A technique to construct an optimal fund of funds

Laurent Favre, founder, AlternativeSoft AG, on defining what kind of risks and what kind of returns are needed in order to construct an optimal fund of funds.


First, we have to define what is the risk for a hedge fund 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, for example lower than 5 per cent annualized return for a Swiss pension fund. Does volatility measures that? The answer is no. This is why a better measure of risk is the downside risk, which 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 in the future the same annualized return as in the past or do we have to change to a lower expected hedge fund return? Clearly, we have to use an expected return for each hedge fund. This is a difficult task, as each hedge fund should have its own expected return.


Third, the interdependence between the each funds have to be measured. Does the correlation coefficient measures this interdependence? The answer is no. This is due to the fact that the hedge funds, first, have non normal distribution and, second, that 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 hedge funds. The technique now is to find a way to measure each of them and combine them together in a simple way.


This is possible with the Omega, the Modified Value-at-Risk or the Conditional Value-at-Risk optimizations. Each of these measures account for downside risks and non-linear interdependence between the hedge funds. For example, if a hedge fund, with a low volatility, active in Distressed, has been badly performing in August 1998, the optimization will reduce its fund of funds optimal weights. This will decrease, at the fund of funds level, the probability to have an extreme negative return.


We illustrate these findings in the table below. Assume we have the choice between three fund of funds and each fund of funds, the universe is composed of 10 hedge funds which have passed the qualitative due diligence process. We do not want more than 20 per cent in a single hedge fund. The used time window, for the optimization, is Jan 00 to Mar 04. Each fund of funds manager has a different technique to allocate the weights to the 10 hedge funds:


FoF1: equally weighted
FoF2: mean-variance optimization
FoF3: downside risk optimization


The table exhibits that the weights in the three fund of funds are different. This is due to the fact that FoF1 has not been optimized, 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 hedge fund1 weight has been decreased from 18% to 0% and the hedge fund4 weight has been increased from 0% to 12%. Why is this the case? Hedge fund1 has a negative (co)skewness, so it will increase the overall fund of funds extreme risks. Hedge fund 4 has a zero (co)skewness, but a high volatility, so it will increase the overall portfolio volatility, but decrease the fund of funds extreme risks.


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                                        FoF1                          FoF2                        FoF3


                                     (equally weighted)  (mean variance)    (downside risk)


Hedge fund1                 10 per cent               18 per cent                        


Hedge fund2                 10 per cent               15 per cent             15 per cent


Hedge fund3                 10 per cent               20 per cent             20 per cent


Hedge fund4                 10 per cent                                             12 per cent


Hedge fund5                 10 per cent               15 per cent             18 per cent


Hedge fund6                 10 per cent               20 per cent             20 per cent


Hedge fund7                 10 per cent               10 per cent             10 per cent


Hedge fund8                 10 per cent                                                


Hedge fund9                 10 per cent                                                


Hedge fund10               10 per cent               2 per cent                5 per cent


Total                             100 per cent             100 per cent           100 per cent


Historical


annualized return        12.15 per cent          11.88 per cent        11.88 per cent


Historical annualized


standard deviation       5.75 per cent            2.35 per cent          2.37 per cent


Historical skewness    -0.12 per cent           0.30 per cent          0.36 per cent


Max monthly loss         -2.21 per cent           -0.26 per cent         -0.30 per cent



In this example, we see that some hedge funds are dedicated to fund of funds volatility reduction, such as hedge funds 2, 3, 5, 6, 7 & 10. Other hedge funds are dedicated to extreme risks reduction such as hedge fund 4. Hedge fund4 is like an implicit hedge in the overall fund of funds. Hedge fund4, historically, was able to be positive when all the other hedge funds in the fund of funds had negative returns. This is why an approach that minimizes the downside risks is valuable for every investor who wants firstly to have a fund of funds with a low volatility, and secondly to have a fund of funds that will not loose money during market turmoil.


The HFOptimizer platform, from AlternativeSoft AG, has solved this issue. It is possible to construct a fund of funds by minimizing, not only volatility, but also the extreme negative risks.


 

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