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Digital Portfolio Theory

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Abstract

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.

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References

  • Alexander, G.J. (1976). The derivation of efficient sets. Journal of Financial and Quantitative Analysis, 11, 817–830.

    Google Scholar 

  • Andersen, T.G. and Bollerslev, T. (1997). Heterogeneous information arrivals and return volatility dynamics: Uncovering the long-run in high frequency returns. Journal of Finance, 52(3), 975–1005.

    Google Scholar 

  • Baillie, R.T. (1996). Long memory processes and fractional integration in economics. Journal of Economics, 73, 5–59.

    Google Scholar 

  • Beller, 0K. and Nofsinger, J.R. (1998). On stock return seasonality and conditional heteroskedasticity. Journal of Financial Research, 21(2), 229–246.

    Google Scholar 

  • Black, F. and Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81, 637–654.

    Google Scholar 

  • Blackman R.B. and Tukey, J.W. (1959). The Measurement of Power Spectra. Dover Publications, Inc.

  • Bollerslev, T. and Engle, R.F. (1993). Common persistence in conditional variances. Econometrica, 61, 167–186.

    Google Scholar 

  • Bollerslev, T. and Mikkelsen, H.O. (1996). Modeling and pricing long memory in stock market volatility. Journal of Econometrics, 73, 151–184.

    Google Scholar 

  • Booth, J.R. and Booth, L.C. (1999). The presidential cycle anomaly in stock market returns.Working Paper, Arizona State University, Tempe.

    Google Scholar 

  • Breidt, F.J., Crato, N. and de Lima, P. (1998). The detection and estimation of long memory in stochastic volatility. Journal of Econometrics, 83, 325–348.

    Google Scholar 

  • Britten-Jones, M. (1999). The sampling error in estimates of mean-variance efficient portfolio weights. Journal of Finance, 54(2), 655–671.

    Google Scholar 

  • Chen, A.H.Y., Jen, F.C. and Zionts, S. (1971). The optimal portfolio revision policy. The Journal of Business, 51–61.

  • Chopra, V.K. and Ziemba, W.T. (1993). The effect of errors in means, variance, and covariances on optimal portfolio choice. Journal of Portfolio Management, Winter, 6–11.

    Google Scholar 

  • Cohen, K.J. and Pogue, G.A. (1967). An empirical evaluation of alternative portfolio selection models. Journal of Business, 40, 166–193.

    Google Scholar 

  • Cooper, R. (1974). Efficient capital markets and the quantity theory of money. Journal of Finance, 29, 887–908.

    Google Scholar 

  • Crum, R.L., Klingman, D.D. and Travis, T.A. (1979). Implementation of large-scale financial planning models: Solution efficient transformations. Journal of Financial and Quantitative Analysis, 14, 137–152.

    Google Scholar 

  • Dantzig, G.B. and Infanger, G. (1993). Multi-stage stochastic linear programs for portfolio optimization. Annuals of Operations Research, 45, 59–76.

    Google Scholar 

  • De Santis, G. and Gerard, B. (1997). International asset pricing and portfolio diversification with time-varying risk. Journal of Finance, 52(5), 1881–1912.

    Google Scholar 

  • Dumas, B. and Luciano, E. (1991). An exact solution to a dynamic portfolio choice problem under transaction costs. Journal of Finance, 46, 577–595.

    Google Scholar 

  • Durlauf, S.W. (1991). Spectral based testing of the martingale hypothesis. Journal of Econometrics, 50, 355–376.

    Google Scholar 

  • Elton, E.J. and Gruber, M.J. (1973). Estimating the dependence structure of share prices – implications for portfolio selection. Journal of Finance, 28, 1203–1233.

    Google Scholar 

  • Elton, E.J. and Gruber, M.J. (1974a). The multi-period consumption investment problem and single period analysis. Oxford Economics Papers, Sept., 289–595.

  • Elton, E.J. and Gruber, M.J. (1974b). On the optimality of some multiperiod portfolio selection criteria. Journal of Business, 47, 231–243.

