Mean-variance Preferences Research Articles

The Role of Public Information in Capital Markets with Investors of Unknown Risk Attitudes

We consider a single-period, pure-exchange setting where investors have mean-variance preferences. Investors are uncertain about the risk attitudes of other capital market participants and, thus, about the market's risk premium. Assuming that there are no strategic interactions among investors, we identify conditions under which investors choose to abstain from trading in the capital market due to the risk associated with an uncertain risk premium. In addition, we find that investors may prefer the disclosure of public information prior to trading, as this information reduces the risk premium and thus relaxes the condition for market participation. Therefore, the presence of investors with unknown risk attitudes suggests a beneficial role for public (accounting) information.

Demand Risks and Term Structure of Volatility Index Futures

In this paper, we develop an equilibrium framework to explain the characteristics of volatility index (VIX) futures prices and returns across maturities. In the framework, the investors prefer VIX futures with specific maturities, and the arbitrageurs optimize portfolios based on mean-variance preferences. The model-implied futures prices are affected by the variance and demand risk factors. Theoretical and empirical analyses show that incorporating jump risks helps to explain the higher-order moments of futures and that including the demand factor improves futures pricing performance.

Optimal Reinsurance and Derivative-Based Investment Decisions for Insurers with Mean-Variance Preference

In our study, we investigate reinsurance issues and optimal investment related to derivatives trading for a mean-variance insurer, employing game theory. Our primary objective is to identify strategies that are time-consistent. In particular, the insurer has the flexibility to purchase insurance in proportion to its needs, explore new business, and engage in capital market investments. This is under the assumption that insurance companies’surplus capital adheres to the classical Cramér-Lundberg model. The capital market is made up of risk-free bonds, equities, and derivatives, with pricing dependent on the underlying stock’s basic price and volatility. To obtain the most profitable expressions and functions for the associated investment strategies and time guarantees, we solve a system of expanded Hamilton–Jacobi–Bellman equations. In addition, we delve into scenarios involving optimal investment and reinsurance issues with no derivatives trading. In the end, we present a few numerical instances to display our findings, demonstrating that the efficient frontier in the case of derivative trading surpasses that in scenarios where derivative trading is absent.

Non-zero-sum investment-reinsurance game with delay and ambiguity aversion

In this paper, we investigate a investment-reinsurance game problem with delay and ambiguity aversion for two insurers under mean–variance preference. Each insurer can purchase proportional reinsurance whose surplus process is a diffusion approximation process, and invest oneself’s wealth in a financial market consisting of a risk-free asset and a risky asset whose price evolution follows a jump–diffusion process. Based on the introduction of delay, we obtain wealth dynamics for each insurer depicted by a stochastic delay differential equation. By the stochastic control theory in the framework of game theory, the robust time-consistent Nash equilibrium investment-reinsurance strategies and the corresponding robust equilibrium value functions for each insurer are derived. Furthermore, some numerical examples are provided to illustrate the effect of market parameters on the optimal investment-reinsurance strategy.

Oil information uncertainty and aggregate market returns: A natural experiment based on satellite data

Satellites can “see” oil inventory in oil tanks, but they are sensitive to cloud cover. Cloud cover introduces a new uncertainty related to information quality. We measure such information uncertainty by assessing cloud cover over floating roof oil tanks. Using a cloud cover index, we demonstrate that higher information uncertainty leads to lower future returns (mean effect) and a stronger momentum anomaly (interaction effect). These two effects can be explained by investor overconfidence and arbitrage costs, respectively. An investor with a mean–variance preference obtains sizable gains in terms of certainty equivalent return, which accounts for the mean effect.

