Optimal Portfolio Choice Research Articles

Optimal consumption and portfolio choice with ambiguous interest rates and volatility

We study continuous-time consumption and portfolio choice in the presence of Knightian uncertainty about interest rates. We develop the stochastic model that involves singular priors and analyze optimal behavior. When there is sufficiently large uncertainty about interest rates, the agent invests in the asset market only and abstains from the bond market.

Optimal asset allocation and consumption rules for commodity-based sovereign wealth funds

This paper studies the optimal asset allocation for a sovereign wealth fund (SWF) subject to a stochastic stream of commodity-based income, where, without loss of generality, we focus on oil-based SWFs. Using CRRA utility, we assume the fund’s objective is to maximize the discounted utility of intertemporal consumption in the presence of time-varying investment opportunities, and given non-zero correlations between shocks to oil income and asset return innovations. We use the log-linear approximation method of Campbell (1993) to solve for the model’s optimal asset allocation and consumption rules. Using historical data, we estimate the model parameters using the maximization-by-parts algorithm of Song et al. (2005). We then calibrate the model to study the optimal allocation and consumption for varying levels of risk aversion, time preference and oil income volatility. Our results are of interest to SWFs seeking optimal portfolio choice in the face of changing investment opportunities which correlate with their stochastic stream of income.

Optimal portfolio choice with tontines under systematic longevity risk

AbstractWe derive optimal portfolio choice patterns in retirement (ages 66–105) for a constant relative risk aversion utility maximising investor facing risky capital market returns, stochastic mortality risk, and income-reducing health shocks. Beyond the usual stocks and bonds, the individual can invest his assets in tontines. Tontines are cost-efficient financial contracts providing age-increasing, but volatile cash flows, generated through the pooling of mortality without guarantees, which can help to match increasing financing needs at old ages. We find that a tontine invested in the risk-free asset dominates stock investments for older investors without a bequest motive. However, with a bequest motive, it is optimal to replace the tontine investment over time with traditional financial assets. Our results indicate that early in retirement, a tontine is only an attractive investment option, if the tontine funds are invested in a risky asset. In this case, they crowd out stocks and risk-free bonds in the optimal portfolios of younger investors. Over time, the average optimal portfolio weight of tontines decreases. Introducing systematic mortality risks noticeably reduces the peak allocation to tontines.

Optimal consumption and portfolio decision with stochastic covariance in incomplete markets

Abstract This paper investigates finite and infinite horizon optimal consumption and portfolio choice problems in incomplete markets with stochastic covariance among stock returns. The stock price dynamics are assumed to follow a multivariate stochastic volatility process. The Hamilton-Jacobi-Bellman (HJB) equation is derived by using dynamic programming method and the closed-form expressions for portfolio–consumption strategies are derived in the case of logarithmic utility. In the case of infinite time horizon, we prove the existence of a classical solution and provide a verification theorem. The closed form approximate solutions to the optimal consumption and portfolio polices for a power utility investor are obtained by solving the same utility maximization problem in two fictitious complete markets. Moreover, we verify the existence and optimality of the solution of the original incomplete market and also provide the upper bound of the utility loss of approximate rules. Finally, a numerical application to an incomplete market with stochastic factors show that the utility loss of the approximation rules is small and the performance of the approximate rules is close to optimal.

Optimal Portfolio Choice Under Shadow Costs with Fixed Assets when Time-Horizon Is Uncertain

We analyze in this paper the problem of choosing the optimal portfolio for investors under uncertain exit random time. We consider the portfolio choice with fixed assets in the presence of information costs and short sales constraints. This context allows us to focus on the optimal portfolio choice with fixed assets. Investors aim to maximize the ratio between the wealth and the value of the fixed assets. We obtain the optimal portfolio choice strategy with fixed assets when the time horizon is a random exit time. Our results are new in the literature. We illustrate the main findings through some simulation results.

