INDUSTRIAL ENGINEERING APPLICATIONS IN FINANCIAL ASSET MANAGEMENT:THE FORECASTING PROBLEM

By -
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:

Industrial Engineering Applications in Financial Asset Management-0015

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:

Industrial Engineering Applications in Financial Asset Management-0016

Industrial Engineering Applications in Financial Asset Management-0017

Comments

Post a Comment

Popular posts from this blog

DUALITY THEORY:THE ESSENCE OF DUALITY THEORY

By -
Image
THE ESSENCE OF DUALITY THEORY Given our standard form for the primal problem at the left (perhaps after conversion from another form), its dual problem has the form shown to the right. Thus, with the primal problem in maximizatio n form, the dual problem is in minimization form instead. Furthermore, the dual problem uses exactly the same pa r amete r s as the primal problem, but in different locations, as summarized below. 1. The coefficients in the objective function of the primal problem are the right-hand sides of the functional constraints in the dual problem. 2. The right-hand sides of the functional constraints in the primal problem are the coef- ficients in the objective function of the dual problem. 3. The coefficients of a variable in the functional constraints of the primal problem are the coefficients in a functional constraint of the dual problem. To highlight the comparison, now look at these same two problems in matrix notation (as introduced at the beginn...
Read more

NETWORK OPTIMIZATION MODELS:THE MINIMUM SPANNING TREE PROBLEM

By -
Image
THE MINIMUM SPANNING TREE PROBLEM The minimum spanning tree problem bears some similarities to the main version of the shortest-path problem presented in the preceding section. In both cases, an undi r ecte d and connected network is being considered, where the given information includes some mea- sure of the positive length (distance, cost, time, etc.) associated with each link. Both problems also involve choosing a set of links that have the shortest total length among all sets of links that satisfy a certain property. For the shortest-path problem, this property is that the chosen links must provide a path between the origin and the destination. For the minimum spanning tree problem, the required property is that the chosen links must provide a path between ea c h pair of nodes. The minimum spanning tree problem can be summarized as follows: 1. You are given the nodes of a network but not the links. Instead, you are given the po- tential links and the positive length for each ...
Read more

INTEGER PROGRAMMING:THE BRANCH-AND-CUT APPROACH TO SOLVING BIP PROBLEMS

By -
TH E BRANCH-AND-CUT APPROACH TO SOLVING BIP PROBLEMS Integer programming has been an especially exciting area of OR since the mid-1980s be- cause of the dramatic progress being made in its solution methodology. Background To place this progress into perspective, consider the historical background. One big break- through had come in the 1960s and early 1970s with the development and refinement of the branch-and-bound approach. But then the state of the art seemed to hit a plateau. Rel- atively small problems (well under 100 variables) could be solved very efficiently, but even a modest increase in problem size might cause an explosion in computation time be- yond feasible limits. Little progress was being made in overcoming this exponential growth in computation time as the problem size was increased. Many important problems arising in practice could not be solved. Then came the next breakthrough in the mid-1980s, with the introduction of the b r an c h- and-cu t approach to sol...
Read more