Forecasting the volatility of crude oil futures: A time‐dependent weighted least squares with regularization constraint

AbstractParameter instability and model uncertainty are two key problems affecting forecasting outcomes. In this paper, we propose a time‐dependent weighted least squares with ridge constraint (TWLS‐Ridge) to solve the above two problems in the forecasting procedure. The new TWLS‐Ridge approach is applied to the heterogenous autoregressive realized volatility model and its various extensions. The empirical results suggest that TWLS‐Ridge produces more accurate volatility forecasts than several alternative models dealing with parameter instability and model uncertainty. The superior performance of TWLS‐Ridge is robust under different forecast horizons, evaluation periods, and loss functions. An investor with mean–variance preference can improve utility using TWLS‐Ridge forecasts of oil volatility instead of ordinary least squares model forecasts.

Revealed statistical consumer theory

We provide a microfoundation to use aggregates (e.g. mean purchases) to evaluate consumer choice data. We study statistical consumer theory where an individual maximizes a preference over distributions of bundles when constrained by a statistic of the distribution (e.g. mean expenditure). We show statistical consumer theory is observationally equivalent to an individual whose preferences depend only on the statistic of the distribution. This means that despite working with distributions, the empirical content of the model only depends on a finite-dimensional statistic. This approach generalizes random quasilinear utility with random income and mean-variance preferences.

Optimal insurance design under mean-variance preference with narrow framing

In this paper, we study an optimal insurance design problem under mean-variance criterion by considering the local gain-loss utility of the net payoff of insurance, namely, narrow framing. We extend the existing results in the literature to the case where the decision maker has mean-variance preference with a constraint on the expected utility of the net payoff of insurance, where the premium is determined by the mean-variance premium principle. We first show the existence and uniqueness of the optimal solution to the main problem studied in the paper. We find that the optimal indemnity function involves a deductible provided that the safety loading imposed on the “mean part” of the premium principle is strictly positive. Our main result shows that narrow framing indeed reduces the demand for insurance. The explicit optimal indemnity functions are derived under two special local gain-loss utility functions – the quadratic utility function and the piecewise linear utility function. As a spin-off result, the Bowley solution is also derived for a Stackelberg game between the decision maker and the insurer under the quadratic local gain-loss utility function. Several numerical examples are presented to further analyze the effects of narrow framing on the optimal indemnity function as well as the interests of both parties.

Optimal investment and reinsurance policies for the Cramér–Lundberg risk model under monotone mean-variance preference

In this paper, an optimisation problem for the monotone mean-variance (MMV) criterion is considered from the perspective of the insurance company. The MMV criterion is an amended version of the classical mean-variance (MV) criterion which guarantees the monotonicity of the utility function. With this criterion we study the optimal investment and reinsurance problem which is formulated as a zero-sum game between the insurance company and an imaginary player. We apply the dynamic programming principle to obtain the corresponding Hamilton–Jacobi–Bellman–Isaacs (HJBI) equation. As the main conclusion of this paper, by solving the HJBI equation explicitly, the closed forms of the optimal strategy and the value function are obtained. Moreover, the MMV efficient frontier is also provided. At the end of the paper, a numerical example is presented.

A Stackelberg reinsurance-investment game under α-maxmin mean-variance criterion and stochastic volatility

ABSTRACT This paper investigates a Stackelberg game between an insurer and a reinsurer under the α-maxmin mean-variance criterion. The insurer can purchase per-loss reinsurance from the reinsurer. With the insurer's feedback reinsurance strategy, the reinsurer optimizes the reinsurance premium in the Stackelberg game. The financial market consists of cash and stock with Heston's stochastic volatility. Both the insurer and reinsurer maximize their respective α-maxmin mean-variance preferences in the market. The criterion is time-inconsistent and we derive the equilibrium strategies by the extended Hamilton-Jacobi-Bellman equations. Similar to the non-robust case in [Li, D. & Young, V. R. (2022). Stackelberg differential game for reinsurance: mean-variance framework and random horizon. Insurance: Mathematics and Economics 102, 42–55.], excess-of-loss reinsurance is the optimal form of reinsurance strategy for the insurer. The equilibrium investment strategy is determined by a system of Riccati differential equations. Besides, the equations determining the equilibrium reinsurance strategy and reinsurance premium rate are given semi-explicitly, which is simplified to an algebraic equation in a specific example. Numerical examples illustrate that the game between the insurer and reinsurer makes the insurance more radical when the agents become more ambiguity averse or risk averse. Furthermore, the level of ambiguity, ambiguity attitude, and risk attitude of the insurer (reinsurer) have similar effects on the equilibrium reinsurance strategy, reinsurance premium, and investment strategy.

