Multiple Linear Regression 69
There are two models reported. The first, denoted “Basic Model,” uses 12
asset class indexes selected by Dor and Jagannathan. As can be seen, the R^2
is 66.9%. However, Putnam Utilities Growth and Income is a sector-oriented
fund. In creating a Sharpe benchmark for sector-oriented funds, it is impor-
tant to use relevant sector indexes. The “Extended Model” reported in Table
3.7 includes three sector indexes: Dow Jones Utilities, Dow Jones Commu-
nications, and Dow Jones Energy. Notice that not only does the R^2 increase
from 66.9%, the weights (regression coefficients) change dramatically. For
example, a 56.8% weight in the basic model is assigned to Large-Cap Value
but only 14.7% in the extended model. Look also at the Treasury 10+-year
asset class index. This is the second largest weight in the basic model; how-
ever, in the extended model it has no weight assigned to it.
Return-based Style Analysis for Hedge Funds
The use of the Sharpe benchmark is typical for evaluating non-hedge fund
managers. The difficulty with employing the Sharpe benchmark for hedge
funds is attributable to the wide range of assets in which they are free to
invest and the dynamic nature of their trading strategy (i.e., flexibility of
shifting among asset classes, the higher leverage permitted, and the ability
to short sell).
Dor and Jagannathan illustrate this difficulty using four hedge funds.^18
Two of the hedge funds are directional funds and two are nondirectional
funds. The former employ strategies seeking to benefit from broad market
movements and the latter employ strategies seeking to exploit short-term
pricing discrepancies between related securities but at the same time main-
tain market exposure to a minimum. Nondirectional funds are referred to
as market-neutral funds. The directional funds are Hillsdale U.S. Market
Neutral Fund (Hillside fund) and The Nippon Performance Fund (Nippon
fund); the nondirectional funds are Axiom Balanced Growth Fund (Axiom
fund) and John W. Henry & Company—Financial and Metals Portfolio
(CTA fund).
Table 3.8 reports two regression results for the four hedge funds. The
first regression (referred to as the “Basic Model” in the table) uses 12 asset
classes. The R^2 is lower for these hedge funds than for mutual funds for the
reason cited earlier regarding the wide range of strategies available to hedge
funds. Note, however, that the R^2 of the nondirectional funds (i.e., market-
neutral funds) is higher than that of the directional funds.
Theory and empirical evidence can help us identify factors to improve
upon the explanatory power of hedge fund returns. Several researchers
(^18) Dor and Jagannathan, “Style Analysis: Asset Allocation and Performance Evaluation.”