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 investigated risk attitudes among different types of individuals using several different measures of risk attitudes, including questions on choices between uncertain income streams suggested by Barsky et al. and a number of ad hoc measures.
Abstract: The paper investigates risk attitudes among different types of individuals. The authors use several different measures of risk attitudes, including questions on choices between uncertain income streams suggested by Barsky et al. (1997) and a number of ad hoc measures. As in Barsky et al. (1997) and Arrondel (2002), the authors first analyse individual variation in the risk aversion measures and explain them by background characteristics (both "objective" characteristics and other subjective measures of risk preference). Next, the authors incorporate the measured risk attitudes into a household partfolio allocation model, which explains portfolio shares, while accounting for incomplete portfolios. The authors results show that the Barsky et al. (1997) measure has little explanatory power, whereas ad hoc measures do a considerably better job. The authors provide a discussion of the reasons for this finding.
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TL;DR: It is shown how background risks might lead to seemingly U-shaped relative risk aversion for a representative investor and can explain some paradoxical choice behavior.
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TL;DR: In this article, the authors investigate Grossman and Laroque's conjecture that costs of adjusting consumption can account, in part, for the empirical failure of the consumption-based capital asset pricing model (CCAPM).
Abstract: We investigate Grossman and Laroque's (1990) conjecture that costs of adjusting consumption can account, in part, for the empirical failure of the consumptionbased capital asset pricing model (CCAPM). We incorporate small fixed costs of consumption adjustment into a CCAPM with heterogeneous agents. We find that undetectably small consumption adjustment costs can account for much of the discrepancy between the observed variance of nondurable aggregate consumption growth and the predictions of the CCAPM, and can partially reconcile nondurable consumption data with the observed equity premium. We conclude that the CCAPM's implications are nonrobust to extremely small adjustment costs. THE CONSUMPTION-BASED CAPITAL ASSET PRICING MODELS (CCAPMs)1 of Lucas (1978), Breeden (1979), and Grossman and Shiller (1982) have difficulty matching the high volatility of equity returns and the high mean equity premium found in U.S. data. First, the variance of the CCAPM asset pricing kernel is too low to generate plausible equity-return volatility. More precisely, Hansen and Jagannathan (1991) and Cochrane and Hansen (1992) show that, for any conjectured pricing kernel mean, the variance of the kernel is too low to satisfy the Hansen-Jagannathan bounds without implausibly high risk aversion or substantial habit formation.2 Second, the covariance between the CCAPM asset pricing kernel and excess equity returns is too low to generate a plausible equity premium. More precisely, let us define EP' as follows:
72 citations
TL;DR: For example, this article showed that an increase in the tax rate reduces growth by much more than predicted by non-stochastic models; theoretically, it is actually possible for a tax increase to increase growth.
72 citations
TL;DR: The authors summarizes the revolution in how financial economists view the world and summarizes the new facts in finance, concluding that stock and bond returns, once thought to be independent over time, turn out to be predictable at long horizons, with no strong tendency for the strategy's returns to move up and down with the market as a whole.
Abstract: Introduction and summary A companion article in this issue, "New facts in finance," summarizes the revolution in how financial economists view the world. Briefly, there are strategies that result in high average returns without large betas, that is, with no strong tendency for the strategy's returns to move up and down with the market as a whole. Multifactor models have supplanted the capital asset pricing model (CAPM) in describing these phenomena. Stock and bond returns, once thought to be independent over time, turn out to be predictable at long horizons. All of these phenomena seem to reflect a premium for holding macroeconomic risks associated with the business cycle and for holding assets that do poorly in times of financial distress. They also all reflect the information in prices - high prices lead to low returns and low prices lead to high returns. The world of investment opportunities has also changed. Where once an investor faced a fairly straightforward choice between managed mutual funds, index funds, and relatively expensive trading on his own account, now he must choose among a bewildering variety of fund styles (such as value, growth, small cap, balanced, income, global, emerging market, and convergence), as well as more complex claims of active fund managers with customized styles and strategies, and electronic trading via the Internet. (Msn.com's latest advertisement suggests that one should sign up in order to "check the hour's hottest stocks." Does a beleaguered investor really have to do that to earn a reasonable return?) The advertisements of investment advisory services make it seem important to tailor an investment portfolio from this bewildering set of choices to the particular circumstances, goals, and desires of each investor. What should an investor do? An important current of academic research investigates how portfolio theory should adapt to our new view of the financial world. In this article, I summarize this research and I distill its advice for investors. In particular, which of the bewildering new investment styles seem most promising? Should you attempt to time stock, bond, or foreign exchange markets, and if so how much? To what extent and how should an investment portfolio be tailored to your specific circumstances? Finally, what can we say about the future investment environment? What kind of products will be attractive to investors in the future, and how should public policy react to these financial innovations? I start by reviewing the traditional academic portfolio advice, which follows from the traditional view that the CAPM is roughly correct and that returns are not predictable over time. In that view, all investors (who do not have special information) should split their money between risk-free bonds and a broad-based passively managed index fund that approximates the "market portfolio." More risk-tolerant investors put more money into the stock fund, more risk averse investors put more money into the bond fund, and that is it. The new academic portfolio advice reacts to the new facts. An investor should hold, in addition to the market portfolio and risk-free bonds, a number of passively managed "style" funds that capture the broad (nondiversifiable) risks common to large numbers of investors. In addition to the overall level of risk aversion, his exposure to or aversion to the various additional risk factors matters as well. For example, an investor who owns a small steel company should shade his investments away from a steel industry portfolio, or cyclical stocks in general; a wealthy investor with no other business or labor income can afford to take on the "value" and other stocks that seem to offer a premium in return for potentially poor performance in times of financial distress. The stock market is a way of transferring risks; those exposed to risks can hedge them by proper investments, and those who are not exposed to risks can earn a premium by taking on risks that others do not wish to shoulder. …
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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