A Tool to Construct an Optimal Fund of Funds

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
The table below shows that the weights in the three funds of funds are different. This is due to the fact that FoF1 has not been optimised; FoF2 is the fund of funds with the lowest volatility; and FoF3 is the fund of funds with the lowest risk of extreme negative returns. In FoF3, the weight for hedge fund 1 has been decreased from 18% to 0% and the weight for hedge fund 4 has been increased from 0% to 12%. Why is this the case? Hedge fund 1 has a negative (co)skewness, so it will increase the overall fund of funds extreme risks. Hedge fund 4 has zero (co)skewness, but a high volatility, so it will increase the overall portfolio volatility, but decrease the fund of funds extreme risks.

  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.