Optimal Portfolio Policies Research Articles

Dynamic mean-risk portfolio selection with multiple risk measures in continuous-time

While our society began to recognize the importance to balance the risk performance under different risk measures, the existing literature has confined its research work only under a static mean-risk framework. This paper represents the first attempt to incorporate multiple risk measures into dynamicportfolio selection. More specifically, we investigate the dynamic mean-variance-CVaR (Conditional value at Risk) formulation and the dynamic mean-variance-SFP (Safety-First Principle) formulation in a continuous-time setting, and derive the analytical solutions for both problems. Combining a downside risk measure with the variance (the second order central moment) in a dynamic mean-risk portfolio selection model helps investors control both a symmetric central risk measure and an asymmetric catastrophic downside risk. We find that the optimal portfolio policy derived from our mean-multiple risk portfolio optimization models exhibits a feature of curved V-shape. Our numerical experiments using real market data clearly demonstrate a dominance relationship of our dynamic mean-multiple risk portfolio policies over the static buy-and-hold portfolio policy.

Empirical likelihood inference for Haezendonck-Goovaerts risk measure

Recently Haezendonck-Goovaerts risk measure is receiving much attention in actuarial science with applications in the study of optimal portfolio and optimal reinsurance policy. Nonparametric estimation is proposed by Ahn and Shyamalkumar (Insur Math Econ 55:78–90, 2014), where the derived asymptotic limit can be employed to construct an interval for the Haezendonck-Goovaerts risk measure. In this paper, we propose an alternative empirical likelihood inference for this risk measure. A simulation study shows the good performance of the proposed method.

Parametric Portfolio Policies in the Surplus Consumption Ratio

AbstractThe surplus consumption ratio plays a central role as a state variable in successful attempts to explain the time series properties of stock and bond prices with consumption‐based asset pricing models. In this paper, optimal portfolio policies for a strategic investor who maximizes the conditionally expected utility of terminal wealth are parameterized as a polynomial in the surplus consumption ratio. Optimal portfolio policies are estimated using a method of moments estimator based on Euler equations. Unconditional portfolio policies are rejected in favor of conditional policies. Lower order polynomials are rejected in favor of higher order polynomials. Optimal stock and bond allocations are clearly countercyclical.

Optimal control of markovian switching systems with applications to portfolio decisions under inflation

This article is concerned with a class of control systems with Markovian switching, in which an Itô formula for Markov-modulated processes is derived. Moreover, an optimal control law satisfying the generalized Hamilton-Jacobi-Bellman (HJB) equation with Markovian switching is characterized. Then, through the generalized HJB equation, we study an optimal consumption and portfolio problem with the financial markets of Markovian switching and inflation. Thus, we deduce the optimal policies and show that a modified Mutual Fund Theorem consisting of three funds holds. Finally, for the CRRA utility function, we explicitly give the optimal consumption and portfolio policies. Numerical examples are included to illustrate the obtained results.

Time cardinality constrained mean–variance dynamic portfolio selection and market timing: A stochastic control approach

An investor does not always invest in risky assets in all the time periods, often due to a market timing consideration and various forms of market friction, including the management fee. Motivated by this observed common phenomenon, this paper considers the time cardinality constrained mean–variance dynamic portfolio selection problem (TCCMV) in markets with correlated returns and in which the number of time periods to invest in risky assets is limited. Both the analytical optimal portfolio policy and the analytical expression of the efficient mean–variance (MV) frontier are derived for TCCMV. It is interesting to note whether investing in risky assets or not in a given time period depends entirely on the realization of the two adaptive processes which are closely related to the local optimizer of the conditional Sharpe ratio. By implementing such a solution procedure for different cardinalities, the MV dynamic portfolio selection problem with management fees can be efficiently solved for a purpose of developing the best market timing strategy. The final product of our solution framework is to provide investors advice on the best market timing strategy including the best time cardinality and its distribution, as well as the corresponding investment policy, when balancing the consideration of market opportunity and market frictions.

Consumption and Portfolio Choice Under Loss Aversion and Endogenous Updating of the Reference Level

We explicitly derive and explore the optimal consumption and portfolio policies of a loss-averse individual who endogenously updates his or her reference level over time. We find that the individual protects current consumption by delaying painful reductions in consumption after a drop in wealth, and increasingly so with higher degrees of endogeneity. The incentive to protect current consumption is stronger with a medium wealth level than with a high or low wealth level. Furthermore, this individual adopts a conservative investment strategy in normal states and typically a more aggressive strategy in good and bad states. Endogeneity of the reference level increases overall risk-taking and generates an incentive to reduce risk exposure with age even without human capital. The welfare loss that this individual would suffer under the conventional constant relative risk aversion (CRRA) consumption and portfolio policies easily exceeds 10%.This paper was accepted by Tyler Shumway, finance.

