Any new investment for inclusion in a portfolio must offer an attractive, yet different, risk and reward profile compared to other asset classes. If not, adding it will produce little value. If hedge funds are included in an investment portfolio along with equities, bonds or other investments, they must not be viewed in isolation. Attention must be paid to how they interact with those other asset classes and whether their inclusion helps to meet its overall investment objectives. In broad terms, it is assumed that investors do not consider taking on an additional unit of risk unless it is accompanied by more than one unit of compensation. Investors want efficient investments that can generate the highest excess return with the lowest level of volatility. Although hedge funds may not produce a higher return than equities and bonds at all times, they do demonstrate consistently lower volatility. If they are mixed with equities and bonds in a hypothetical portfolio, portfolio optimisation can suggest that up to 100% of the portfolio should be allocated to hedge funds. Of course, intuitively investors would not tend to invest 100% of a portfolio in one asset class. Measures such as skewness and kurtosis can help to give a fuller picture of how hedge funds behave when combined with equities and bonds and how they can be weighted in portfolios.
Skewness and Kurtosis
Although hedge funds offer stable returns most of the time, they are occasionally subject to large movements, either positive or negative. For instance, convertible bond arbitrage managers typically establish long positions in convertible bond issues and at the same time implement short positions in the common stock of the bond issuers as a hedge. According to the HFR Convertible Arbitrage index, the strategy has achieved an average annual return of over 10% during the past 15 years with only 3.4% volatility. This creates a favourable Sharpe ratio of 1.8.
Firstly, the bulk of the returns delivered, shown in the middle right region of the graph, are positive and around 1% to 2%. However, there are a small number of large negative monthly returns ranging from 2% to 3% in the left-hand corner. By simply counting the occurrences, we can calculate that the probability of the convertible bond arbitrage index declining by 2% or more works out at once every five years. Yet normal distribution analysis, which is often applied to traditional asset classes, predicts that this sort of drawdown would almost never occur. This explains the importance of using other risk measurement statistics such as skewness and kurtosis. Skewness describes the asymmetry of distribution of an investment's returns. If a hedge fund posts more large, positive returns than large, negative returns, it is said to have positive skew and vice versa - the higher the skewness the better.
If a hedge fund experiences large swings in performance in either direction, it is said to have high kurtosis. Kurtosis explains the shape of the distribution curve. Higher kurtosis means that the majority of returns are close to the average but the outlying or extraordinary returns are widespread. Lower kurtosis suggests there is a more even pattern to the frequency of returns between highest and lowest, ie there are more results in the mid-range. Lower kurtosis is often more desirable in an asset class or fund performance because then neither the best nor worst recorded results are as distant from the mean. Unlike skewness, where a high value is most desirable, most investors are likely to prefer a more balanced kurtosis measure. The method of calculating skewness and kurtosis emphasises large negative movements in performance more than standard deviation does. This would seem to tie in with investor preference; since investors tend to dislike large losses more than they like large gains.
How Do Different Asset Classes Compare?
In the above chart, asset classes are ranked from that with the lowest Sharpe ratio (commodities) to that with the highest Sharpe ratio, (funds of hedge funds) taking an average measure over the past 15 years. Neither stocks nor bonds rank highly but their skewness and kurtosis scores are varied. Hedge funds display a favourable Sharpe ratio, slightly negative skew and quite high kurtosis. This is the price that seems to have to be paid for a superior Sharpe ratio. It should be noted that the chart highlights the features of the indices at the aggregate level. Individual securities or managers may or may not behave similarly.
Clearly, the optimal solution would be to retain good performance but strip out the risk. While it is not possible to eliminate risk totally, we can mitigate it. From a portfolio manager's and investor's perspective, it makes sense to work with managers who demonstrate the aptitude, as well as attitude, to deal not only with everyday risk, but also event risk through the use of qualitative and quantitative tools. By implementing a robust manager selection and monitoring process it is possible to allocate money across managers prudently and be rewarded appropriately. The analysis that we have looked at here suggests that portfolio managers need to realise the pros and cons associated with hedge funds in order for the asset class to be beneficial within a well-diversified portfolio.
Interaction with Other Asset Classes
It has been well-documented that combining hedge funds with equities and bonds in a portfolio enhances overall returns and reduces volatility (as measured by standard deviation). However, what happens when this combined portfolio experiences large movements in performance, as described earlier? The chart on the following page shows four portfolio simulations which demonstrate this.
The initial portfolio (the far left column) is equally weighted between stocks and bonds. In the next three portfolios hedge funds are added as a weighting of 30% of the portfolio in three different ways. Firstly, (the second column from the left) equities and bonds are replaced by hedge funds in equal proportions, (equities 35%, bonds 35% and hedge funds 30%). This results in an improved Sharpe ratio but deteriorating skewness and kurtosis. In the third portfolio, bonds are replaced with hedge funds so the portfolio comprises 50% equities, 30% hedge funds and 20% bonds. This time, the Sharpe ratio improves only marginally, yet skewness and kurtosis both deteriorate even more significantly. Finally, equities are replaced by hedge funds (50% bonds, 30% hedge funds and 20% equities). This time, skewness improves while kurtosis rises only moderately. These results imply that hedge funds can improve the Sharpe ratio of portfolios but they react quite differently with other assets. In this example, we can see that hedge funds can sometimes mix better with bonds than with equities. By and large though, it should be noted that different researchers produce different results, probably due to the different measurement periods used.
Asset allocation is not a one-off decision. A fixed formula of how much to allocate to equities, bonds, hedge funds or any other type of investment makes no allowance for changing market conditions. The table below explains why asset allocation must be an ongoing activity.
The returns of different asset classes vary considerably. Equities, represented by the S&P 500, performed best during the four years from 1995 to 1998 and moderately well in 1999. However, they would have warranted an underweight position relative to the other assets in portfolios in the following three years and an increased weighting in 2003 and 2004. Bonds offered reasonable returns in the early 1990s and in 1998 and 2002, as shown, but warranted an underweight position in portfolios in other years. In some years, bonds and equities have both languished at the bottom of the rankings, whilst hedge funds have only occasionally appeared in the bottom half of the table, in terms of relative performance.
This is a reminder of the need to spread investment risk and the value of including hedge funds in that spread. This does not mean an abandonment of bonds or equities. Hedge funds do not come top year after year. Hedge funds should be considered as a part of a balanced portfolio, managed in a dynamic fashion. As we have illustrated in this piece, hedge funds can be constructive when introduced into a portfolio but this does not replace the need for active asset allocation, whereby exposures to different asset classes are adjusted in response to the prevailing economic and investment conditions, in order to achieve optimal results.
