S+NuOPT is a cutting-edge software package capable
of solving very large optimization problems. Designed
for analysts and decision makers, NUOPT for S-PLUS
is used for a wide range of applications including
portfolio optimization, nonlinear and robust statistical
modeling, and circuit optimization. The full power
of the S-PLUS language is integrated with NUOPT.
No other package can match this combination of
powerful statistics and graphics with large-scale
optimization problem solving, including:
- Linear programming
- Mixed integer programming
- Quadratic programming
- Unconstrained nonlinear optimization
- Multi-objective programming
1: S+NuOPT allows you to explore different portfolio optimization
methods and build in features that reflect real-world constraints.
The above figure displays optimized weights computed using
two different methods. The weights on the left are rebalanced
during each time period independently of the weights during
the previous time period. The weights on the right are constrained
to smoothly evolve from one time period to the next, resulting
in a more stable portfolio allocation.
- Optimize portfolios of assets incorporating
a variety of realistic constraints, going well beyond the
classical Mean-Variance (Markowitz) formulation.
- Build complex models that combine different
classes of assets and subgroups of assets simultaneously.
- Solve problems involving large portfolios
Nonlinear and Robust Statistical Modeling
- Apply new penalized and robust regression
methods, traditionally only applicable to small data sets,
to very large problems.
- Find better parameter estimates for nonparametric
models using global fitting
Applications of Mixed Integer Programming in Quantitative
- Basket Selection: given an initial portfolio, select basket
of trades given that only a maximum number of trades are
allowed (along with other turnover constraints).
- Cardinality Constraints (number of names
constraints): given the asset universe, portfolio managers
often need to limit the total number of holdings (both long
and short) in their final portfolio.
- Buy In Threshold Constraints: some assets
can only be purchased or sold at certain minimum levels,
or overly small holdings or trades may need to be excluded
in an optimum portfolio.
- Round Lots: restrictions defining the
basic investment unit. For instance, investors are only
allowed to make transactions in integer multiples of these
- Lower Partial Moments Optimization: Instead of using variance as
a risk measure, it is sometimes desirable to optimize on downside
deviation. The ability to declare and use integer variables makes it
easy to formulate the problem elegantly and therefore solve more