Optimum consumption and portfolio rules in a continuous-time model☆
TL;DR: In this paper, the authors considered the continuous-time consumption-portfolio problem for an individual whose income is generated by capital gains on investments in assets with prices assumed to satisfy the geometric Brownian motion hypothesis, which implies that asset prices are stationary and lognormally distributed.
About: This article is published in Journal of Economic Theory.The article was published on 1971-12-01 and is currently open access. It has received 4952 citations till now. The article focuses on the topics: Geometric Brownian motion & Intertemporal portfolio choice.
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TL;DR: In this article, the authors demonstrate how a simple risk management practice that accounts for benchmarking can ameliorate the adverse effects of managerial incentives, and contrast with the conventional view that benchmarking a fund manager is not in the best interest of investors.
Abstract: Money managers are rewarded for increasing the value of assets under management. This gives a manager an implicit incentive to exploit the well-documented positive fund-flows to relative-performance relationship by manipulating her risk exposure. The misaligned incentives create potentially significant deviations of the manager’s policy from that desired by fund investors. In the context of a familiar continuous-time portfolio choice model, we demonstrate how a simple risk management practice that accounts for benchmarking can ameliorate the adverse effects of managerial incentives. Our results contrast with the conventional view that benchmarking a fund manager is not in the best interest of investors.
41 citations
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TL;DR: The authors examined the effect of liquidity constraints on consumption expenditures using a single-time cross-section data set and estimated a reduced-form equation for consumption on high-saving households by the Tobit procedure to account for the selectivity bias.
Abstract: This paper examines the effect of liquidity constraints on consumption expenditures using a single-time cross-section data set A reduced-form equation for consumption is estimated on high-saving households by the Tobit procedure to account for the selectivity bias Since high-saving households are not likely to be liquidity constrained, the estimated equation is an appropriate description of how desired consumption dictated by the life cycle-permanent income hypothesis is related to the variables available in the cross-section data When the reduced-form equation is used to predict desired consumption, the gap between desired consumption and measured consumption is most evident for young households
41 citations
TL;DR: In this article, the authors hypothesize that news that contradicts investors' sentiment causes cognitive dissonance, which slows the diffusion of signals that oppose the direction of sentiment, and show that momentum profits arise only under optimism, and are driven principally by strong momentum in losing stocks.
Abstract: This paper sheds empirical light on whether sentiment affects the profitability of price momentum strategies. We hypothesize that news that contradicts investors’ sentiment causes cognitive dissonance, which slows the diffusion of signals that oppose the direction of sentiment. This phenomenon tends to cause underpricing of losers under optimism and underpricing of winners under pessimism. While the latter phenomenon can be corrected by arbitrage buying, short-selling constraints impede arbitraging of losers under optimism, causing momentum to be stronger in optimistic periods. Our empirical analysis supports this argument by showing that momentum profits arise only under optimism, and are driven principally by strong momentum in losing stocks. This result survives a host of robustness checks including controls for market returns, firm size and analyst following. An analysis of net order flows from small and large trades indicates that small (but not large) investors are slow to sell losers during optimistic periods. Momentum-based hedge portfolios formed during optimistic periods experience long-run reversals.
41 citations
Cites background from "Optimum consumption and portfolio r..."
...…the point estimate of 40 This result may be reinforced by portfolio rebalancing; specifically, since both winners and losers lose value in pessimistic periods, institutions may become net buyers to restore their appropriate weight in a standard asset allocation setting [e.g., Merton (1971)]....
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TL;DR: In this article, the authors outline the origin of the modern theory of risk premiums, the history of its testing, and surveys the current failure of this theory across over 20 different asset classes.
Abstract: Risk premiums are presumably omnipresent and extremely difficult if not impossible to measure. This paper outlines the origin of the modern theory of risk premiums, the history of its testing, and surveys the current failure of this theory across over 20 different asset classes. A new theory that can explain the absence of a risk premium is presented. The key is that when agents are concerned about relative wealth, risk taking is then deviating from the consensus or market portfolio. In this environment, all risk becomes like idiosyncratic risk in the standard model, avoidable so unpriced. (JEL D01, D81, G11, G12)
41 citations
TL;DR: In this paper, the authors provide a theoretical analysis of how endogenous time-varying margin requirements affect capital market equilibrium and find that margin requirements, when there are no other market frictions, reduce the volatility and correlation of returns as well as the risk-free rate, but increase the market price of risk, the risk premium, and the price of risky assets.
Abstract: This paper provides a novel theoretical analysis of how endogenous time-varying margin requirements affect capital market equilibrium. I find that margin requirements, when there are no other market frictions, reduce the volatility and correlation of returns as well as the risk-free rate, but increase the market price of risk, the risk premium, and the price of risky assets. Furthermore, margin requirements generate a strong cross-sectional dispersion of stock return volatilities. The results emphasize that a general equilibrium analysis may reverse the conclusions of a partial equilibrium analysis often employed in the literature.
41 citations
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TL;DR: In this paper, the combined problem of optimal portfolio selection and consumption rules for an individual in a continuous-time model was examined, where his income is generated by returns on assets and these returns or instantaneous "growth rates" are stochastic.
Abstract: OST models of portfolio selection have M been one-period models. I examine the combined problem of optimal portfolio selection and consumption rules for an individual in a continuous-time model whzere his income is generated by returns on assets and these returns or instantaneous "growth rates" are stochastic. P. A. Samuelson has developed a similar model in discrete-time for more general probability distributions in a companion paper [8]. I derive the optimality equations for a multiasset problem when the rate of returns are generated by a Wiener Brownian-motion process. A particular case examined in detail is the two-asset model with constant relative riskaversion or iso-elastic marginal utility. An explicit solution is also found for the case of constant absolute risk-aversion. The general technique employed can be used to examine a wide class of intertemporal economic problems under uncertainty. In addition to the Samuelson paper [8], there is the multi-period analysis of Tobin [9]. Phelps [6] has a model used to determine the optimal consumption rule for a multi-period example where income is partly generated by an asset with an uncertain return. Mirrless [5] has developed a continuous-time optimal consumption model of the neoclassical type with technical progress a random variable.
4,908 citations
Book•
01 Jan 1965
TL;DR: This book should be of interest to undergraduate and postgraduate students of probability theory.
Abstract: This book should be of interest to undergraduate and postgraduate students of probability theory.
3,597 citations
TL;DR: In this paper, the optimal consumption-investment problem for an investor whose utility for consumption over time is a discounted sum of single-period utilities, with the latter being constant over time and exhibiting constant relative risk aversion (power-law functions or logarithmic functions), is discussed.
Abstract: Publisher Summary This chapter reviews the optimal consumption-investment problem for an investor whose utility for consumption over time is a discounted sum of single-period utilities, with the latter being constant over time and exhibiting constant relative risk aversion (power-law functions or logarithmic functions). It presents a generalization of Phelps' model to include portfolio choice and consumption. The explicit form of the optimal solution is derived for the special case of utility functions having constant relative risk aversion. The optimal portfolio decision is independent of time, wealth, and the consumption decision at each stage. Most analyses of portfolio selection, whether they are of the Markowitz–Tobin mean-variance or of more general type, maximize over one period. The chapter only discusses special and easy cases that suffice to illustrate the general principles involved and presents the lifetime model that reveals that investing for many periods does not itself introduce extra tolerance for riskiness at early or any stages of life.
2,369 citations
Book•
17 Jan 2012
TL;DR: In this article, a book on stochastic stability and control dealing with Liapunov function approach to study of Markov processes is presented, which is based on the work of this article.
Abstract: Book on stochastic stability and control dealing with Liapunov function approach to study of Markov processes
1,293 citations
987 citations