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16th July 2024


Below are links to research papers by Ken Jones, more papers can be found on ResearchGate or on SSRN. If you are interested in this research, are interested in collaboration, or participating in developments in this area submit the contact form with Subject: Research.

Mean-reversion Risk and the Random Walk Hypothesis
C. Kenneth Jones,
Review of Financial Economics
2023, Volume 41, pp 493-516

ABSTRACT The nature of risk and long-term returns is not fully understood. There is need for a measure of long-term risk at multiple horizons. Frequency domain digital signal processing, with an additive noise model, tests the random walk hypothesis for individual firm total and idiosyncratic risk at 2-month to 4-year periods. All firms have significant 12-month risk. Monthly effects influence small firms. Large firm total risk and mid-cap firm idiosyncratic risk are influenced by annual and 8-year mean reversions. Large firm idiosyncratic risk has 4-year mean-reversion risk. Results suggest that single-period risk is composed of multiple long-term calendar and non-calendar-length variances.(Download Full text)

Modern Portfolio Theory, Digital Portfolio Theory and Intertemporal Portfolio Choice
C. Kenneth Jones,
American Journal of Industrial and Business Management
2017, Volume 7, pp 833-854

ABSTRACT The paper compares three portfolio optimization models. Modern portfolio theory (MPT) is a short-horizon volatility model. The relevant time horizon is the sampling interval. MPT is myopic and implies that investors are not concerned with long-term variance or mean-reversion. Intertemporal portfolio choice is a multiple period model that revises portfolios continuously in response to relevant signals to reduce variance of terminal wealth over the holding period. Digital portfolio theory (DPT) is a non-myopic, discrete time, long-horizon variance model that does not include volatility. DPT controls mean-reversion variances in single period solutions based on holding period and hedging and speculative demand. (Download Full text)

Digital Portfolio Theory: Portfolio Size, versus Alpha, Beta, and Horizon Risk
C. Kenneth Jones,
Mar 2009 · SSRN Electronic Journal

ABSTRACT I examine capabilities of Digital Portfolio Theory(DPT) and extend it to control portfolio size. DPTis a static, single period mean-variance-autocovariance portfolio optimization paradigm that allows returns to be mean-reverting. The optimal dynamic single period solutions depend on the unconditional predictability of second moments. Optimal portfolios and feasible sizes are examined in a universe of US sector indexes for three strategies; total risk, passive versus active risk, and horizon   dependent   risk.   Individual   allocations   depend   on   holding   period,   risk   tolerance,   aggressiveness, and time dependent expectations. Large efficient portfolios are infeasible for low total, high active, and high long horizon risk. (Download Full text)

Portfolio Size in Stochastic Portfolio Networks using Digital Portfolio Theory
C. Kenneth Jones,
Journal of Mathematical Finance
2013, Volume 3, pp 280-290

ABSTRACT. The investment portfolio with stochastic returns can be represented as a maximum flow generalized network with stochastic multipliers. Modern portfolio theory (MPT) [1] provides a myopic short horizon solution to this network by adding a parametric variance constraint to the maximize flow objective function. MPT does not allow the number of securities in solution portfolios to be specified. Integer constraints to control portfolio size in MPT results in a nonlinear mixed integer problem and is not practical for large universes. Digital portfolio theory (DPT) [2] finds a non-myopic long-term solution to the nonparametric variance constrained portfolio network. This paper discusses the long horizon nature of DPT and adds zero-one (0-1) variables to control portfolio size. We find optimal size constrained allocations from a universe of US sector indexes. The feasible size of optimal portfolios depends on risk. Large optimal portfolios are infeasible for low risk investors. High risk investors can increase portfolio size and diversification with little effect on return. (Download Full text)

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 Full text)

A Network Model For Foreign Exchange Arbitrage, Hedging and Speculation
C.Kenneth Jones
Journal of Theoretical and Applied Finance.
Volume 4 No 6, December 2001, p 837-852.

ABSTRACT. This paper presents alternative approach to foreign exchange market trading decisions. The model is equally applicable to the arbitrage practices of international banks, to the hedging decisions of multinational corporations, to the investment decisions of currency fund managers and to the uncovered positions of currency speculators. By using a network model to represent these situations complex problems can be modeled and the optimization problem required to maximize profit or eliminate risk can be accurately formulated. (Download Full text)

Calendar Based Risk, Firm Size and the Additive Market Noise Model
C. Kenneth Jones
December 2001.

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 Full text)