Quantile Regressions 151
The results of this quantile process are shown in Table 7.2. The results
show that the mid cap value index is statistically significant across the quan-
tiles reported in the table. Other indexes are small in magnitude and statisti-
cally insignificant. If the intercept is a measure of manager’s talent, it is large
in magnitude and statistically significant only in higher return quantiles.
Since Russell’s Mid Cap Value Index influences the entire return distribu-
tion, it is safe to assume that the Fidelity Mid Cap Value Fund did not
deviate from its stated style.
To ensure that inferences made across quantiles are meaningful, a Wald
test is implemented. There are four restrictions^10 for each coefficient and five
estimated coefficients for a total of 20 restrictions. The estimated test statis-
tic is 23.93 and the critical χ^2 value with 20 degrees of freedom at the 5%
significance level is 31.41. Thus, the null hypothesis that the coefficients are
the same cannot be rejected. This is an additional evidence that the Fidelity
Mid Cap Value Fund did not deviate from its stated style across the distribu-
tion of returns.
Determining the Factors that Impact Capital Structure
A key issue in corporate finance theory is how management determines the
firm’s capital structure (i.e., the mixture of debt and equity). Empirical evi-
dence suggests that a firm’s size, profitability, asset utilization, liquidity, and
growth prospects have a significant effect on the capital structure decision.
Furthermore, it has been found that leverage or debt structure (debt to assets)
varies across industries, indicating that specific industry factors are at work.
To see how quantile regressions can be used to assess the factors that
impact a firm’s capital structure, we use company-specific fundamental
data as reported each year by Bloomberg Financial.^11 We will focus on the
petroleum industry for the year 2010. Our sample in this illustration is
189 firms in the petroleum industry. Since we are looking at information
about firms in a given year, this is an illustration of an application using
cross-sectional data.
We need firm-level data on debt and total assets. For the purpose of
this illustration, we used the book value of total debt (short- and long-term
debt) and divided it by the total assets. This is defined as the leverage ratio.
The mean leverage ratio for the petroleum industry in 2010 was 31.1% with
a standard deviation of 31% and the median was 22%. The range for the
(^10) The restrictions are (β 1 Q0.1 − β 1 Q0.3, β 1 Q0.3 − β 1 Q0.5, β 1 Q0.5 − β 1 Q0.7, β 1 Q0.7 −
β 1 βQ0.9 ).
(^11) http://www.bloomberg.com/markets.