by Ken Yiu | Nov 18, 2017 | SuanShu

A Quadratic Programming problem (QP) in the form of where , can be transformed to a Second-Order Cone Programming (SOCP) problem in the form of Consider , and As is non-negative, minimizing is equivalent to minimizing , and hence is equivalent to minimizing . If we have and , then the objective function in QP can be written as . We can thus minimize . Thus, the QP problem can now be written as As , by definition of QP, is symmetric, a symmetric can be found such that . If the QP is assumed to be a convex QP, is positive semidefinite, applying Cholesky factorization gives (or ). In this case, (or ). Next, as is always non-negative, the equality constraint can be written as Finally, each row in the inequality constraint can be written as where is the i-th row of , and is the i-th element of . Therefore, a QP problem can be transformed to an equivalent SOCP problem in the following way. We need to introduce a few variables first. The sub-vector with the first elements in the solution of the transformed SOCP problem is the solution of the original QP problem. SuanShu has implementations to solve both SOCP and QP problems. SOCP interior point solver QP active set...
by Ken Yiu | Jun 19, 2013 | AlgoQuant, Algorithmic Trading, Investment

Many portfolio optimization methods (e.g., Markowitz/Modern Portfolio Theory in 1952) face the well-known predicament called the “corner portfolio problem”. When short selling is allowed, they usually give efficient allocation weighting that is highly concentrated in only a few assets in the portfolio. This means that the portfolio is not as diversified as we would like, which makes the optimized portfolio less practically useful. In [Corvalan, 2005], the author suggests to look for instead an “almost efficient” but “more diversified” portfolio within the close neighborhood of the Mean-Variance (MV) optimal solution. The paper shows that there are many eligible portfolios around the MV optimal solution on the efficient frontier. Specificially, given the MV optimal solution, those “more diversified” portfolios can be computed by relaxing the requirements for the portfolio return and risk in an additional optimization problem: where , is the Markowitz MV optimal weights, are the relaxation tolerance parameters, and is a diversification measure for the portfolio (for example, , ). In other words, the new optimization problem looks for a portfolio with the maximal diversification around the optimal solution. Corvalan’s approach can be extended to create an approximate, sufficiently optimal and well diversified portfolio from the optimal portfolio. The approximate portfolio keeps the constraints from the original optimization problem. References: SuanShu Javadoc Alejandro Corvalan (2005). Well Diversified Efficient Portfolios. Documentos de trabajo del Banco Central, no....
by Ken Yiu | Feb 16, 2013 | AlgoQuant, Algorithmic Trading

[Lai, Xing and Chen, 2010], in the paper “Mean-Variance Portfolio Optimization When Means And Covariances Are Unknown”, proposed a ground breaking method to do portfolio optimization. In what follows we summarize their idea and use it to implement a periodic rebalancing strategy based on the AlgoQuant framework. Harry Markowitz won the Nobel prize for his work in mean-variance (MV) portfolio optimization in 1950s. The theory is widely regarded as fundamental in financial economics. It says, given a target return of a portfolio of m assets, the optimal (in terms of information ratio) weighting is given by where is the expected future returns, and is the expected covariance matrix of future returns. This problem is readily solved by quadratic programming. Nonetheless, the assumption that and are known in advance is very dubious. This has been referred to as the “Markowitz optimization engima”. The attempts made so far are to better forecast these estimators, namely and , as accurately as possible. The maximum likelihood estimate (MLE) from the training sample is an example. It turns out, however, that MLE performs poorly because the estimators are quite different from the realized values [Michaud, 1989]. Since then, three approaches have been proposed to address the difficulty. The first approach uses a multi-factor model to reduce the dimensionality in estimating [Fan, Fan and Lv, 2008]. The second approach uses Bayes or other shrinkage estimates of [Ledoit and Wolf, 2004]. Both approaches attempt to use improved estimates of for the plug-in efficient frontier. They have also been modified to provide better estimates of , for example, in the quasi-Bayesian approach of [Black and Litterman, 1990]. The third approach uses bootstrapping...
by Ken Yiu | Dec 21, 2012 | AlgoQuant, Programming

Bloomberg maintains tick-by-tick historical data for only 140 days. However, you may want to backtest your strategies with a longer history. In this case, you can archive these tickdata by yourself and do backtesting with the archived data. Since version 0.2, AlgoQuant supports downloading tick-by-tick data from Bloomberg and saving them as CSV files via the Bloomberg Java API v3 (assuming that you have access to a Bloomberg terminal). After you download the AlgoQuant package, you will find that there is a folder lib/blpapi-dummy which contains the Bloomberg API jar file (blpapi3.jar). This file is a dummy for AlgoQuant to compile. To use the Bloomberg Java API, you need to replace the file with the real API jar file. If your machine has been deployed the Bloomberg API, you can find the real jar file in your hard drive, for example, C:\blpAPI\APIv3\JavaAPI\v3.4.3.2\lib\blpapi3.jar Note that the version number of the API may be automatically upgraded by Bloomberg. The code for connecting, downloading and saving the tickdata is located in the package com.numericalmethod.algoquant.data.historicaldata.bloomberg. You can find in the package a simple demo application “TickDataDownloadApp“, which accepts command-line arguments and downloads tickdata of a given period for a given security: Usage: TickDataDownloadApp <security> <startDate (yyyy-MM-dd)> <endDate (yyyy-MM-dd)> <output dir> Note that the start date should be within 140 days as it is the oldest history you can download from Bloomberg. Here is how it works. The Bloomberg system provides a core service named “//blp/refdata” which allows downloading a wide range of market data. The code opens a session to connect to the localhost at port 8194 (change the settings in SimpleSessionFactory if you are using a...
by Ken Yiu | May 21, 2012 | SuanShu

Cloud computing is very popular nowadays. Delegating your CPU-intensive computation (or simulation) to the cloud seems to be a smart choice. Many of our users asked if SuanShu can be run on Amazon’s Elastic Compute Cloud (EC2), because SuanShu license requires a MAC address and they have no control on which machine being used when they launch an EC2 instance. Here comes a good news! Amazon Web Service (AWS) now supports Elastic Network Interface (ENI), by which you can bind your EC2 instance to a specified network interface. Therefore, you can license your SuanShu against the MAC address of the ENI, and launch an instance with the same ENI and MAC address. For details, please visit the blog here. User guide for ENI can also be found...
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