318 The Basics of financial economeTrics
of freedom in that estimates are made based on the estimates of previous
steps. The “risk control” procedure becomes dependent to the process of
estimating expected returns. Consequently, an independent risk control pro-
cedure, usually through an optimization process, should be performed as an
overlay on the stock selections that are determined initially by the predicted
expected returns.
For computing efficiency, the iterations can be significantly reduced if
several other conditions are simultaneously imposed. For example, it has
been shown that the largest source of tracking error is the deviation of port-
folio sector weights from its benchmark sector weights.^17 Consequently,
most optimal benchmarked portfolios are “sector neutral,” that is, port-
folios do not make sector bets against the benchmark. This consideration
would indicate the need to include a constraint that sets maximum accept-
able deviations of portfolio sector weights from benchmark sector weights.
Along the same line, tracking error can be further controlled when
the individual stock weight is constrained to conform to its corresponding
weight in the benchmark. It is also accomplished by setting a maximum
allowed deviation of stock weight in the portfolio from the weight in the
benchmark.
Additional realistic portfolio constraints may be considered. Examples
would include specification of a (1) minimum level of market liquidity
for individual stocks, (2) maximum absolute weight in which any stock is
allowed to invest, (3) minimum total number of stocks held, (4) minimum
number of stocks held in each sector, and (5) maximum level of portfolio
turnover allowed.
Key Points
■ (^) In evaluating financial econometric models for potential implementa-
tion of investment strategies, two guiding principles are model simplic-
ity and out-of-sample validation.
■ (^) A higher level of confidence can be placed on a simple model validated
on data different from those on which it has been built.
■ (^) In the quantitative process the identification of any persistent pattern in
the data is sought and must then be converted into implementable and
profitable investment strategies. How this is done requires the develop-
ment of underlying economic theories, an explanation of actual returns,
estimation of expected returns, and construction of corresponding
portfolios.
(^17) See Ma, “Nonlinear Factor Payoffs?”