INDUSTRIAL ENGINEERING APPLICATIONS IN FINANCIAL ASSET MANAGEMENT:EXTENSIONS AND NEW FRONTIERS

EXTENSIONS AND NEW FRONTIERS

There are numerous extensions of the basic MV model beyond those already described. For example, by dropping the constraint that portfolio weights be positive, the model can be used to ascertain short and long positions that should be held for various assets. Similarly, incorporating borrowing rates allows MV models to be used to design optimal leverageable portfolios. Furthermore, the MV ap- proach can be applied to specific asset classes to build portfolios of individual securities such as equities or bonds. Beyond this, MV analysis has even broader strategic uses. For example, it can be applied by corporations to design portfolios of businesses.

One additional application of MV analysis is to use the technique to reengineer implied market returns. This requires the problem be reformulated to select a set of returns given asset weights, risk, and correlations. The weights are derived from current market capitalizations for equities, bonds, and other assets. The presumption is that today’s market values reflect the collective portfolio optimiza- tions of all investors. Thus, the set of returns that minimizes risk is the market’s forecast of future expected returns. This information can be compared with the user’s own views as a reliability check. If the user’s views differ significantly, they may need to be modified. Otherwise the user can establish the portfolio positions reflecting his or her outlook under the premise his or her forecasts are superior.

Other variants of MV optimization have been proposed to address some of its shortcomings. For example, MV analysis presumes normal distributions for asset returns. In actuality, financial asset return distributions sometimes possess ‘‘fat tails.’’ Alternative distributions can be used. In addition, the MV definition of risk as the standard deviation of returns is arbitrary. Why not define risk as first- or third-order deviation instead of second? Why not use absolute or downside deviation?

Recently, Duarte (1999) has suggested that value-at-risk approaches be used to derive efficient frontiers. This approach differs from MV analysis in that it uses Monte Carlo simulation to determine the dollar value of the portfolio that is at risk with a particular degree of statistical confidence. That

is, a $10 million portfolio might be found to have a value at risk on a specific day of $1.1 million with 95% confidence. This means the value of the portfolio would be expected to fall more than this only 5% of the time. Changing the composition of the portfolio allows a value-at-risk efficient frontier to be traced out.

Duarte also proposes a generalized approach to asset allocation that includes mean semi-variance, mean absolute deviation, MV, and value-at-risk as special cases. While cleverly broad, Duarte’s method relies on simulation techniques and is computationally burdensome. In addition, because simulation approaches do not have explicit analytical solutions, the technique loses some of the precision of MV analysis. For example, one can examine solution sensitivities from the second-order conditions of MV problems, but this is not so easy with the simulation. It remains to be seen whether simulation approaches receive widespread acceptance for solving portfolio problems. Nonetheless, simulation techniques offer tremendous potential for future applications.