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Merton's portfolio problem
About: Merton's portfolio problem is a research topic. Over the lifetime, 714 publications have been published within this topic receiving 39414 citations.
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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.
4,952 citations
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
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
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TL;DR: Merton's most notable works include the intertemporal capital asset pricing model, the Black-Scholes-Merton option pricing formula, and the Merton structural model for credit risk.
Abstract: Robert C Merton is John and Natty McArthur University Professor at Harvard Business School He shared the Nobel Prize in Economic Sciences in 1997 He introduced Ito calculus to finance and economics and made significant contributions in asset pricing, corporate finance, empirical finance, and financial systems His most notable works include the intertemporal capital asset pricing model, the Black–Scholes–Merton option pricing formula, the Merton jump-diffusion model, and the Merton structural model for credit risk
Keywords:
Robert Merton;
continuous-time finance;
intertemporal capital asset pricing model;
derivatives;
options;
Merton model;
credit risk;
institutions;
financial systems
1,715 citations
TL;DR: In this paper, the authors examined the accuracy and contribution of the Merton distance to default (DD) model, which is based on Merton's (1974) bond pricing model, and compared the model to a "naive" alternative, which uses the functional form suggested by Merton model but does not solve the model for an implied probability of default.
Abstract: We examine the accuracy and contribution of the Merton distance to default (DD) model, which is based on Merton's (1974) bond pricing model. We compare the model to a “naive” alternative, which uses the functional form suggested by the Merton model but does not solve the model for an implied probability of default. We find that the naive predictor performs slightly better in hazard models and in out-of-sample forecasts than both the Merton DD model and a reduced-form model that uses the same inputs. Several other forecasting variables are also important predictors, and fitted values from an expanded hazard model outperform Merton DD default probabilities out of sample. Implied default probabilities from credit default swaps and corporate bond yield spreads are only weakly correlated with Merton DD probabilities after adjusting for agency ratings and bond characteristics. We conclude that while the Merton DD model does not produce a sufficient statistic for the probability of default, its functional form is useful for forecasting defaults.
1,662 citations