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RJS Software

The following products are developed by RJS Software - a third party company, for use with GAUSS. Technical support is provided directly through the developer.

QP v1.0- Quadratic Programming

QP solves the standard quadratic programming problem: min{1/2x'Qx - x'R}, subject to constraints: Ax = B and Cx >= D, with bounds: Xl <= x <= Xu, where x is a vector of unknown coefficients, and Q, R, A, B, C, D, Xl, and Xu are known matrices.

CLSQ

Constrained least squares is a special case of the the quadratic programming problem. CLSQ is a procedure included in the QP module for computing constrained least squares regression estimates. The ability to specify inequality constraints and to place bounds on the coefficients is unique to this procedure and not available in other GAUSS applications. CLSQ also computes the correct standard errors of the constrained coefficients.

Most regression models contain coefficients that can be bounded or constrained in some way. For example, it is often known that one or more coefficients are positive or are in some range. Incorporating this information into the estimation using CLSQ always improves the t-statistics of the estimates over the unconstrained estimation. Even specifying very broad ranges for the coefficients can improve the efficiency of the estimates, and for that reason the use of CLSQ could be recommended for all least squares problems.

Portfolio Management

The "Mean-Variance", "Mean-SemiVariance" and "Effective Mix" models are important applications of the QP problem in investment portfolio management. The Effective Mix model is a constrained least squares problem for which CLSQ is suited. The Mean-Variance and Mean-Semivariance models are quadratic programming problems where Q is the covariance matrix of a portfolio of stocks, bonds, options, etc., and R is a vector of their mean values. The QP solution yields estimates of the ideal distribution of the portfolio among the securities.

Parametric Quadratic Programming

PQP is a procedure included in the QP module for simulating portfolio distribution under various assumptions about investment strategies. Mean values, risk tolerance and structural constraints can all be varied, and the implications for the portfolio distribution can be explored.

Platform: Windows, LINUX and UNIX