INDUSTRIAL ENGINEERING APPLICATIONS IN FINANCIAL ASSET MANAGEMENT:THE FORECASTING PROBLEM

THE FORECASTING PROBLEM

Beyond asset selection, the key to successful investment performance via MV asset allocation depends largely on the accuracy of return, risk, and correlation forecasts. These forecasts may be subjective or quantitative. A subjective or purely judgmental approach allows one the luxury of considering any number of factors that can influence returns. The disadvantage of pure judgment is that it is sometimes nebulous, not always easily explained, and may sometimes be theoretically inconsistent with mac- roeconomic constraints.

Model forecasts are rigorous and explicit. They derive straightforwardly from a particular variable set. Most quantitative approaches to forecasting are based on time series methods, explored in great depth in the finance literature over the years. Beckers (1996) provides a good review of such methods used to forecast returns, while Alexander (1996) surveys risk and correlation forecasting. In addition, Lummer et al. (1994) describe an extrapolative method as a basis for long-term asset allocation. An alternative to pure time series is causal models. For example, Connor (1996) explored macroeconomic factor models to explain equity returns. Lamm (2000) proposes a modified bivariate Garch model as one way of improving MV forecast accuracy.

In the case of a two-asset stock and bond portfolio, the modified Garch model proposed by Lamm is simply:

The other symbols are estimated parameters. The first two equations predict returns, while the second two forecast associated risk. The correlation between stocks and bonds in any period is simply p = u12t / u1tu2t, which is derived from the last three equations. This model postulates that when extraneous changes occur that are not reflected in economic variables, the resulting prediction errors push up risk and reduce correlation—exactly the pattern observed in response to market shocks through time.

Lamm reports that augmenting Garch with exogenous variables significantly improves forecast accuracy. These findings have important implications for portfolio management. Critically, augmented Garch provides a more logical and systematic basis for reallocation decisions through the economic cycle (Figure 5) and changing inflation scenarios, which shift efficient frontiers (Figure 6). The augmented Garch process also allows one to distinguish economic influences from purely unexpected shocks, which are often event driven. A pure time series approach provides no such delineation.

If one desires to focus only on return forecasting, a useful approach is vector autoregression (VAR). Although largely atheoretic, except regarding system specification, such models have been shown to have superior predictive capability. In particular, VAR forecasts are more accurate the longer the periodicity of the data. For example, monthly VAR models typically explain 5–10% of the variation in returns, while annual VAR models often explain 90% or more. Quarterly forecasting models produce results in between. VAR models thus provide a reasonably good method for annual asset allocation while providing only a slight edge for monthly allocation.

VAR models are fairly simple and are specified as: