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Portfolio Selection System: Digital Portfolio Theory Release 2.0 User's Guide

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Abstract

The Portfolio Selection System (PSS) software package is based on the theoretical concepts developed in Professor C. Kenneth Jones' book Portfolio Management, published by McGraw-Hill in 1992. In this theoretical text a comprehensive modeling language is developed that can be applied generally to all financial problems. In addition, the use of digital signal processing is introduced for the first time to model risk, in a more precise manner than has previously been possible. The PSS software package applies the signal processing techniques for risk management to the investment decision problem. Digital Portfolio Theory as derived in the text Portfolio Management is applied in the PSS software package. PSS is the state of the art in quantitative portfolio selection software. It brings a more powerful quantitative portfolio selection approach to the individual investor than is currently being used by multimillion dollar portfolio fund managers. Not only does PSS solve for optimal portfolios controlling for multiple calendar risk levels, but it also simultaneously controls growth in Earning per Share (EPS), change in the growth of EPS, market capitalization, Price/Earnings (P/E) ratio relative to industry P/E, dividend yield and book value relative to market value. The PSS software package is the most advanced system of security selection available on the market today.
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... The Power Spectral Density (PSD) function of MATLAB can compute Fourier Transforms from return series with calendar signal lengths.2 MATLAB uses the Welch method to find the spectral density and allows rectangular and Hanning windows.3Jones (1997) has developed a software package available to researchers based on Digital Portfolio Theory (http://www.portfolionetworks.com). The software package can find efficient portfolios from a universe of 8000 securities and uses the Welch method to measure risk. ...
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The Modern Portfolio Theory of Markowitz maximized portfolio expected return subject to holding total portfolio variance below a selected level. Digital Portfolio Theory is an extension of Modern Portfolio Theory, with the added dimension of memory. Digital Portfolio Theory decomposes the portfolio variance into independent components using the signal processing decomposition of variance. The risk or variance of each security's return process is represented by multiple periodic components. These periodic variance components are further decomposed into systematic and unsystematic parts relative to a reference index. The Digital Portfolio Theory model maximizes portfolio expected return subject to a set of linear constraints that control systematic, unsystematic, calendar and non-calendar variance. The paper formulates a single period, digital signal processing, portfolio selection model using cross-covariance constraints to describe covariance and autocorrelation characteristics. Expected calendar effects can be optimally arbitraged by controlling the memory or autocorrelation characteristics of the efficient portfolios. The Digital Portfolio Theory optimization model is compared to the Modern Portfolio Theory model and is used to find efficient portfolios with zero calendar risk for selected periods. Copyright 2001 by Kluwer Academic Publishers
... There is often a fixed cost component to the portfolio management decision process that can be modelled in this framework. The DPT software is available to researchers (Jones, 1997). ...
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In this study, we use zero-one variables to control fixed transaction costs independent of trade size in the portfolio selection problem. The optimal solution to the maximum flow, risk constrained stochastic portfolio network is found using Digital Portfolio Theory (DPT). Digital signals describe return processes and power spectral densities describe variances of long and short horizon returns. We find high fixed trading costs reduce size and affect composition of optimal portfolios for small investors or long holding periods. High risk portfolios are more sensitive to trading costs. Optimal portfolios for active traders or large portfolios are largely unaffected by fixed commission costs.
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The nature of the long-term time-varying risk return relation is not fully understood. It is widely believed, incorrectly, that a risk based explanation of time-varying equilibrium return would require corresponding time variation in risk. There is a need for a new methodology to measure long-term risk at multiple horizons. In this paper we test an alternative risk based explanation of time-varying returns by investigating a variety of models and using new digital signal processing method to estimate risk. We identify multiple time horizon deviation from white noise by examining the variances of two-month to four-year returns. The spectral densities of monthly returns are used to measure independent variance contributions to monthly risk generated by long and short horizon returns for calendar and non-calendar periods. New digital signal processing techniques and an additive noise model are used to test the white noise hypothesis for both total and idiosyncratic risk of individual firms. We find that multiple calendar effects including; January, quarterly, annual, summer, presidential, and Joseph effects influence different segments of the US stock market. Small firm total and idiosyncratic risk is dominated by the January effect. Mid-cap firms' idiosyncratic risk is influenced by Joseph, annual and six-month effects. Large firm total risk is dominated by Joseph, annual, and January effects while idiosyncratic risk is dominated by presidential and annual effects. The results suggest that risk is composed of multiple long horizon calendar related holding period variances that are stationary. We conclude that multiple long-term variances of calendar length returns explain shorter term time-varying returns. Further tests are needed to determine if calendar based risk is coincident to known calendar anomalies.
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