Assessing multivariate predictors of financial market movements: A latent factor framework for ordinal data

TL;DR

This paper introduces a latent factor structural equation model with ordinal data to evaluate the predictive ability of broker-dealer forecasts on financial market movements, providing a statistical basis for assessing soft dollar value.

Contribution

It develops a novel multivariate logit model with a latent factor framework and a Laplace-based estimator for ordinal data, enabling testing of broker-dealer predictive accuracy.

Findings

The estimator is consistent and asymptotically normal.

Monte Carlo simulations show good performance in small samples.

Application to real data demonstrates the model's practical utility.

Abstract

Much of the trading activity in Equity markets is directed to brokerage houses. In exchange they provide so-called "soft dollars," which basically are amounts spent in "research" for identifying profitable trading opportunities. Soft dollars represent about USD 1 out of every USD 10 paid in commissions. Obviously they are costly, and it is interesting for an institutional investor to determine whether soft dollar inputs are worth being used (and indirectly paid for) or not, from a statistical point of view. To address this question, we develop association measures between what broker--dealers predict and what markets realize. Our data are ordinal predictions by two broker--dealers and realized values on several markets, on the same ordinal scale. We develop a structural equation model with latent variables in an ordinal setting which allows us to test broker--dealer predictive ability of financial market movements. We use a multivariate logit model in a latent factor framework, develop a tractable estimator based on a Laplace approximation, and show its consistency and asymptotic normality. Monte Carlo experiments reveal that both the estimation method and the testing procedure perform well in small samples. The method is then used to analyze our dataset.