Optimal portfolios under a correlation constraint
TL;DR: In this paper, the optimal constant/fixed-mix portfolio consists of the market portfolio, the riskless bond and the benchmark under a correlation constraint, and the optimal fixed/fixed mix portfolio is defined as a mixture of market portfolios and riskless bonds.
Abstract: Under a correlation constraint the optimal constant/fixed-mix portfolio consists of the market portfolio, the riskless bond and the benchmark
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TL;DR: In this paper, the authors study portfolio selection under the objective of maximizing the Omega ratio, proposed by Keating and Shadwick (2002) as an alternative to the Sharpe ratio for performance assessment of investment strategies.
15 citations
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TL;DR: It is found that investors' optimal terminal wealth distribution has larger probability masses in regions that reduce their risk measure relative to the benchmark while preserving some aspects of the benchmark.
Abstract: We study the problem of active portfolio management where an investor aims to outperform a benchmark strategy's risk profile while not deviating too far from it. Specifically, an investor considers alternative strategies whose terminal wealth lie within a Wasserstein ball surrounding a benchmark's -- being distributionally close -- and that have a specified dependence/copula -- tying state-by-state outcomes -- to it. The investor then chooses the alternative strategy that minimises a distortion risk measure of terminal wealth. In a general (complete) market model, we prove that an optimal dynamic strategy exists and provide its characterisation through the notion of isotonic projections.
We further propose a simulation approach to calculate the optimal strategy's terminal wealth, making our approach applicable to a wide range of market models. Finally, we illustrate how investors with different copula and risk preferences invest and improve upon the benchmark using the Tail Value-at-Risk, inverse S-shaped, and lower- and upper-tail distortion risk measures as examples. We find that investors' optimal terminal wealth distribution has larger probability masses in regions that reduce their risk measure relative to the benchmark while preserving the benchmark's structure.
8 citations
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TL;DR: In this article, the authors study the problem of active portfolio management where an investor aims to outperform a benchmark strategy's risk profile while not deviating too far from it, and propose a simulation approach to calculate the optimal strategy's terminal wealth, making their approach applicable to a wide range of market models.
Abstract: We study the problem of active portfolio management where an investor aims to outperform a benchmark strategy's risk profile while not deviating too far from it. Specifically, an investor considers alternative strategies whose terminal wealth lie within a Wasserstein ball surrounding a benchmark's -- being distributionally close -- and that have a specified dependence/copula -- tying state-by-state outcomes -- to it. The investor then chooses the alternative strategy that minimises a distortion risk measure of terminal wealth. In a general (complete) market model, we prove that an optimal dynamic strategy exists and provide its characterisation through the notion of isotonic projections.
We further propose a simulation approach to calculate the optimal strategy's terminal wealth, making our approach applicable to a wide range of market models. Finally, we illustrate how investors with different copula and risk preferences invest and improve upon the benchmark using the Tail Value-at-Risk, inverse S-shaped, and lower- and upper-tail distortion risk measures as examples. We find that investors' optimal terminal wealth distribution has larger probability masses in regions that reduce their risk measure relative to the benchmark while preserving the benchmark's structure.
4 citations
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06 Feb 2020
TL;DR: In this paper, the authors consider the problem of portfolio optimization with a correlation constraint and find analytical expressions for the constrained subgame perfect (CSGP) and the constrained precommitment (CPC) portfolio strategies.
Abstract: We consider the problem of portfolio optimization with a correlation constraint. The framework is the multi-period stochastic financial market setting with one tradable stock, stochastic income, and a non-tradable index. The correlation constraint is imposed on the portfolio and the non-tradable index at some benchmark time horizon. The goal is to maximize a portofolio’s expected exponential utility subject to the correlation constraint. Two types of optimal portfolio strategies are considered: the subgame perfect and the precommitment ones. We find analytical expressions for the constrained subgame perfect (CSGP) and the constrained precommitment (CPC) portfolio strategies. Both these portfolio strategies yield significantly lower risk when compared to the unconstrained setting, at the cost of a small utility loss. The performance of the CSGP and CPC portfolio strategies is similar.
2 citations
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TL;DR: In this article, the problem of portfolio optimization with a correlation constraint is considered, and two types of optimal portfolio strategies are considered: the subgame perfect and the precommitment ones.
Abstract: We consider the problem of portfolio optimization with a correlation constraint. The framework is the multiperiod stochastic financial market setting with one tradable stock, stochastic income and a non-tradable index. The correlation constraint is imposed on the portfolio and the non-tradable index at some benchmark time horizon. The goal is to maximize portofolio's expected exponential utility subject to the correlation constraint. Two types of optimal portfolio strategies are considered: the subgame perfect and the precommitment ones. We find analytical expressions for the constrained subgame perfect (CSGP) and the constrained precommitment (CPC) portfolio strategies. Both these portfolio strategies yield significantly lower risk when compared to the unconstrained setting, at the cost of a small utility loss. The performance of the CSGP and CPC portfolio strategies is similar.
1 citations
References
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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
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01 Jan 2002
TL;DR: This article deals with the static (nontime- dependent) case and emphasizes the copula representation of dependence for a random vector and the problem of finding multivariate models which are consistent with prespecified marginal distributions and correlations is addressed.
Abstract: Modern risk management calls for an understanding of stochastic dependence going beyond simple linear correlation. This paper deals with the static (non-time-dependent) case and emphasizes the copula representation of dependence for a random vector. Linear correlation is a natural dependence measure for multivariate normally and, more generally, elliptically distributed risks but other dependence concepts like comonotonicity and rank correlation should also be understood by the risk management practitioner. Using counterexamples the falsity of some commonly held views on correlation is demonstrated; in general, these fallacies arise from the naive assumption that dependence properties of the elliptical world also hold in the non-elliptical world. In particular, the problem of finding multivariate models which are consistent with prespecified marginal distributions and correlations is addressed. Pitfalls are highlighted and simulation algorithms avoiding these problems are constructed.
2,052 citations
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TL;DR: In this article, a martingale technique is employed to characterize optimal consumption-portfolio policies when there exist nonnegativity constraints on consumption and on final wealth, and a way to compute and verify optimal policies is provided.
1,606 citations
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26 Sep 2006
TL;DR: Preliminaries from Probability Theory and Statistical Methods are used in this article to estimate the probability that a stock market will be a buy or sell in the next five years.
Abstract: Preliminaries from Probability Theory.- Statistical Methods.- Modeling via Stochastic Processes.- Diffusion Processes.- Martingales and Stochastic Integrals.- The Ito Formula.- Stochastic Differential Equations.- to Option Pricing.- Various Approaches to Asset Pricing.- Continuous Financial Markets.- Portfolio Optimization.- Modeling Stochastic Volatility.- Minimal Market Model.- Markets with Event Risk.- Numerical Methods.- Solutions for Exercises.
423 citations
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TL;DR: In this paper, the authors compared trading in a market with receiving some particular consu mption bundle, given increasing state-independent preferences and complete markets, focusing on the distribution price of a particular bundle.
Abstract: Trading in a market is compared with receiving some particular consu mption bundle, given increasing state-independent preferences and complete markets. The analysis focuses on the distribution price of t he particular bundle. The distributional price is the price of the ch eapest utility-equivalent bundle sold in the market. The distribution al price is determined by the distribution functions of the outside b undle and the state price density. Simple portfolio performance measu res illustrate the value of the approach. Unlike CAPM-based measures, these measures are valid even when superior information is the sourc e of superior performance. Copyright 1988 by the University of Chicago.
189 citations