Multiple Linear Regression 73
If the spread predicted by the model (i.e., model spread) exceeds the
actual spread, the market is viewed as rich; it is viewed as cheap if
the model spread is less than actual spread. The market is fairly priced if
the two spreads are equal. The predicted and actual spreads for March
2004 are the last ones shown in Figure 3.2. While the model suggests that
the market is rich, it is less rich in comparison to the prior months. In
fact, at the close of March 9, 2004, when the article was written, it was
only 5 basis points.
Testing for Strong-Form Pricing Efficiency
At the heart of the debate as to whether investors should pursue an active
or passive equity strategy is the pricing efficiency of the market. The pric-
ing efficiency of a market can be classified into three forms: (1) weak form,
(2) semistrong form, and (3) strong form. The distinction among these
forms lies in the relevant information that is hypothesized to be locked
into the price of the security. Weak efficiency means that the price of the
security reflects the past price and trading history of the security. Semis-
trong efficiency means that the price of the security fully reflects all public
information (which, of course, includes but is not limited to historical
price and trading patterns). Strong efficiency exists in a market where the
price of a security reflects all information, whether or not it is publicly
available.
Multiple linear regression analysis is used in most tests of the pricing
efficiency of the market. These tests examine whether it is possible to gener-
ate abnormal returns from an investment strategy. An abnormal return is
defined as the difference between the actual return and the expected return
from an investment strategy. The expected return used in empirical tests is
the return predicted from a pricing model. The pricing model itself adjusts
for risk. Because the testing relies on the pricing model used, tests of market
pricing efficiency are joint tests of both the efficiency of the market and the
validity of the pricing model employed in the study.
Let’s illustrate a test for strong-form pricing efficiency using multiple
linear regression analysis. This will be done by comparing the performance
of equity mutual fund managers against a suitable stock market index to
assess the performance of fund managers in general. For example, it is
common to compare the average large-cap mutual fund’s performance to
that of the S&P 500 Index. But this is not a fair comparison because it
ignores risk. Specifically, the risk parameters of the average mutual fund
may be different than that of the benchmark, making a simple direct com-
parison of the mutual fund’s performance and that of the benchmark inap-
propriate.