>26</strong> – NOVEMBER 2004

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