Robust optimal excess-of-loss reinsurance and investment strategy for an insurer in a model with jumps

This paper considers a robust optimal excess-of-loss reinsurance-investment problem in a model with jumps for an ambiguity-averse insurer (AAI), who worries about ambiguity and aims to develop a robust optimal reinsurance-investment strategy. The AAI’s surplus process is assumed to follow a diffusion model, which is an approximation of the classical risk model. The AAI is allowed to purchase excess-of-loss reinsurance and invest her surplus in a risk-free asset and a risky asset whose price is described by a jump-diffusion model. Under the criterion for maximizing the expected exponential utility of terminal wealth, optimal strategy and optimal value function are derived by applying the stochastic dynamic programming approach. Our model and results extend some of the existing results in the literature, and the economic implications of our findings are illustrated. Numerical examples show that considering ambiguity and reinsurance brings utility enhancements.     

A Generalisation of the Mean-Variance Analysis

In this paper we consider a decision maker whose utility function has a kink at the reference point with different functions below and above this reference point. We also suppose that the decision maker generally distorts the objective probabilities. First we show that the expected utility function of this decision maker can be approximated by a function of mean and partial moments of distribution. This 'mean-partial moments' utility generalises not only mean-variance utility of Tobin and Markowitz, but also mean-semivariance utility of Markowitz. Then, in the spirit of Arrow and Pratt, we derive an expression for a risk premium when risk is small. Our analysis shows that a decision maker in this framework exhibits three types of aversions: aversion to loss, aversion to uncertainty in gains, and aversion to uncertainty in losses. Finally we present a solution to the optimal capital allocation problem and derive an expression for a portfolio performance measure which generalises the Sharpe and Sortino ratios. We demonstrate that in this framework the decision maker's skewness preferences have first-order impact on risk measurement even when the risk is small.     

UK stock returns and robust tests of mean variance efficiency

We test both the unconditional and conditional Mean Variance Efficiency of the UK stockmarket, paying particular attention to choosing a suitable set of instruments for the conditional version of the model. By considering more carefully than previous authors the pricing of economic risk within the mean-variance framework we show that certain instruments can enhance the basic model structure. Given the tendency for financial market data to display non-constancy in variance and non-normality we employ the GMM procedure described in Hansen (1982), which requires much weaker distributional assumptions than the more traditional OLS techniques. We discuss forming portfolios of stocks using both size and dividend yield as a criterion to achieve a suitable spread of risk and return, and find that our conclusions are sensitive both to the method of portfolio formation and to the choice of estimator. This is an important finding given the problem of thin trading associated with the size ordering of UK stocks. We find some support for both the unconditional and conditional version of the CAPM, though we are cautious about our conclusions given the instability of the parameter estimates.     

Variance Vulnerability, Background Risks, and Mean-Variance Preferences

An agent with two-parameter, mean-variance preferences is called variance vulnerable if an increase in the variance of an exogenous, independent background risk induces the agent to choose a lower level of risky activities. Variance vulnerability resembles the notion of risk vulnerability in the expected utility (EU) framework. First, we characterize variance vulnerability in terms of two-parameter utility functions. Second, we identify the multivariate normal as the only distribution such that EU- and two-parameter approach are compatible when independent background risks prevail. Third, presupposing normality, we show that—analogously to risk vulnerability—temperance is a necessary, and standardness and convex risk aversion are sufficient conditions for variance vulnerability.     

A Shrinkage Approach to Model Uncertainty and Asset Allocation

This article takes a shrinkage approach to examine the empiricalimplications of aversion to model uncertainty. The shrinkageapproach explicitly shows how predictive distributions incorporatedata and prior beliefs. It enables us to solve the optimal portfoliosfor uncertainty-averse investors. Aversion to uncertainty aboutthe capital asset pricing model leads investors to hold a portfoliothat is not mean-variance efficient for any predictive distribution.However, mean-variance efficient portfolios corresponding toextremely strong beliefs in the Fama–French model areapproximately optimal for uncertainty-averse investors. Theempirical Bayes approach does not result in optimal portfoliosfor investors who are averse to model uncertainty.     