    Google Scholar 

  • Elton, E.J. and Gruber, M.J. (1975). Finance as a Dynamic Process. Prentice Hall, Englewood Cliffs, NJ.

    Google Scholar 

  • Elton, E.J., Gruber, M.J. and Padberg, M.W. (1976). Simple criteria for optimal portfolio selection. Journal of Finance, 31(5), 1341–1357.

    Google Scholar 

  • Elton, E.J., Gruber, M.J. and Padberg, M.W. (1977). Simple criteria for optimal portfolio selection with upper bounds. Operations Research, 25, 952–967.

    Google Scholar 

  • Fama, E.F. (1970). Multiperiod consumption-investment decisions. American Economic Review, 60, 163–174.

    Google Scholar 

  • Fama, E.F. (1991). Efficient capital markets: II. Journal of Finance, 46(5), 1575–1617.

    Google Scholar 

  • Fama, E.F. and French, K.R. (1988). Permanent and temporary components of stock prices. Journal of Political Economy, 96(2), 246–273.

    Google Scholar 

  • Glover, F. and Jones, C.K. (1988). A stochastic generalized network model and large-scale algorithm for portfolio selection. Journal of Information and Optimization Science, 9, 299–316.

    Google Scholar 

  • Granger, C.W.J. (1988). Models that generate trends. Journal of Time Series Analysis, 9(4), 329–343.

    Google Scholar 

  • Granger, C.W.J. (1992). Forecasting stock market prices: Lessons for forecasters. International Journal of Forecasting, 8, 3–13.

    Google Scholar 

  • Granger, C.W.J. and Ding, Z. (1996). Varieties of long memory models. Journal of Econometrics, 73, 61–77.

    Google Scholar 

  • Granger, C.W.J. and Morgenstern, O. (1970). Predictability of Stock Market Prices. D.C. Heath Company, Mass.

    Google Scholar 

  • Grauer, R.R. and Hakansson, N.H. (1993). On the use of mean-variance and quadratic approximations in implementing dynamic investment strategies: A comparision of returns and investment policies. Management Science, 39, 856–871.

    Google Scholar 

  • Grinblatt, M. and Titman, S. (1987). The relation between mean-variance efficiency and arbitrage pricing. Journal of Business, 60(1), 97–112.

    Google Scholar 

  • Grinold, R.C. (1999). Mean-variance and scenario-based approaches to portfolio selection. Journal of Portfolio Management, Winter, 10–22.

  • Gunthorpe, D. and Levy, H. (1994). Portfolio composition and the investment horizon. Financial Analysts Journal, January–February, 51–56.

  • Hansen, L.P. and Richard, S.F. (1987). The role of conditioning information in deducing testable restrictions implied by dynamic asset pricing models. Econometrica, 55(3), 587–613.

    Google Scholar 

  • Harkansson, N. (1971a). Multi-period mean-variance analysis: Toward a general theory of portfolio choice. Journal of Finance, 26, 857–884.

    Google Scholar 

  • Harkansson, N. (1971b). On optimal myopic portfolio policies, with and without serial correlation of yields. Journal of Business, 44, 324–334.

    Google Scholar 

  • Harkansson, N. (1979). A characterization of optimal multi-period portfolio policies. TIMS Studies in the Management Sciences, 11, 169–177.

    Google Scholar 

  • Harris, F.J. (1978). On the use of windows for harmonic analysis with the discrete Fourier transform. Proceedings of the IEEE, 66(1), 51–83.

    Google Scholar 

  • Harvey, C.R. (1989). Time-varying conditional covariances in tests of asset pricing models. Journal of Financial Economics, 24, 289–317.

    Google Scholar 

  • Hensel, C.R. and Ziemba, W.T. (1996). Investment results from exploiting turn-of-the-month effects. Journal of Portfolio Management, Spring, 17–23.

