Quantile Regressions 149
determine a portfolio manager’s style. The data used in this application
are times series data. In our second illustration, we look at how a quantile
regression can be used to empirically investigate the determinants of a cor-
poration’s capital structure. In this application, cross-sectional data are used.
Determining a portfolio Manager’s Style
A quantile regression can be applied to identify a portfolio manager’s
investment style. The manager’s performance is compared to a benchmark.
The benchmark selected should be consistent with a portfolio manager’s
investment style. For example, a portfolio of stocks categorized as value
stocks may appear to have an unsatisfactory performance relative to a
broad stock index, but its performance could be outstanding relative to
a value stock benchmark. Such performance is attributed to the portfolio
manager’s stock selection skill.
To classify the investment style of a manager, a regression-based
approach has been proposed by Sharpe and is discussed in Chapter 3.^8 This
approach regresses a fund’s time series return on the returns to a variety of
equity indexes. The statistical significance and the magnitude of the esti-
mated coefficients represent the fund’s style. However, as noted earlier, in the
presence of outliers, the inferences made about the style of the manager at
the average may not apply to the entire distribution of returns.
As an illustration, quantile regressions are applied to Fidelity Mid Cap
Value mutual fund returns to identify the investment style of the manager
across the distribution of returns. As the name suggests, the proclaimed
investment style of the fund is to invest in a portfolio of mid cap stocks.
The monthly returns of the fund from December 2001 through March 2013
(136 observations) are regressed against the equity index returns of large
cap value, large cap growth, small cap value, small cap growth, and the
Russell’s Mid Cap Value Index. The data for all these variables are obtained
from Morningstar EnCorr database.
The results are presented in Table 7.2. The slope coefficients of the
regression show, other things being equal, the impact of a change in the index
returns on the fund’s return. If a mutual fund manager sticks to the fund’s
stated style, the index that represents the stated style should be the only
factor that would influence the fund’s return. The regression results show
that only the mid cap value index has a statistical and positive effect on the
returns of Fidelity Mid Cap Value Fund. A 1% increase in the index will
(^8) William F. Sharpe, “Asset Allocation: Management Style and Performance Measure-
ment,” Journal of Portfolio Management 16, no. 2 (1992): 7−19.