Optimal Investment Policy for Insurers under the Constant Elasticity of Variance Model with a Correlated Random Risk Process

This paper investigates the optimal portfolio choice problem for a large insurer with negative exponential utility over terminal wealth under the constant elasticity of variance (CEV) model. The surplus process is assumed to follow a diffusion approximation model with the Brownian motion in which is correlated with that driving the price of the risky asset. We first derive the corresponding Hamilton–Jacobi–Bellman (HJB) equation and then obtain explicit solutions to the value function as well as the optimal control by applying a variable change technique and the Feynman–Kac formula. Finally, we discuss the economic implications of the optimal policy.

Bayesian mean–variance analysis: optimal portfolio selection under parameter uncertainty

The paper solves the problem of optimal portfolio choice when the parameters of the asset returns distribution, for example the mean vector and the covariance matrix, are unknown and have to be estimated by using historical data on asset returns. Our new approach employs the Bayesian posterior predictive distribution which is the distribution of future realizations of asset returns given the observable sample. The parameters of posterior predictive distributions are functions of the observed data values and, consequently, the solution of the optimization problem is expressed in terms of data only and does not depend on unknown quantities. By contrast, the optimization problem of the traditional approach is based on unknown quantities which are estimated in the second step, and lead to a suboptimal solution. We also derive a very useful stochastic representation of the posterior predictive distribution whose application not only gives the solution of the considered optimization problem, but also provides the posterior predictive distribution of the optimal portfolio return which can be used to construct a prediction interval. A Bayesian efficient frontier, the set of optimal portfolios obtained by employing the posterior predictive distribution, is constructed as well. Theoretically and using real data we show that the Bayesian efficient frontier outperforms the sample efficient frontier, a common estimator of the set of optimal portfolios which is known to be overoptimistic.

Limited attention and portfolio choice: The impact of attention allocation on mutual fund performance

AbstractThis study proposes that the performance of mutual fund managers is linked to how efficiently they allocate attention across assets in their investment set. Motivated by existing models of optimal portfolio choice and rational inattention, we posit that the efficiency of attention allocation increases when a manager chooses larger (smaller) active positions in assets that need more (less) information acquisition effort to resolve uncertainty about future payoffs. We show that the efficiency of attention allocation has a significantly positive impact on future fund performance. Efficient attention allocation has a lesser impact on performance as the total demands on a manager's limited attention increase.

Beyond expected utility: Subjective risk aversion and optimal portfolio choice under convex shortfall risk measures

We conduct a decision-theoretic analysis of convex shortfall risk measures regarding their flexibility to represent subjective risk aversion, and discuss the implications for the choice of optimal portfolios. As convex shortfall risk measures are closely related to the expected utility functional, we draw upon the expected utility framework as our benchmark. First, we show that, unlike expected utility, convex shortfall risk measures do always represent constant absolute risk aversion. This constitutes a significant limitation when changing initial wealth of, e.g., investors, is relevant. Interestingly, though, it is exactly this limitation that provides additional degrees of freedom in representing subjective risk aversion beyond expected utility when initial wealth is fixed, as, e.g., in returned-based portfolio selection models in the tradition of Markowitz (1952). Second, we apply convex shortfall risk measures to the standard portfolio problem between a riskless and a risky asset. We provide a procedure that allows inferring the optimal portfolios under convex shortfall risk measures from certain optimal expected utility-portfolios. The procedure incorporates the additional degrees of freedom in modeling subjective risk aversion and, thus, allows more flexible and realistic portfolios compared to expected utility. Third, we address the optimal portfolio choice between a riskless and a risky asset in the presence of an additional background risk. Again, we prove a correspondence result between optimal portfolios under convex shortfall risk measures and expected utility and obtain more flexible and realistic portfolios compared to expected utility. We also compare the optimal risky investments without and with background risk and provide a necessary and sufficient condition for a reduction of the risky investment.

