88 The Basics of financial economeTrics
because Dor and Jagannathan use a stepwise regression to further illustrate
their point.
Dor and Jagannathan show how the style analysis can be further
improved by including peer-group performance as measured by hedge fund
indexes created by several organizations. Three examples of such organiza-
tions are Hedge Fund Research Company (HFR), CSFB/Tremont (TRE),
and MAR Futures (MAR). The five hedge fund indexes that are used by Dor
and Jagannathan in their illustration are (1) Market Neutral, (2) Emerging
Markets, (3) Managed Futures, (4) Fixed Income, and (5) Event Driven.
A total of 21 explanatory variables then can be used in the style analysis:
twelve asset classes, five hedge fund indexes, and four of the S&P 500
option strategies. Because of the large number of variables and their high
correlations, Dor and Jagannathan employ stepwise regression analysis. The
results are shown in Table 4.1. In implementing the stepwise regression, Dor
and Jagannathan specify a 10% significance level for deleting or adding an
explanatory variable in the stepwise regression procedure. The results of the
stepwise regression results show a higher ability to track the returns of the
two directional funds relative to the two nondirectional funds by including
the five hedge fund indexes (i.e., peer groups).
Testing the Assumptions of the Multiple Linear Regression Model
After we have come up with some regression model, we have to perform
a diagnosis check. The question that must be asked is: How well does the
model fit the data? This is addressed using diagnosis checks that include the
coefficient of determination, R^2 as well as Rad^2 j, and the standard error or
square root of the mean squared error (MSE) of the regression. In particu-
lar, the diagnosis checks analyze whether the linear relationship between
the dependent and independent variables is justifiable from a statistical
perspective.
As we also explained in the previous chapter, there are several assump-
tions that are made when using the general multiple linear regression model.
The first assumption is the independence of the independent variables used
in the regression model. This is the problem of multicollinearity that we
discussed earlier where we briefly described how to test and correct for this
problem. The second assumption is that the model is in fact linear. The third
assumption has to do with assumptions about the statistical properties of
the error term for the general multiple linear regression model. Furthermore,
we assumed that the residuals are uncorrelated with the independent vari-
ables. Here we look at the assumptions regarding the linearity of the model