S+NuOPT: Large-Scale Constrained Optimization

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
* Transportation
* Quadratic programming
* Unconstrained nonlinear optimization
* Multi-objective programming

Figure 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.

SAMPLE APPLICATIONS

Portfolio Optimization

* 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 efficiently.

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
criterion.

Applications of Mixed Integer Programming in Quantitative Finance

* 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 round lots.
* 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 efficiently.

Statistical analysis software