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 examine the implications of Max M. Weber's hypothesis for consumption, savings, and stock prices, concluding that when investors care about relative social status, propensity to consume and risk-taking behavior will depend on social standards and stock price will be volatile.
Abstract: In existing theory, wealth is no more valuable than its implied consumption rewards. In reality, investors acquire wealth not just for its implied consumption but for the resulting social status. Max M. Weber (1958) refers to this desire for wealth as the spirit of capitalism. The authors examine, both analytically and empirically, implications of Weber's hypothesis for consumption, savings, and stock prices. When investors care about relative social status, propensity to consume and risk-taking behavior will depend on social standards and stock prices will be volatile. The spirit of capitalism seems to be a driving force behind stock-market volatility and economic growth. Copyright 1996 by American Economic Association.
386 citations
TL;DR: In this paper, the permanent income hypothesis with rational expectation is restated, estimated, and tested by an instrumental variables technique on the postwar U.S. aggregate time-series data.
Abstract: The permanent income hypothesis with rational expectation is restated, estimated, and tested by an instrumental variables technique on the postwar U.S. aggregate time-series data. The hypothesis is accepted on a consumption series which includes service flows from consumer durables. If the consumption series is the one in the National Income and Product Accounts, the hypothesis is decisively rejected. An explanation is suggested to reconcile the conflicting test results.
379 citations
TL;DR: In this article, the authors examined the effects of uncertainty about the stock return predictability on the optimal dynamic portfolio choice in a continuous time setting for a longhorizon investor.
Abstract: This paper examines the effects of uncertainty about the stock return predictability on optimal dynamic portfolio choice in a continuous time setting for a longhorizon investor. Uncertainty about the predictive relation affects the optimal portfolio choice through dynamic learning, and leads to a state-dependent relation between the optimal portfolio choice and the investment horizon. There is substantial market timing in the optimal hedge demands, which is caused by stochastic covariance between stock return and dynamic learning. The opportunity cost of ignoring predictability or learning is found to be quite substantial. How MUCH SHOULD A "long-horizon" investor allocate to equity? The conventional wisdom says that a long-horizon investor should invest more in equity because, over long horizons, above-average returns tend to offset belowaverage returns. This is the notion of "time diversification." Samuelson (1989, 1990), among others, has argued that the notion of time diversification is spurious: when stock returns are i.i.d., for example, the optimal portfolio is independent of the horizon for an investor with an isoelastic utility function. When stock returns are predictable, however, the optimal stock allocation does depend on the investment horizon, even if the investor has an isoelastic utility. In this setting, the investment opportunity set is stochastic and the intertemporal hedge demand introduced by Merton (1971) becomes central to the dynamics of asset allocation. In this paper, we study how learning about stock return predictability affects the intertemporal hedge demand and the optimal dynamic portfolio rules, and re-examine the validity of the prediction of time diversification in the context of uncertain predictability. Although there is a growing body of evidence that stock returns are predictable, the existence of predictability is still subject to considerable debate. On the one hand, many studies have identified variables that predict future
379 citations
TL;DR: A portfolio formed from a given list of assets is defined as a numeraire portfolio for the list if (a) it is self-financing, (b) its value is always positive, and (c) zero is always the best conditional forecast of the numeraire-dominated rate of return of every asset on the list.
378 citations
TL;DR: Lewellen et al. as mentioned in this paper studied the asset-pricing implications of parameter uncertainty and showed that when investors must learn about expected cash-f lows, empirical tests can find patterns in the data that differ from those perceived by rational investors.
Abstract: This paper studies the asset-pricing implications of parameter uncertainty We show that, when investors must learn about expected cash f lows, empirical tests can find patterns in the data that differ from those perceived by rational investors Returns might appear predictable to an econometrician, or appear to deviate from the Capital Asset Pricing Model, but investors can neither perceive nor exploit this predictability Returns may also appear excessively volatile even though prices react efficiently to cash-f low news We conclude that parameter uncertainty can be important for characterizing and testing market efficiency THERE IS MUCH EVIDENCE THAT STOCK RETURNS are predictable At the aggregate level, variables such as interest rates, financial ratios, and the default premium appear to forecast stock returns ~eg, Fama and French ~1989! and Lewellen ~2001!! Further, LeRoy and Porter ~1981! and Shiller ~1981! argue that price volatility cannot be explained solely by changes in dividends, providing indirect evidence that stock returns are predictable At the firm level, Fama and French ~1992, 1996! and Jegadeesh and Titman ~1993! show that size, book-to-market, and past returns together explain much of the crosssectional variation in average returns There seems little doubt that expected returns vary both cross-sectionally and over time The interpretation of predictability is more contentious The empirical results are potentially consistent with either market efficiency or mispricing In general terms, market efficiency implies that prices fully ref lect available information To formalize this idea for empirical testing, Fama ~1976! distinguishes between the probability distribution of returns perceived by “the market,” based on whatever information investors view as relevant, and the true distribution of returns conditional on all information The market is said to be ~informationally! efficient if these distributions are the same It follows that, in an efficient market, investors should be aware of any cross* Lewellen is from the MIT Sloan School of Management and Shanken is from the Simon Graduate School of Business Administration at the University of Rochester, and NBER We are
378 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