  • Jenkins, G.M. and Watts, D.G. (1969). Spectral Analysis and Its Applications. Holden-Day.

  • Jones, C.K. (1992). Portfolio Management: New Models for Successful Investment Decisions. Mc-Graw Hill, Inc., London.

    Google Scholar 

  • Jones, C.K. (1997). PSS Release 2.0: Digital Portfolio Theory. Portfolio Selection Systems, Gainesville, Florida, http://www.portfolionetworks.com.

    Google Scholar 

  • Keim, D.B. (1983). Size-related anomalies and stock return seasonality. Journal of Financial Economics, 12, 13–32.

    Google Scholar 

  • Kleiner, B., Martin, R.D. and Thomson, D.J. (1979). Robust estimation of power spectra. Journal of the Royal Statistical Society B, 41(3), 313–351.

    Google Scholar 

  • Kroll, Y., Levy, H. and Markowitz, H.M. (1984). Mean-variance versus direct utility maximization. Journal of Finance, 39(1), 47–61.

    Google Scholar 

  • Lemke, C.E. (1965). Bimatrix equilibrium points and mathematical programming. Management Science, 11, 681–689.

    Google Scholar 

  • Li, D. and Ng, W.L. (2000). Optimal dynamic portfolio selection: Multiperiod mean-variance formulation. Mathematical Finance, 10(3), July, 87–406.

    Google Scholar 

  • Linn, S.C. and Lockwood, L.J. (1988). Short-termstock price patterns: NYSE,AMEX, OTC. Journal of Portfolio Management, Winter, 30–34.

  • Markowitz, H.M. (1952). Portfolio selection. Journal of Finance, 7, 77–91.

    Google Scholar 

  • Markowitz, H.M. (1956). The optimization of a quadratic function subject to linear constraints. Naval Research Logistics Quarterly, 3, 111–133.

    Google Scholar 

  • Markowitz, H.M. and Perold, A.F. (1981). Portfolio analysis with factors and scenarios. Journal of Finance, 36(14), 871–877.

    Google Scholar 

  • Markowitz, H.M., Todd, P., Xu, G. and Yamane, Y. (1992). Fast computation of mean-variance efficient sets using historical covariances. Journal of Financial Engineering, 1(2), 117–132.

    Google Scholar 

  • Merton, R.C. (1969). Lifetime portfolio selection under uncertainty: The continuous-time case. Review of Economics and Statistics, 51, 247–257.

    Google Scholar 

  • Merton, R.C. (1973). The theory of rational option pricing. Bell Journal of Economics and Management Science, 4, 141–183.

    Google Scholar 

  • Marple, S.L. (1987). Digital Spectral Analysis. Prentice-Hall, Inc.

  • Modigliani, F. and Miller, M. (1958). The cost of capital, corporation finance, and the theory of investment. American Economic Review, 48, 261–297.

    Google Scholar 

  • Mossin, J. (1968). Optimal multiperiod portfolio policies. Journal of Business, 215–229.

  • Mulvey, J.M. (1987). Nonlinear network models in finance. In Advances in Mathematical Programming and Financial Planning, 1, 253–262. JAI Press.

    Google Scholar 

  • Mulvey, J.M. and Vladimirou, H. (1989). Stochastic network optimization models for investment planning. Annuals of Operations Research, 20, 187–217.

    Google Scholar 

  • Mulvey, J.M. and Vladimirou, H. (1991). Applying the progressive hedging algorithm to stochastic generalized networks. Annuals of Operations Research, 31, 99–424.

    Google Scholar 

  • Mulvey, J.M. and Vladimirou, H. (1992). Stochastic network programming for financial planning problems. Management Science, 38(11), 1642–1664.

    Google Scholar 

  • Mulvey, J.M. and Ziemba, W.T. (1998). Asset and liability management systems for long-term investors: Discussion of the issues. Worldwide Asset and Liability Modeling, 3–38. Cambridge University Press, Cambridge, England.

