Formulating and Implementing Investment Strategies Using Financial Econometrics 317
the consistent performance of the three-period process suggests that it is not
driven by a constant set of artificial rules introduced by data snooping.
test against a random Walk hypothesis After completing the modeling exer-
cise it is always wise to test the model against an artificial data set formed
from independent and identically distributed returns. Any trading strat-
egy applied to purely random data should yield no average excess return.
Of course, purely random fluctuations will produce positive and negative
excess returns. However, because we can simulate very long sequences of
data, we can test with high accuracy that our models do not actually intro-
duce artifacts that will not live up to a real-life test.
Independent risk Control
Even if the expected return is modeled properly at the individual stock level,
the bottom line of implementable investment strategies is evaluated by an
acceptable level of risk-adjusted portfolio excess returns. As most institu-
tional portfolios are benchmarked, the goal is to minimize tracking error
(standard deviation of active returns), given some level of portfolio excess
return. Consequently, risk control becomes technically much more complex
than the conventional efficient portfolio concept. As shown by Richard
Roll, an optimal portfolio which minimizes tracking error subject to a level
of excess return is not a mean-variance efficient portfolio.^16 It should be
noted that, due to the objective and competitive nature of the quantita-
tive approach in its strong form, most models produce similar rankings in
expected returns. The variation in performance among quantitative portfo-
lios is mainly attributed to a superior risk control technology.
One commonly used but less preferred practice in risk management is
often performed right at the stage of identifying the model for expected
returns. It involves revising the estimates from the model to explain the
actual return. The purpose is to control the risk by attempting to reduce
the estimation error for the model of expected returns. This approach has
several flaws. First, in most cases, the procedure of revising the parameter
estimates (from the model of actual returns) so they can be used in the
model of expected returns is often performed on an ad hoc basis, and vul-
nerable to data snooping. Second, in revising the parameter estimates, the
task of building a relevant expected model with low prediction errors is
mistaken for risk control on portfolio returns. Finally, there is a lesser degree
(^16) Richard R. Roll, “A Mean/Variance Analysis of Tracking Error,” Journal of Portfo-
lio Management (Summer 1992): 13–23.