58 Optimizing Optimization
where L and U are the lower and upper bounds and A is the matrix of constraints.
● Nonlinear constraints including portfolio risk expressed as absolute risk (relative to
cash) or tracking error (relative to a benchmark) and turnover
● Threshold constraints, e.g., minimum holding, minimum trade
● Basket (integer number) constraints, e.g., number of stocks, number of trades
● Absolute value constraints, e.g., absolute factor exposure, portfolio gross value
LAwUiijj
j∑ i
● Lot size (Normal Market Size) trading constraints
● Long/short ratio constraints
LUS
Lwhere L and U are the lower and upper bounds and the ratio S / L is always
defined.
● Use of composite assets (e.g., index futures, exchange-traded funds)
● Calculation of portfolio utility, and utility per stock
● Calculation of portfolio ex ante risk, and marginal contributions from assets and
factors
● Calculation of portfolio transaction cost, and cost per stock
● Stand-alone .dll that is platform-independent, enabling easy integration through its
API interfacing through MatLab, .Net C, Java, VB, Perl, Python, and with all major
data integrators.
3.4 Robust optimization
3.4.1 Background
Robust optimization can help eliminate some of the instability/cost associated
with the traditional approach by reducing the optimizer’s need to trade, as
opposed to directly controlling the amount of trading it does. This reduction
is achieved by reducing the influence of alphas on stocks that have historically
been wrong, volatile, or both.
3.4.2 Introduction
BITA Risk developed a new optimizer (BITA Robust) that focuses on man-
aging uncertainty in the expectations that input into portfolio construction.
That is, it copes with ranges of inputs for key factors such as expected returns.
Traditional mean – variance portfolio optimization and quadratic optimization
solutions are notoriously sensitive with respect to inputs. It is also well known
that errors in forecasts lead to unrealistic portfolios. BITA Robust accomplishes
a more stable solution, which requires less trading to maintain the portfolio’s
expected risk/return trade-off, thus reducing turnover and costs.