Industry portfolio allocation with asymmetric correlations

We develop a new framework of optimal consumption and portfolio choice at industry portfolio level under dynamic and asymmetric correlations between industry and market portfolios. We derive in closed form the optimal consumption and investment strategies under regime-dependent correlations environment. Overall, we find that ignoring time-varying and asymmetric correlations between portfolios can be costly to investors when applied to a construction of the optimal portfolio. Finally, we empirically test the performance of the model-based investment strategy.

On the Equivalence Between Value-at-Risk and Expected Shortfall in Non-Concave Optimization

This paper studies an optimal asset allocation problem for a surplus-driven financial institution facing a Value-at-Risk (VaR) or an Expected Shortfall (ES) constraint corresponding to a non-concave optimization problem under constraints. We obtain the closed-form optimal wealth with the ES constraint as well as with the VaR constraint respectively, and explicitly calculate the optimal trading strategy for constant relative risk aversion (CRRA) utility functions. We find that both VaR and ES-based regulation can effectively reduce the probability of default for a surplus-driven financial institution. However, the liability holders' benefits cannot be fully protected under either VaR- or ES-based regulation. In addition, we show that the VaR and ES-based regulation can induce the same optimal portfolio choice for a surplus-driven financial institution. This differs from the conclusion drawn in Basak and Shapiro 2001 where the financial institution aims at maximizing the expected utility of the total assets, and ES provides better loss protection.

A generalized stochastic differential utility driven by G-Brownian motion

This paper introduces a class of generalized stochastic differential utility (GSDU) models in a continuous-time framework to capture ambiguity aversion on the financial market. This class of GSDU models encompasses several classical approaches to ambiguity aversion and includes new models about ambiguity aversion. For a general GSDU model, we demonstrate its continuity, monotonicity, time consistency, concavity, and homotheticity. We investigate its comparative ambiguity aversion and direction aversion under sufficient conditions. We further solve an optimal portfolio choice problem in one GSDU model as an application.

Joint tails impact in stochastic volatility portfolio selection models

This paper examines the impact of the joints tails of the portfolio return and its empirical volatility on the optimal portfolio choices. We assume that the portfolio return and its volatility dynamic is approximated by a bivariate Markov chain constructed on its historical distribution. This allows the introduction of a non parametric stochastic volatility portfolio model without the explicit use of a GARCH type or other parametric stochastic volatility models. We describe the bi-dimensional tree structure of the Markov chain and discuss alternative portfolio strategies based on the maximization of the Sharpe ratio and of a modified Sharpe ratio that takes into account the behaviour of a market benchmark. Finally, we empirically evaluate the impact of the portfolio and its stochastic volatility joint tails on optimal portfolio choices. In particular, we examine and compare the out of sample wealth obtained optimizing the portfolio performances conditioned on the joint tails of the proposed stochastic volatility model.

Dynamic consumption and portfolio choice under prospect theory

This paper explicitly derives the optimal dynamic consumption and portfolio choice of an individual with prospect theory preferences. The individual is loss averse, endogenously updates his reference level over time, and distorts probabilities. We show that the optimal consumption strategy is rather insensitive to economic shocks. In particular, in case the individual sufficiently overweights unlikely unfavorable events, our model generates an endogenous floor on consumption. As a result, an individual with prospect theory preferences typically implements a (very) conservative portfolio strategy. We discuss implications of our results for the design of investment-linked annuity products.

Theory of Leveraged Portfolio Selection Under Liquidity Risk

We study the impact of liquidity in optimal portfolio choice under leveraging to improve risk-adjusted and absolute returns. We consider a quasi-elastic market with continuous trading where temporary liquidity costs are sufficiently large relative to permanent impact. We show analytically that the Sharpe-maximizing unlevered portfolio is no longer a tangency portfolio. As target mean increases, required portfolio-leverage increases at an increasing-rate, while Sharpe-Leverage frontiers are progressively-dominated. Moreover, security-market relationships are no-longer linear and the usual proportionate-leveraging is not an optimal strategy. We develop insights for choosing return targets for leverage-constrained investors, and provide computational analyses to highlight the analytical findings.