Mean–variance asset–liability management with asset correlation risk and insurance liabilities

Consider an insurer who invests in the financial market where correlations among risky asset returns are randomly changing over time. The insurer who faces the risk of paying stochastic insurance claims needs to manage her asset and liability by taking into account of the correlation risk. This paper investigates the impact of correlation risk to the optimal asset–liability management (ALM) of an insurer. We employ the Wishart process to model the stochastic covariance matrix of risky asset returns. The insurer aims to minimize the variance of the terminal wealth given an expected terminal wealth subject to the risk of paying out random liabilities of compound Poisson process. This ALM problem then becomes a linear–quadratic stochastic optimal control problem with stochastic volatilities, stochastic correlations and jumps. The recognition of an affine form in the solution process enables us to derive the explicit closed-form solution to the optimal ALM portfolio policy, obtain the efficient frontier, and identify the condition that the solution is well behaved.

Discrete-Time Behavioral Portfolio Selection Under Prospect Theory

We formulate and study a general multi-period behavioral portfolio selection model under Kahneman and Tversky's prospect theory, featuring an incomplete market and an S-shaped utility function. We first discuss the ill-posedness issue under a multi-period framework and identify the conditions for the well-posedness under which infinitely leveraging an asset is not optimal for the investor. Moreover, we show that the well-posedness of the multi-period portfolio selection problem can be characterized in terms of an induced loss-aversion measure, which is an increasing function of time. Under the conditions for well-posedness, we solve the multi-period behavioral portfolio selection problem completely by deriving its semi-analytical optimal policy. In particular, we identify two cases: the case with one risky asset and the case with multiple risky assets that are jointly elliptically distributed, under which the optimal behavioral portfolio policy takes a piecewise linear feedback form. For the multiple risky assets case, we further demonstrate that the two-fund separation is still valid under the S-shaped utility. We also discuss the implications of our findings to the well documented phenomena of non-participation effect and horizon effect.

An optimal job, consumption/leisure, and investment policy

In this paper we investigate an optimal job, consumption, and investment policy of an economic agent in a continuous and infinite time horizon. The agent’s preference is characterized by the Cobb–Douglas utility function whose arguments are consumption and leisure. We use the martingale method to obtain the closed-form solution for the optimal job, consumption, and portfolio policy. We compare the optimal consumption and investment policy with that in the absence of job choice opportunities.

Mean–variance portfolio selection with correlation risk

The Markowitz mean–variance portfolio selection (MVPS) problem is the building block of modern portfolio theory. Since Markowitz (1952) published his seminal study, there have been numerous extensions to the continuous-time MVPS problem under different market conditions. This paper further enriches the literature by taking account of correlation risk among risky asset returns. Empirical studies reveal that correlations among economic variables change randomly over time and affect hedging and investment demand in different correlation regimes. By incorporating correlation risk into the dynamic MVPS through the Wishart variance–covariance matrix process, this paper derives the explicit closed-form solution to the optimal portfolio policy and determines the market regime in which the optimal policy is stable and well-behaved. This stable market regime is found to be fully characterized by the correlation between market returns and their variance–covariance matrix or, equivalently, the effects of market leverage.

Optimal Control of Uncertain Stochastic Systems with Markovian Switching and Its Applications to Portfolio Decisions

This article first describes a class of uncertain stochastic control systems with Markovian switching, and derives an Itô-Liu formula for Markov-modulated processes. We characterize an optimal control law, that satisfies the generalized Hamilton-Jacobi-Bellman (HJB) equation with Markovian switching. Then, by using the generalized HJB equation, we deduce the optimal consumption and portfolio policies under uncertain stochastic financial markets with Markovian switching. Finally, for constant relative risk-aversion (CRRA) felicity functions, we explicitly obtain the optimal consumption and portfolio policies. Moreover, we make an economic analysis through numerical examples.

Dynamic Mean-Risk Portfolio Selection with Multiple Risk Measures in Continuous-Time

Different risk measures emphasize different aspects of a random loss. If we examine the investment performance according to different spectra of the risk measures, any policy generated from a mean-risk portfolio model with a sole risk measure may not be a good choice. We study in this paper the dynamic portfolio selection problem with multiple risk measures in a continuous-time setting. More specifically, we investigate the dynamic mean-variance-CVaR (Conditional value at Risk) formulation and the dynamic mean-variance-SFP (Safety-First-Principle) formulation, and derive analytical solutions for both problems, when all the market parameters are deterministic. Combining a downside risk measure with the variance (the second order central moment) in a dynamic mean-risk portfolio selection model helps investors control both the symmetric central risk measure and the asymmetric downside risk at the tail part of the loss. We find that the optimal portfolio policy derived from our mean-multiple risk portfolio optimization model exhibits a feature of two-side threshold type, i.e., when the current wealth level is either below or above certain threshold, the optimal policy would dictate an increase in the allocation of the risky assets. Our numerical experiments using real market data further demonstrate that our dynamic mean-multiple risk portfolio models reduce significantly both the variance and the downside risk, when compared with the static buy-and-hold portfolio policy.

