# Large-Scale Optimizer™

##### The Large-Scale Optimizer™ has been developed jointly by Michael Best, Professor Emeritus, Department of Combinatorics and Optimization, University of Waterloo, and Jivendra Kale, President, Financiometrics Inc. It is an exceptionally fast quadratic optimizer for constructing long-only, long-short, and market-neutral portfolios with thousands of assets, and managing their risk relative to a normal, or benchmark portfolio. You can also use it for asset allocation, based on Markowitz mean-variance analysis. For a description of the underlying methodology see, “Quadratic Programming for Large-Scale Portfolio Optimization,” by Michael Best and Jivendra Kale, in Financial Services Information Systems, edited by Jessica Keyes.

#### LSO-20™

This is an app. It is a stand-alone, 20-asset version of the Large-Scale Optimizer™, which is adequate for most asset allocation applications using Markowitz mean-variance analysis, and is very reasonably priced. To get it, click Contact and submit your request in the Message box with your affiliation, and information about your computer and operating system.

#### LSO-MAX™

## Features

The Large-Scale Optimizer™ uses an active set method, which we have enhanced by using penalty function methodology, to gain dramatic increases in speed to reach a true global optimal solution for very large, real world portfolio optimization problems with variable transactions costs. For long-short and market neutral portfolios it allows long positions to migrate to short positions and vice versa.

#### Special features include…

Set a gross leverage constraint.

Set transactions costs that vary individually for each asset based on transaction size.

Set transactions costs that jump when an asset starts moving into a short position.

Set linear equality and inequality constraints for portfolio attributes and asset-group weights.

Set a non-linear constraint on portfolio standard deviation.

Set quadratic penalty functions around targeted portfolio attribute values and asset-group weights.

Set a turnover constraint.

Set an upper bound on the number of assets in the portfolio.

Set upper and lower bounds on asset weights individually for each asset.

Set quadratic penalty functions around targeted asset weights individually for each asset.

Set quadratic penalty functions around targeted asset weights individually for each asset.

Include risk-free assets.

Interface with an in-house factor model, or a factor model supplied by a vendor.

Maximize expected active return for a given standard deviation of active return, where active return is measured relative to a benchmark or normal portfolio.

Minimize standard deviation of active return for a given expected active return, where active return is measured relative to a benchmark or normal portfolio.

Maximize the mean-variance utility function for active return.

Maximize expected total return for a given standard deviation of total return.

Minimize standard deviation of total return for a given expected total return.

Maximize the mean-variance utility function for total return.

Maximize the Sharpe ratio for a given threshold return.

Maximize the threshold return for a given Sharpe ratio.

## Platforms

Customizable application for Windows.

Customizable application for Linux.

Customizable application for the Mac.

C/C++ object code library for Windows.

C/C++ object code library for Linux.

C/C++ object code library for the Mac.

C/C++ source code library for all platforms.

Fortran object code library for Windows.

Fortran object code library for Linux.

Fortran source code library for all platforms including supercomputers.

The libraries can be used with systems developed with Java, C/C++, R, Visual Basic and Fortran.

No limits in the subroutine libraries, and they are thread safe.

We provide support by e-mail and telephone during business hours Pacific Time, U.S.A.

We provide consulting services for building in-house systems that incorporate LSO-MAX™.