Wealth Effect on Portfolio Allocation in Incomplete Markets

This paper provides a novel five-component decomposition of optimal dynamic portfolio choice. It reveals the simultaneous impacts from market incompleteness and wealth-dependent utilities. The decomposition leads to implementation via either closed-form solutions or Monte Carlo simulations. With a nonrandom but time-varying interest rate, we can explicitly solve for the optimal policy under the wealth-dependent HARA utility. It is a combination of a bond holding scheme and the corresponding simpler CRRA strategy. Under incomplete markets with a stochastic volatility model estimated on US equity data, wealth-dependence introduces sophisticated cycle-dependence for optimal policy and hysteresis effect in Sharpe ratio.

Optimal Portfolio Choices to Split Orders Under Supply Disruption Risks: An Application of Sport’s Principle for Routine Sourcing

This paper focuses on developing flexible sourcing strategies to mitigate supply disruptions using the resource dependency theory (RDT). Sourcing under supply chain disruptions has been seen as one of the challenging tasks of decision-makers because maintaining a strategic partner and getting the desired quantity from backup suppliers within the stipulated time is difficult. Hence, this study seeks to understand how to set a revised target of a primary supplier under supply disruptions by applying the well-known Duckworth–Lewis-Stern (DLS) method. Further, we also model the buyer's preferences towards supply disruption risks where the primary supplier fails to meet the DLS-specified target within the pre-fixed duration and trying to obtain the remaining quantity from some backup supplier(s). We apply the mean-variance decision-theoretic model to derive testable comparative static properties regarding how the buyer optimally manages the portfolio of risky options based on her relative trade-offs between risks and returns. Then, we demonstrate the robustness of the theoretical predictions with a set of experimental evidence, comprising a total of 300 purchase managers, across 30 different groups of respondents. Finally, using this experimental data, this paper also applies quantile regression to estimate the preference structure across different quantiles of the risk distribution for all the respondents.

Preference Heterogeneity and Optimal Monetary Policy

We study optimal policy design in a monetary model with heterogeneous preferences. In the model markets are incomplete and households are heterogeneous with respect to their current consumption preferences and discount factors. The government controls the supply of money (liquid) and nominal bonds (illiquid) based on which households make optimal portfolio choices. We uncover that the two types of preference heterogeneity have distinct implications for the optimal policy mix of the government. While the heterogeneity in current consumption preferences pushes the economy towards a zero-lower-bound (ZLB) associated with nominal interest rates, the heterogeneity in discount factors moves the economy away from the ZLB. We characterize the optimal policy design and quantify the welfare losses associated a binding ZLB - and thus potential welfare benefits from allowing negative interest rates on government bonds.

Optimal Investing after Retirement Under Time-Varying Risk Capacity Constraint

This paper explores an optimal investing problem for a retiree facing longevity risk and living standard risk. We formulate the optimal investing problem as an optimal portfolio choice problem under a time-varying risk capacity constraint. Under the specific condition on model parameters, we show that the value function is a $C^2$ solution of the HJB equation and derive the optimal investment strategy in terms of second-order ordinary differential equations. The optimal portfolio is nearly neutral to the stock market movement if the portfolio's value is at a sufficiently high level; but, if the portfolio is not worth enough to sustain the retirement spending, the retiree actively invests in the stock market for the higher expected return. In addition, we solve an optimal portfolio choice problem under a leverage constraint and show that the optimal portfolio would lose significantly in stressed markets. This paper shows that the time-varying risk capacity constraint has important implications for asset allocation in retirement.

Risk apportionment: The dual story

By specifying new model free preferences towards simple nested classes of lottery pairs, we develop the dual story to stand on equal footing with that of (primal) risk apportionment. The dual story provides an intuitive interpretation, and full characterization, of dual counterparts of such concepts as prudence and temperance. The direction of preference between these nested classes of lottery pairs is equivalent to signing the successive derivatives of the probability weighting function within Yaari's (1987) dual theory. We explore implications of our results for optimal portfolio choice and show that the sign of the third derivative of the probability weighting function may be naturally linked to a self-protection problem.