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Digital Portfolio Theory
"... 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 ..."
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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 noncalendar variance. The paper formulates a single period, digital signal processing, portfolio selection model using crosscovariance 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. Key words: portfolio optimization, portfolio theory, digital signal processing, calendar anomalies 1.
Biases and violations of Modigliani and Miller’s Proposition I
, 2005
"... The notion of Net Present Value (NPV) is thought to formally translate the notion of economic profit, where the discount rate is the cost of capital. The latter is the expected rate of return of an equivalentrisk alternative that the investor might undertake and is often found by making recourse to ..."
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The notion of Net Present Value (NPV) is thought to formally translate the notion of economic profit, where the discount rate is the cost of capital. The latter is the expected rate of return of an equivalentrisk alternative that the investor might undertake and is often found by making recourse to the Capital Asset Pricing Model. This paper shows that the notions of disequilibrium NPV and economic profit are not equivalent: NPVminded agents are open to framing effects and to arbitrage losses, which imply violations of Modigliani and Miller’s Proposition I. The notion of disequilibrium (present) value, deductively derived from the CAPM by several authors and widely used in applied corporate finance, should therefore be dismissed.
for valuation and decision making
, 2005
"... Abstract. This paper shows that a decision maker using the CAPM for valuing firms and making decisions may contradict Modigliani and Miller’s Proposition I, if he adopts the widelyaccepted disequilibrium NPV. As a consequence, CAPMminded agents employing this NPV are open to arbitrage losses and m ..."
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Abstract. This paper shows that a decision maker using the CAPM for valuing firms and making decisions may contradict Modigliani and Miller’s Proposition I, if he adopts the widelyaccepted disequilibrium NPV. As a consequence, CAPMminded agents employing this NPV are open to arbitrage losses and miss arbitrage opportunities. As a result, even though the use of the disequilibrium NPV for decisionmaking is deductively drawn from the CAPM, its use for both valuation and decision should be rejected.
Primed in U.S.A. STATE DEPENDENT EXPECTED UTILITY EOR SAVAGE'S STATE SPACE
"... This paper generalizes the Debreu/Gorman characterization of additively decomposable functionals and separable preferences to infinite dimensions. The first novelty concerns the very definition of additively decomposable functional for infinite dimensions. For decision under uncertainty, our result ..."
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This paper generalizes the Debreu/Gorman characterization of additively decomposable functionals and separable preferences to infinite dimensions. The first novelty concerns the very definition of additively decomposable functional for infinite dimensions. For decision under uncertainty, our result provides a statedependent extension of Savage's expected utility. A characterization in terms of preference conditions identifies the empirical content of the model; it amounts to Savage's axiom system with P4 (likelihood ordering) dropped. Our approach does not require that a (probability) measure on the state space be given a priori, or can be derived from extraneous conditions outside the realm of decision theory. Bayesian updating of new information is still possible, even though no prior probabilities are given. The finding suggests that the surething principle, rather than prior probability, is at the heart of Bayesian updating. 1. Introduction. Separability