    Google Scholar 

  • Nau, R.F. and McCardle, K.F. (1991). Arbitrage, rationality, and equilibrium. Theory and Decision, 31, 199–240.

    Google Scholar 

  • Ostermark, R. (1991). Vector forecasting and dynamic portfolio selection: Empirical efficiency of recursive multiperiod strategies. European Journal of Operational Research, 55, 46–56.

    Google Scholar 

  • Pang, J.S. (1980). A parametric linear complementary technique for optimal portfolio selection with a risk-free asset. Operations Research, 28, 927–941.

    Google Scholar 

  • Parzen, E. (1957). On choosing an estimate of the spectral density function of a stationary time series. Annals of Mathematical Statistics, 28, 921–932.

    Google Scholar 

  • Penman, S.H. (1987). The distribution of earnings news over time and seasonalities in aggregate stock returns. Journal of Financial Economics, 18, 199–228.

    Google Scholar 

  • Perold, A.F. (1984). Large-scale portfolio optimization. Management Science, 30(10), 1143–1160.

    Google Scholar 

  • Poterba, J.M. and Summers, L.H. (1988). Mean reversion in stock prices: Evidence and implications. Journal of Financial Economics, 22, 27–59.

    Google Scholar 

  • Praetz, P. (1979). Testing for a plat spectrum on efficient market price data. Journal of Finance, 34, 645–658.

    Google Scholar 

  • Rosenberg, B. (1974). Extra-market components of covariance in security returns. Journal of Financial and Quantitative Analysis, 9, 263–274.

    Google Scholar 

  • Ross, S. (1976). The arbitrage theory of capital asset pricing. Journal of Economic Theory, 13, 341–360.

    Google Scholar 

  • Rozeff, M.S. and Kinnery, W.R. (1976). Capital market seasonality: The case of stock returns. Journal of Financial Economics, 3, 379–402.

    Google Scholar 

  • Samuelson, P.A. (1969). Lifetime portfolio selection by dynamic stochastic programming. Review of Economics and Statistics, 51, 239–246.

    Google Scholar 

  • Sharpe, W.F. (1971). A linear programming application for the general portfolio analysis problem. Journal of Financial and Quantitative Analysis, 6, 1263–1275.

    Google Scholar 

  • Sharpe, W.F. (1963). A simplified model for portfolio analysis. Management Science, 9, 277–293.

    Google Scholar 

  • Smith, K.V. (1967). A transition model for portfolio revision. Journal of Finance, 22, 425–439.

    Google Scholar 

  • Thorley, S.R. (1995). The time-diversification controversy. Financial Analysts Journal, May–June, 68–76.

  • Wachtel, S.B. (1942). Certain observations on seasonal movements in stock prices. Journal of Business, 15(2), 184–193.

    Google Scholar 

  • Watson, M.W. (1986). Univariate detrending methods with stochastic trends. Journal of Monetary Economics, 18, 49–75.

    Google Scholar 

  • Welch, P.D. (1967). The use of fast Fourier transforms for the estimation of power spectra: A method based on time averaging over short modified periodograms. IEEE Transactions in Audio Electroacoustics, AU-15, June, 70–73.

    Google Scholar 

  • Wiener, N. (1930). Generalized harmonic analysis. Acta Math., 55, 117–258.

    Google Scholar 

  • Wiener, N. (1970). Time Series. M.I.T. Press.

  • Winkler, R.L. and Barry, C.B. (1975). A Bayesian model for portfolio selection and revision. Journal of Finance, 30, 179–192.

    Google Scholar 

  • Wolfe, P. (1959). The Simplex method for quadratic programming. Econometrica, 27, 382–398.

    Google Scholar 

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  1. Portfolio Selection Systems, 4300 NW 23rd Ave. Suite 125, Gainesville, FL, 32606, U.S.A.

    C. Kenneth Jones

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Jones, C.K. Digital Portfolio Theory. Computational Economics 18, 287–316 (2001). https://doi.org/10.1023/A:1014824005585

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