150 The Basics of financial economeTrics
cause an average increase of 1.04% in the fund’s return. Since the classical
multivariate regression only captures the mean change in returns, the above
results may not capture the investment style of the manager across the distri-
bution of returns. Furthermore, the Jarque-Bera (JB) normality test^9 shows
that regression errors are not normally distributed.
Quantile regressions provide a complete view of investment style of the
fund. The following quantile regression model is estimated:
Qτ(Fidelity Mid Cap Value Fund return) = Large value index returns
- Large growth index returns
- Small value index returns
- Small growth index returns
- Mid cap value index returns
where Q is the quantile and τ represents the quantile levels. For the purpose
of this illustration, the selected quantile levels are 0.10, 0.30, 0.50, 0.70,
and 0.90.
tabLe 7.2 Multivariate and Quantile Regressions, Sample from December 2001
through March 2013
Multivariate
Regression Q(0.1) Q(0.3) Q(0.5) Q(0.7) Q(0.9)Constant −0.077 −1.022 −0.393 −0.092 0.261 0.986
−0.987 −7.094 −4.338 −1.014 2.505 5.501
Large Value −0.053 0.058 0.016 −0.039 −0.086 −0.100
−1.026 2.122 0.369 −0.829 −2.447 −4.128
Large Growth −0.014 −0.054 −0.055 0.002 −0.042 −0.035
−0.386 −1.580 −1.074 0.028 −0.847 −1.068
Small Value 0.037 −0.154 −0.125 −0.091 −0.024 −0.028
0.974 −4.770 −2.573 −1.696 −0.356 −0.634
Small Growth −0.084 0.051 0.013 0.017 0.069 0.056
−2.384 1.758 0.324 0.405 1.456 1.799
Mid Cap 1.040 0.928 1.009 1.028 1.078 1.114
18.395 19.112 15.624 14.925 14.497 22.085
Fidelity Mid Cap Value return = Large value index returns
- Large growth index returns
- Small value index returns
- Small growth index returns
- Mid cap value index returns
These data are obtained from Morningstar EnCorr.
(^9) The Jarque-Bera normality test is explained in Chapter 4.