Formulating and Implementing Investment Strategies Using Financial Econometrics 315
a Model to estimate expected returns
The estimation for the model to explain past returns from Step 3, by itself, is
not enough, since the objective of the process is to predict future returns. A
good model for expected return is much harder to come by since we simply
don’t have enough data. As pointed out by Fischer Black, people are often
confused between a model to explain average returns and a model to pre-
dict expected returns.^14 While the former can be tested on a large number
of historical data points, the latter requires a long time period (sometimes
decades) to cover various conditions to predict the expected return. Since we
do not have that time to wait, one common shortcut is to simply assume that
the model to explain average returns will be the model to predict expected
returns. Of course, such predictions are highly inaccurate, given the assump-
tion of constant expected returns.
We can easily find evidence to show it is a bad assumption. For example,
if one can look at the actual model that explains the cross sections of short-
term stock returns, even the most naive researcher can easily conclude that
there is little resemblance between the models from one period to the next.
This would in turn suggest, at least in the short term, the model to explain
past returns cannot be used to predict expected returns.
This calls for brand new efforts to establish an ex ante expected return
model. The process has to pass the same strict tests for quality that are
required for any good modeling, as discussed earlier in this chapter and in
the previous chapter. These tests would include the independent formulation
of the hypothesis for expected return and a methodology and sample period
free from data snooping and survivorship bias. While they are not necessar-
ily related, the process of developing hypotheses for conditional expected
return models can greatly benefit from the insights from numerous models
of past returns estimated over a long time period.
largest Value added Apparently, the final risk-adjusted returns from a strat-
egy can be attributed to the proper execution of each step described in
Figure 15.1. The entire process can be generally described in a three-step
procedure consisting of economic hypothesis, model estimation, and predic-
tion. It is only natural for researchers to ask how to allocate their efforts
among the three steps to maximize the return contribution.
To answer this question, let’s examine the return contribution from model
estimation and prediction. For this purpose, we use a typical multifactor
model to explain the return for all stocks in the Standard & Poor’s 500
(^14) Fischer Black, “Estimating Expected Return,” Financial Analysts Journal 49
(1993): 36–38.