Dynamic Portfolio Choice

Mapping Intimacies ◽

10.1093/acprof:oso/9780190241148.003.0009 ◽

2017 ◽

Author(s):

Kerry E. Back

Keyword(s):

Portfolio Choice ◽

Optimal Portfolio ◽

Value Functions ◽

Marginal Value ◽

First Order ◽

Complete Market ◽

Dynamic Portfolio ◽

Static Approach ◽

Dynamic Portfolio Choice ◽

Period Model

The first‐order condition for optimal portfolio choice is called the Euler equation. Optimal consumption can be computed by a static approach in a dynamic complete market and by orthogonal projection for a quadratic utility investor. Dynamic programming and the Bellman equation are explained. The envelope condition and hedging demands are explained. Investors with CRRA utility have CRRA value functions. Whether the marginal value of wealth is higher for a CRRA investor in good states or in bad states depends on whether risk aversion is less than or greater than 1. With IID returns, the optimal portfolio for a CRRA investor is the same as the optimal portfolio in a single‐period model.

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A Dynamic Mean-Variance Analysis for Log Returns

Management Science ◽

10.1287/mnsc.2019.3493 ◽

2020 ◽

Cited By ~ 5

Author(s):

Min Dai ◽

Hanqing Jin ◽

Steven Kou ◽

Yuhong Xu

Keyword(s):

Portfolio Choice ◽

Choice Model ◽

Risky Assets ◽

Complete Market ◽

Dynamic Portfolio ◽

Short Sell ◽

Dynamic Portfolio Choice ◽

Risk Free Rate ◽

Mean Variance

We propose a dynamic portfolio choice model with the mean-variance criterion for log returns. The model yields time-consistent portfolio policies and is analytically tractable even under some incomplete market settings. The portfolio policies conform with conventional investment wisdom (e.g., richer people should invest more absolute amounts of money in risky assets; the longer the investment time horizon, the more proportional amount of money should be invested in risky assets; and for long-term investment, people should not short-sell major stock indices whose returns are higher than the risk-free rate), and the model provides a direct link with the constant relative risk aversion utility maximization in a complete market. This paper was accepted by Kay Giesecke, finance.

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Continuous-Time Portfolio Choice and Pricing

10.1093/acprof:oso/9780190241148.003.0014 ◽

2017 ◽

Author(s):

Kerry E. Back

Keyword(s):

Portfolio Choice ◽

Bellman Equation ◽

Value Function ◽

Optimal Portfolio ◽

Growth Optimal Portfolio ◽

Complete Market ◽

Investment Opportunity Set ◽

Hamilton Jacobi Bellman Equation ◽

Static Approach ◽

Hamilton Jacobi Bellman

The Euler equation is defined. The static approach can be used to derive an optimal portfolio in a complete market and when the investment opportunity set is constant. In the latter case, the optimal portfolio is proportional to the growth‐optimal portfolio and two‐fund separation holds. Dynamic programming and the Hamilton‐Jacobi‐Bellman equation are explained. An optimal portfolio consists of myopic and hedging demands. The envelope condition is explained. CRRA utility implies a CRRA value function. The CCAPM and ICAPM are derived.

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