Encyclopedia of Financial Models, 3 Volume Set

Quantile Regression

CHRIS GOWLLAND, CFA

Senior Quantitative Analyst, Delaware Investments

Abstract: Many of the statistical methods that are most commonly used by researchers and practitioners in finance are mainly focused on identifying the central tendency within a data set. However, there are numerous situations where it may be equally or more important to understand the dispersion between outcomes that are higher or lower than the central tendency. One statistical method that can be useful in such investigations is quantile regression, which conceptually can be viewed as a logical extension of ordinary least squares methods.

Many investors1 use regression methods to gauge the relative attractiveness of different firms, the risks inherent in active or passive portfolios, the historical performance of investment factors, and similar topics. Such research often focuses on understanding the “central tendency” within a data set, and for this purpose perhaps the most commonly used tool is regression based on ordinary least squares (OLS) approaches. OLS methods are designed to find the “line of best fit” by minimizing the sum of squared errors from individual data points. OLS analysis generally does a good job of describing the central tendency within a data set, but typically will be much less effective at describing the behavior of data points that are distant from the line of best fit. Quantile regressions, however, can be useful in such investigations. This statistical approach ...