To construct an optimal fund of funds,
the risk and return of each hedge fund included
need to be identified. In this article,
we will focus on defining the kinds of risk
and return required.

First, we have to define what the risk is
for a hedge fund investor or a fund of funds
investor. Risk is the possibility that,
in the future, the investment's value will
be lower than today's value or lower than
a certain threshold. This threshold might,
for example, be the 5% annualised return
for a Swiss pension fund. Does volatility
measure that? The answer is no. This is
why a better measure of risk is downside
risk. Downside risk can be the Omega measure,
the Modified Value-at-Risk, the Conditional
Value-at-Risk or the downside volatility.

Second, the hedge fund return has to be
assessed. Do we expect the same annualised
return in the future as in the past or do
we have to adjust our expectations to a
lower hedge fund return? Clearly, we have
to use an expected return for each hedge
fund. This is a non-trivial task.

Third, the interdependence between each
fund has to be measured. Does the correlation
coefficient measure this interdependence?
Definitely not. This is due to the fact
that hedge funds, firstly, have non-normal
distribution and, secondly, they are exposed
to global market event risk.

The three ingredients needed to construct
an optimal fund of funds have been selected:
the downside risk, the expected return and
the interdependence between the hedge funds.
The challenge is now to find a way on how
to measure each of these and how to combine
them together in a simple manner. This is
possible with the Omega, the Modified Value-at-Risk
or the Conditional Value-at-Risk optimisations.
Each of these measures account for downside
risks and non-linear interdependence between
the hedge funds, at the fund of funds level.
For example, if a hedge fund, with a low
volatility and is active in distressed securities,
has been badly performing since August 1998,
the optimisation will reduce its optimal
weight in the fund of funds. This will decrease,
at the fund of funds level, the probability
to have an extreme negative return.

We illustrate these findings below using
the example of three different funds of
funds. For each fund of funds, the universe
is comprised of ten hedge funds which have
passed the qualitative due diligence process.
We do not want more than 20% in a single
hedge fund. The used time window for the
optimisation is Jan-00 to Mar-04. Each fund
of funds manager has a different technique
to allocate the weights to the ten hedge
funds:

- FoF1: equally weighted

- FoF2: mean-variance optimisation

- FoF3: downside risk optimisation

FoF1 (equally weighted) | FoF2 (mean-variance) | FoF3 (downside risk) | |
---|---|---|---|

Hedge fund 1 | 10% | 18% | |

Hedge fund 2 | 10% | 15% | 15% |

Hedge fund 3 | 10% | 20% | 20% |

Hedge fund 4 | 10% | 12% | |

Hedge fund 5 | 10% | 15% | 18% |

Hedge fund 6 | 10% | 20% | 20% |

Hedge fund 7 | 10% | 10% | 10% |

Hedge fund 8 | 10% | ||

Hedge fund 9 | 10% | ||

Hedge fund 10 | 10% | 2% | 5% |

Total | 100% | 100% | 100% |

Historical annualised return | 12.15% | 11.88% | 11.88% |

Historical annualised standard deviation | 5.75% | 2.35% | 2.37% |

Historical skewness | -0.12 | 0.30 | 0.36 |

Max monthly loss | -2.21% | -0.26% | -0.30% |

In this example, we see that some hedge funds contribute to fund of funds volatility reduction such as hedge funds 2, 3, 5, 6, 7 or 10. Others play a role to extreme risks reduction such as hedge fund 4. Hedge fund 4 is like an implicit hedge in the overall fund of funds. Hedge fund 4, historically, was able to generate positive return when all the other hedge funds in the fund of funds had negative returns. This is why an approach which minimises the downside risks is valuable for every investor who wants a fund of funds with low volatility, as well as one that will not lose money during market turmoil.

The HFOptimizer platform from AlternativeSoft AG will help solve this issue. With this tool, it is possible to construct a fund of funds by not only minimising volatility but also the extreme negative risks. With this and many other features, HFOptimizer is therefore well suited for fund of funds construction.