Options Procurement Policy for Option Contracts with Supply and Spot Market Uncertainty

Supplier’s reliability is a major issue in procurement management. In this paper, we establish a decision making model from the perspective of the firm who will procure from the multiple suppliers and the spot markets. The suppliers are unreliable and provide different types of option-type supply contracts which should be made before demand realization, while the spot market can only be used after demand realization and has both the price and liquidity risks. We establish the optimal portfolio policies for the firm with conditions to find the qualified suppliers. By defining a new function which contains the demand risk, the supplier’s risk, and the liquidity risk, we find that the optimal policy is to allocate different curves of this function to different suppliers. We also study some special cases to derive some managerial insights. At last, we numerically study how the various risks affect the choice of suppliers and the value of the option contract.

Multiperiod Mean-Variance Portfolio Optimization with General Correlated Returns

While rich empirical evidence always shows certain degree of dependency among different time periods for the returns of risky assets, the current literature on dynamic portfolio selection has been dominated by the results under an independency assumption, although in various forms. We consider in this paper a multiperiod mean-variance (MV) portfolio selection problem for a market with multiple risky assets whose returns are statistically correlated among time periods. Instead of assuming some particular stochastic processes to model the correlation, we adopt a formulation with a general form of correlation, which enables us to better matching our model with real markets. Recognizing the fact that, under this general setting, parameters in the portfolio policy become path-dependent adaptive processes themselves, we solve the problem analytically and derive an explicit form for the optimal portfolio policy, which remains as a linear affine function of the current wealth.

Dynamic Trading with Predictable Returns and Transaction Costs

ABSTRACTWe derive a closed‐form optimal dynamic portfolio policy when trading is costly and security returns are predictable by signals with different mean‐reversion speeds. The optimal strategy is characterized by two principles: (1) aim in front of the target, and (2) trade partially toward the current aim. Specifically, the optimal updated portfolio is a linear combination of the existing portfolio and an “aim portfolio,” which is a weighted average of the current Markowitz portfolio (the moving target) and the expected Markowitz portfolios on all future dates (where the target is moving). Intuitively, predictors with slower mean‐reversion (alpha decay) get more weight in the aim portfolio. We implement the optimal strategy for commodity futures and find superior net returns relative to more naive benchmarks.

Portfolio and Consumption Choice with Habit Formation Under Inflation

We investigate the optimal portfolio and consumption policies for a finite-horizon investor in a life-cycle model with habit formation and inflation risk. We consider two types of habit investors: one forms habit based on real past consumption, while the other on nominal past consumption, which is motivated by money illusion. The optimal strategy is expressed explicitly in terms of the solution to a linear partial differential equation. We find that the effects of inflation on the optimal strategy depend on the type of habit investor, because it determines the risk profile of the hedge portfolio and subsistence portfolio. This dependence is robust to the incompleteness of the financial market.

Portfolio optimization with uncertain exit time in infinite-time horizon

In this paper, we study infinite-period mean-variance formulations for portfolio selections with an uncertain exit time. We employ the convergence control method together with the dynamic programming algorithm to derive analytical expressions for the optimal portfolio policy and the mean-variance efficient frontier under certain conditions. We illustrate these results by an numerical example.

Multiperiod Portfolio Optimization with General Transaction Costs

We analyze the optimal portfolio policy for a multiperiod mean-variance investor facing a large number of risky assets in the presence of general transaction cost. For proportional transaction costs, we give a closed-form expression for a no-trade region, shaped as a multi-dimensional parallelogram, and show how the optimal portfolio policy can be efficiently computed by solving a single quadratic program. For market impact costs, we show that at each period it is optimal to trade to the boundary of a state-dependent rebalancing region. Finally, we show empirically that the utility loss associated with ignoring transaction costs may be large.

Optimal multi-period mean–variance policy under no-shorting constraint

We consider in this paper the mean–variance formulation in multi-period portfolio selection under no-shorting constraint. Recognizing the structure of a piecewise quadratic value function, we prove that the optimal portfolio policy is piecewise linear with respect to the current wealth level, and derive the semi-analytical expression of the piecewise quadratic value function. One prominent feature of our findings is the identification of a deterministic time-varying threshold for the wealth process and its implications for market settings. We also generalize our results in the mean–variance formulation to utility maximization with no-shorting constraint.

Optimal consumption and portfolio under inflation and Markovian switching

In this paper, a financial market with Markovian switching and inflation is described, and the problem of maximizing expected utility of consumption discounted by inflation is given. Then, by a generalized Itô formula for Markov-modulated processes, the verification theorems of optimal policies are derived. Finally, the optimal consumption and portfolio policies for the constant relative risk aversion utility are given explicitly, and an economic analysis is made by numerical examples.