Investment Forecasting With Multivariate Linear Regression

Abstract

The procedure for estimating probabilities of future investment returns using time-shifted indexes is based on the simple principle that a multi-dimensional conditional probability distribution can be envisioned involving investment total returns (for a single investment or a fixed portfolio of investments as the dependent variate) and the total returns of one or more market indexes shifted forward in time by one year as the independent variate(s). Furthermore, it is shown that the probability function involving the dependent investment return is decoupled from the independent index return variate(s) by linear regression. The deviations of the investment returns from the regressed line, surface, or hypersurface is characterized with a one-dimensional normal cumulative probability distribution function, (estimated by the Students t-distribution), to determine the probabilities for the next years returns. Thus, the expected investment total returns at a given probability level is the regressed return based on last year's index return(s) plus the accepted risk (deviation) increment. Adjustments are made in the statistical parameters to account for the extrapolation of the regression information beyond the period covered by the data in the return records. A hierarchy of regression variates is determined by selecting the variates, one at a time, which will provide the greatest error reduction; then, the viability of the last variate chosen is assessed by the F-significance test. It is concluded that the use of multiple time-shifted indexes can improve the estimates of future investment returns. Also, it was shown that properly diversified asset allocations could be established to take advantage of the predictive power of the time-shifted index technique. It is obvious that the approach could be employed to further refine the allocations within a broad asset class - to establish, for example, the relative allocations between large company, small company, and specialty company stock.