Digital Portfolio Theory
C. Kenneth Jones,
Journal of Computational Economics.
December 2001, Volume 18, Number 3, pp287-316

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.(Download PDF file - dpt.pdf 30pages-182kb)

ABSTRACT. A model of risk is presented based on multiple calendar-based risk factors rather than a single variance risk measure. The total variance of return is decomposed into calendar and non-calendar variance components using the variance spectral density. Linear digital signal processing theory is applied by representing return processes as digital signals. The digital signal processing additive market noise model specifies that observed risk is made up of information signal risk plus additive market noise risk. Calendar and non-calendar variance components of the information signal describe the memory of return processes. The empirical test examines the risk of security information signals using small sample techniques. Large firms are dominated by four-year and one-year calendar variance. Small firms display January-like risk. Security exposure to various calendar anomalies can be measured using this approach. The conclusion is that the calendar-based risk of security's information signals corresponds to the seasonal variation in the returns to large and small firms. (Download PDF file - mktnoise.pdf 43pages-270kb)