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 whether one can use option-implied information to improve the selection of mean-variance portfolios with a large number of stocks, and to document which aspects of option implied information are most useful to improve their out-of-sample performance.
Abstract: Our objective in this paper is to examine whether one can use option-implied information to improve the selection of mean-variance portfolios with a large number of stocks, and to document which aspects of option-implied information are most useful to improve their out-of-sample performance. Portfolio performance is measured in terms of volatility, Sharpe ratio, and turnover. Our empirical evidence shows that using option-implied volatility helps to reduce portfolio volatility. Using option-implied correlation does not improve any of the metrics. Using option-implied volatility, risk premium, and skewness to adjust expected returns leads to a substantial improvement in the Sharpe ratio, even after prohibiting short sales and accounting for transaction costs.
148 citations
TL;DR: Detemple et al. as mentioned in this paper provided a simple binomial framework to value American-style derivatives subject to trading restrictions, where the optimal investment of liquid wealth is solved simultaneously with the early exercise decision of the nontraded derivative.
Abstract: We provide a simple binomial framework to value American-style derivatives subject to trading restrictions. The optimal investment of liquid wealth is solved simultaneously with the early exercise decision of the nontraded derivative. Noshort-sales constraints on the underlying asset manifest themselves in the form of an implicit dividend yield in the risk-neutralized process for the underlying asset. One consequence is that American call options may be optimally exercised prior to maturity even when the underlying asset pays no dividends. Applications to executive stock options (ESO) are presented: it is shown that the value of an ESO could be substantially lower than that computed using the Black‐Scholes model. We also analyze nontraded payoffs based on a price that is imperfectly correlated with the price of a traded asset. The economics of asset pricing when one or more of the assets in the opportunity set are either subject to trading restrictions or entirely nontraded is a matter of great interest. Viewed from a practical perspective, we have several important examples of such assets that are subject to trading restrictions. Pensions, which represent perhaps the most significant of assets held by individual households, are subject to trading restrictions. It is typically the case that assets in pensions are not available for immediate consumption. Borrowing against pension assets is subject to significant direct and indirect costs by way of taxes and early withdrawal penalties. Human capital is another example. Housing investment is also illiquid and subject to significant transaction costs. Together, pensions, human capital, and housing constitute a substantial part of a typical household’s assets. The significance of such nontraded assets for risk premia has already been noted by Bewley (1982). There are other circumstances where lack of unrestricted trading plays an important role. Executive compensation plans usually take the This article was presented at Boston University. We would like to thank the editor, Bernard Dumas, and two anonymous referees for very helpful comments. We also thank Nalin Kulatilaka and seminar participants for useful suggestions. Ganlin Chang, Fei Guan, and Carlton Osakwe provided valuable research assistance. J. Detemple acknowledges support from the Social Sciences and Humanities Research ‐
147 citations
01 Jan 1989
TL;DR: For example, the authors pointed out that very large increases or decreases would always be possible even if changes in stock prices were normally distributed, but they would occur only rarely and that the variation of stock prices does not nicely match the familiar bell-shaped normal distribution.
Abstract: MOST PEOPLE AGREE that stock prices sometimes behave in strange ways. Going beyond this simple observation typically proves more difficult. For at least the past quarter century, economists have been well aware that the variation of stock prices does not nicely match the familiar bell-shaped normal distribution.1 The problem is too many extreme movements. Very large increases or decreases would always be possible even if changes in stock prices were normally distributed, but they would occur only rarely. By contrast, actual stock prices rise or fall by large percentage amounts fairly often-certainly often enough to raise serious doubts that the usual normal distribution provides a useful way to think about how they vary. Economists and other analysts of the stock market have tended to react to this problem in either of two ways. The most common approach is simply to ignore it and go ahead to analyze changes in stock prices as
146 citations
TL;DR: In this article, the authors studied the time series of illiquidity for different maturities over an extended period of time and compared time-series determinants of on-the-run and off-the run illiquidities.
Abstract: Previous studies of Treasury market illiquidity span short time periods and focus on particular maturities. In contrast, we study the time series of illiquidity for different maturities over an extended period of time. We also compare time-series determinants of on-the-run and off-the-run illiquidity. Illiquidity increases and the difference between spreads of long- and short-term bonds significantly widens during recessions, suggesting a “flight to liquidity,” wherein investors shift into the more liquid short-term bonds during economic contractions. Macroeconomic variables such as inflation and federal funds rates forecast off-the-run illiquidity significantly but have only modest forecasting ability for on-the-run illiquidity. Bond returns across maturities are forecastable by off-the-run but not on-the-run bond illiquidity. Thus, off-the-run illiquidity, by reflecting macro shocks first, is the primary source of the liquidity premium in the Treasury market.
146 citations
Cites background from "Optimum consumption and portfolio r..."
...For instance, the portfolio-rebalancing arguments of Merton (1971) imply return-dependent investing behavior, and such order imbalances in response to a price change may strain liquidity....
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TL;DR: In this paper, the authors compare parametric and nonparametric estimators of asset pricing with or without assuming a distribution for security returns and show that the parametric estimator is robust to departures from any particular distribution, and it is more consistent with the spirit underlying utility-based asset pricing models.
Abstract: Utility-based models of asset pricing may be estimated with or without assuming a distribution for security returns; both approaches are developed and compared here The chief strength of a parametric estimator lies in its computational simplicity and statistical efficiency when the added distributional assumption is true In contrast, the nonparametric estimator is robust to departures from any particular distribution, and it is more consistent with the spirit underlying utility-based asset pricing models since the distribution of asset returns remains unspecified even in the empirical work The nonparametric approach turns out to be easy to implement with precision nearly indistinguishable from its parametric counterpart in this particular application The application shows that log utility is consistent with the data over the period 1926-1981 THE DISTRIBUTION OF ASSET returns is a fundamental quantity to be explained by financial economics Consequently, utility-based models of asset pricing are of special interest since they allow the distributions of returns to be explained rather than assumed as in distribution-based models
144 citations
Cites background from "Optimum consumption and portfolio r..."
..., Cox, Ingersoll, and Ross [4], Hakansson [14], Kraus and Litzenberger [23], Merton [27], Rubinstein [35], and Samuelson [36]); by estimating the difference between RRA and one, the appropriateness of these results can be judged....
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References
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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