INDUSTRIAL ENGINEERING APPLICATIONS IN FINANCIAL ASSET MANAGEMENT: COMBINING MEAN-VARIANCE ANALYSIS WITH OTHER TECHNIQUES—CONSTRUCTING OPTIMAL HEDGE FUND PORTFOLIOS

COMBINING MEAN-VARIANCE ANALYSIS WITH OTHER TECHNIQUES—CONSTRUCTING OPTIMAL HEDGE FUND PORTFOLIOS

Because of the difficulty of identifying new assets that shift the efficient frontier upward, some investment managers have taken to creating their own. These assets are often ‘‘bottoms-up’’ construc- tions that in aggregate possess the desired return, risk, and correlation characteristics In the case of funds of hedge funds, the current industry practice is simply to assemble judg- mentally a montage consisting of well-known managers with established track records. Although some effort is expended towards obtaining diversification, a quantitative approach is seldom em- ployed. As a consequence, most portfolios of hedge funds exhibit positive correlation with other asset classes such as stocks. This became obvious in 1998 when many hedge fund portfolios produced negative performance at the same time equity prices fell following the Russian debt default.

Lamm and Ghaleb-Harter (2000a) have proposed a methodology for constructing portfolios of hedge funds that have zero correlation with other asset classes. Their approach brings more rigor to the design of hedge fund portfolios by using an MV optimization format under the constraint that aggregate correlation with traditional assets is zero.

The steps in this process are as follows. First, hedge fund returns are decomposed into two components using a reformulation of Sharpe’s (1992) style analysis. Specifically:

This is the same as the standard MV model except the portfolio return takes a more complex form (21) and an additional constraint (23) is added that forces net exposure to traditional assets to zero.

Also, constraint (26) forces sufficient diversification in the number of hedge funds.

Obtaining a feasible solution for this problem requires a diverse range of beta exposures across the set of hedge funds considered for inclusion. For example, if all equity betas for admissible hedge funds are greater than zero, a feasible solution is impossible to attain. Fortunately, this problem is alleviated by the availability of hundreds of hedge funds in which to invest.

A significant amount of additional information is required to solve this problem compared to that needed for most MV optimizations. Not only are individual hedge fund returns, risk, and correlations necessary, but returns must also be decomposed into skill and style components. This requires a series of regressions that link each hedge fund’s return to those of traditional assets. If 200 hedge funds are candidates, then the same number of regressions is necessary to estimate the ex and � parameters.

Table 7 presents optimum hedge fund portfolios that maximize returns for given risk levels while constraining beta exposure to traditional assets to zero. The optimization results are shown for (1) no constraints; (2) restricting net portfolio beta exposure to traditional assets to zero; (3) restricting the weight on any hedge fund to a maximum of 10% to assure adequate diversification; and (4) imposing the maximum weight constraint and the requirement that net beta exposure equals zero. Alternatives are derived for hedge fund portfolios with 3% and 4% risk.

Adding more constraints shifts the hedge fund efficient frontier backward as one progressively tightens restrictions. For example, with total portfolio risk set at 3%, hedge fund portfolio returns fall from 27.4% to 24.4% when zero beta exposure to traditional assets is required. Returns decline to 23.0% when hedge fund weights are restricted to no more than 10%. And returns decrease to 20.4% when net beta exposure is forced to zero and hedge fund weights can be no more than 10%.

CONCLUSION

This chapter has presented a brief introduction to asset management, focusing on primary applica- tions. The basic analytical tool for portfolio analysis has been and remains MV analysis and variants of the technique. Mean-variance analysis is intellectually deep, has an intuitive theoretical foundation, and is mathematically efficient. Virtually all asset-management problems are solved using the ap- proach or modified versions of it.

The MV methodology is not without shortcomings. It must be used cautiously with great care paid to problem formulation. The optimum portfolios it produces are only as good as the forecasts used in their derivation and the asset universe from which the solutions are derived. Mean-variance analysis without a concerted effort directed to forecasting and asset selection is not likely to add significant value to the quality of portfolio decisions and may even produce worse results than would otherwise be the case.

While MV analysis still represents the current paradigm, other approaches to portfolio optimi- zation exist and may eventually displace it. Value-at-risk simulation methodologies may ultimately prove more than tangential. Even so, for many practitioners there is still a long way to go before forecasting techniques, asset identification, and time horizon considerations are satisfactorily inte-

grated with core MV applications. Greater rewards are likely to come from efforts in this direction rather than from devising new methodologies that will also require accurate forecasting and asset selection in order to be successful.