Portfolio selection with exploration of new investment assets

We introduce a model for portfolio selection with an extendable investment universe where an agent with mean-variance preferences faces a trade-off between exploiting existing and exploring for new investment opportunities. When the agent chooses to explore, a new risky asset is discovered and the agent subsequently invests in the extended universe. We first provide conditions for wellposedness and characterize the optimal amount devoted to exploration. Our model shows that incremental exploration does not pay off, that it is increasingly worthwhile to explore in worse market environments, and that investment performance measured by the Sharpe ratio is increasing in the initial wealth of the agent indicating that richer agents can make better use of new investment opportunities. We further generalize our model and verify the robustness of the main findings with regard to various modeling assumptions.

A Deep Neural Network Algorithm for Linear-Quadratic Portfolio Optimization With MGARCH and Small Transaction Costs

We analyze a fixed-point algorithm for reinforcement learning (RL) of optimal portfolio mean-variance preferences in the setting of multivariate generalized autoregressive conditional-heteroskedasticity (MGARCH) with a small penalty on trading. A numerical solution is obtained using a neural network (NN) architecture within a recursive RL loop. A fixed-point theorem proves that NN approximation error has a big-oh bound that we can reduce by increasing the number of NN parameters. The functional form of the trading penalty has a parameter ϵ > 0 that controls the magnitude of transaction costs. When ϵ is small, we can implement an NN algorithm based on the expansion of the solution in powers of ϵ. This expansion has a base term equal to a myopic solution with an explicit form, and a first-order correction term that we compute in the RL loop. Our expansion-based algorithm is stable, allows for fast computation, and outputs a solution that shows positive testing performance.

Monotone and Classical Mean-Variance Preferences Coincide When Asset Prices are Continuous

Monotone and Classical Mean-Variance Preferences Coincide When Asset Prices are Continuous

Short Communication: Cone-Constrained Monotone Mean-Variance Portfolio Selection under Diffusion Models

We consider monotone mean-variance (MMV) portfolio selection problems with a conic convex constraint under diffusion models, and their counterpart problems under mean-variance (MV) preferences. We obtain the precommitted optimal strategies to both problems in closed form and find that they coincide, with and without the presence of the conic constraint. This result generalizes the equivalence between MMV and MV preferences from nonconstrained cases to a specific constrained case. A comparison analysis reveals that the orthogonality property under the conic convex set is a key to ensuring the equivalence result.

An integrated theory of dispatch and hedging in wholesale electric power markets

The literature on optimal dispatch of wholesale power systems implicitly assumes that market participants are risk-neutral. But, in practice, most wholesale electricity market participants behave as though they are risk averse, seeking to insulate themselves from the market risks they face. In this context, achieving the overall social-welfare maximum requires simultaneously finding both the optimal dispatch and optimal hedging arrangements. Assuming that market participants have mean–variance preferences, we show that the dispatch task can be separated from the hedging task. We show how market participants can achieve a perfect hedge by forming a portfolio of inter-temporal hedge contracts. Departing from the previous literature, we assume the system operator is risk averse. We show how the system operator can achieve a perfect hedge using a portfolio of inter-nodal hedging instruments which we refer to as generalised Financial Transmission Rights. The total risk experienced by market participants when optimally hedged is equal to the variation in the total surplus or total economic welfare. This approach therefore leads naturally to a form of merchant transmission investment where network upgrade decisions are carried out by a coalition of risk-bearers in the market. In addition, we propose a natural extension in which transmission network operators provide a form of insurance against network outages, and face the correct social incentive for avoiding network outages. This approach resolves a number of outstanding issues in the economic analysis of power markets.

Cooperative solutions for TU and NTU stochastic game-theoretical approach

The player's payoff in stochastic games is a stochastic variable. In most studies, predicted payout is referred to as a payoff, implying that the players are risk averse. However, there may be risk-averse players that consider "risk" while calculating their stochastic payoffs. We offer a model of stochastic games using mean-variance reward functions, which are the sum of expectation and standard deviation multiplied by a coefficient indicating a player's risk aversion. By adopting a maxmin technique to define the characteristic function, we may create a cooperative version of a stochastic game with mean-variance preferences. This paper contains an analysis of a cooperative solution concept of stochastic games for both TU (transferable utility) and NTU (non-transferable utility) games. We proposed a cooperative game solution method of extension of two-person zero sum strategic game to n-agent stochastic stage game using both Shapley and Banzhaf index functions. Results are proved for both discounted and undiscounted payoff situations. Existing models of discrete-time stochastic games and ways to finding cooperative solutions in these games are extended in this study.

Sourcing decision under interconnected risks: an application of mean–variance preferences approach

Supply chains are customarily associated with multiple interconnected risks originated from supply side, demand side, or from the unanticipated background uncertainties faced by a firm. Also, effective functioning of supply chain hinges on sourcing decisions of inputs (raw materials). Therefore, there is a striking need to analyse the risk preference of the decision maker while going for optimal sourcing decision under varying degree of interconnected supply chain risks. This study addresses this issue by analysing the comparative static effects under interconnected supply chain risks for a risk averse decision-maker, manufacturing and selling products in a regulated market under perfect competition. The decision-maker faces not only supply-side risk (due to random input material prices) but also interconnected risks arising out of background risk (setup costs risk) and demand-side risk (output prices risk). With preferences defined over the mean and standard deviation of the uncertain final profit, this study illustrates the effects of the changes in the pairwise correlations between the three above mentioned risks on the optimum input choice of the manufacturer. To contextualise this study, an India-based generic drug manufacturer cum seller has been considered as a case in the parametric example of our model. Adaptation of the mean–variance framework helps obtaining all the results in terms of the relative trade-off between risk and return, with simple yet intuitive interpretations.

Optimal deductible and coinsurance policies under mean-variance preferences

Optimal deductible and coinsurance policies under mean-variance preferences

MEAN–VARIANCE INSURANCE DESIGN WITH COUNTERPARTY RISK AND INCENTIVE COMPATIBILITY

AbstractThis paper studies the optimal insurance design from the perspective of an insured when there is possibility for the insurer to default on its promised indemnity. Default of the insurer leads to limited liability, and the promised indemnity is only partially recovered in case of a default. To alleviate the potential ex post moral hazard, an incentive compatibility condition is added to restrict the permissible indemnity function. Assuming that the premium is determined as a function of the expected coverage and under the mean–variance preference of the insured, we derive the explicit structure of the optimal indemnity function through the marginal indemnity function formulation of the problem. It is shown that the optimal indemnity function depends on the first and second order expectations of the random recovery rate conditioned on the realized insurable loss. The methodology and results in this article complement the literature regarding the optimal insurance subject to the default risk and provide new insights on problems of similar types.

Good volatility, bad volatility, and time series return predictability

We propose a least squares estimator weighted by a combination of lagged realized semivariances related to positive and negative returns (WLS-CRS) and use univariate models alone and in combination to reveal significant return predictability. For an investor with a mean-variance preference who allocates a portfolio based on an equal-weighted combination of WLS-CRS model forecasts, the annual certainty equivalent return is 242.8 basis points higher than that received by an investor whose portfolio is allocated based on historical average forecasts. In forecasting stock returns, WLS-CRS estimates outperform the popular ordinary least squares estimates in both statistical and economic evaluation frameworks. WLS-CRS also outperforms estimators based on least squares weighted by lagged realized volatility. We further demonstrate the dominant role of negative return semivariance in improved forecasting performance. Our main findings hold through several robustness checks, including alternative validation samples, different risk aversion coefficients, and various forecast combinations.