Mean-variance vs. stochastic dominance some empirical findings on efficient sets

The study attempts to shed additional light on the issue of the costs and benefits of using the mean-variance criterion as opposed to stochastic dominance criteria for investment decisions. Relevant probabilities which facilitate measurement of these costs and benefits are identified. The mean-variance criterion is shown to be useful to some extent in identifying potentially optimal portfolios. However, it is shown that the informationally less demanding mean-variance criterion admits two types of errors: (i) including portfolios that no expected utility maximizing risk averters would choose, and (ii) excluding portfolios which some risk averters would find optimal. The empirical investigation also indicates that although the composition of the efficient sets appears to be unstable over time, the relationships between the efficient sets are persistent over time.     

Stock return predictability and model uncertainty

We use Bayesian model averaging to analyze the sample evidence on return predictability in the presence of model uncertainty. The analysis reveals in-sample and out-of-sample predictability, and shows that the out-of-sample performance of the Bayesian approach is superior to that of model selection criteria. We find that term and market premia are robust predictors. Moreover, small-cap value stocks appear more predictable than large-cap growth stocks. We also investigate the implications of model uncertainty from investment management perspectives. We show that model uncertainty is more important than estimation risk, and investors who discard model uncertainty face large utility losses.     

More on Properness: The Case of Mean-Variance Preferences

This paper focuses on the situations where individuals with mean-variance preferences add independent risks to an already risky situation. Pratt and Zeckhauser (Econometrica, 55, 143–154, 1987) define a concept called proper risk aversion in the expected utility framework to describe the situation where an undesirable risk can never be made desirable by the presence of an independent undesirable risk. The assumption of mean-variance preferences allows us to study proper risk aversion in an intuitive manner. The paper presents an economic interpretation for the quasi-concavity of a utility function derived over mean and variance. The main result of the paper says that quasi-concavity plus decreasing risk aversion is equivalent to proper risk aversion.     

Predictability and diversification benefits of investing in commodity and currency futures

We re-examine diversification benefits of investing in commodities and currencies by considering a risk-averse investor with mean-variance preferences who exploits the possibility of predictable time variation in asset return means, variances, and covariances. We implement unconditional and conditional efficient portfolio strategies designed to exploit this predictability, together with more traditional and/or ad hoc ones yet hitherto relatively unexplored in this context (including the equally weighted, fixed weight, volatility timing, and reward-to-risk timing strategies). We find that, for all portfolio strategies, commodities and currencies do not improve the investment opportunity set of the investor with an existing portfolio of stocks, bonds and T-bills, and an investment horizon of one month. Our findings, which reverse the conclusions of previous studies that focus on static portfolio strategies, are robust across several performance metrics.     

Optimal allocation to hedge funds: an empirical analysis

What percentage of their portfolio should investors allocate to hedge funds? The only available answers to the above question are set in a static mean-variance framework, with no explicit accounting for uncertainty on the active manager's ability to generate abnormal return, and usually generate unreasonably high allocations to hedge funds. In this paper, we apply the model introduced in Cvitanic et al (2002b Working Paper USC) for optimal investment strategies in the presence of uncertain abnormal returns to a database of hedge funds. We find that the presence of the model risk significantly decreases an investor's optimal allocation to hedge funds. Another finding of this paper is that low beta hedge funds may serve as natural substitutes for a significant portion of investor risk-free asset holdings.     

REGULATORY INFLUENCES ON PORTFOLIO PERFORMANCE: SHORT SELLING AND REGULATION T

Several models are developed to examine the portfolio effect of short selling. Three things are demonstrated in this study. First, that for many assets, short selling is a useful strategy for reducing risk when constructing mean-variance efficient portfolios. Second, Regulation T can be used in combination with short selling to further improve expected portfolio performance. Third, the performance of the suggested models is superior to previously suggested allocation models. Ex ante and ex post tests are conducted to arrive at the above conclusions.     

Robust portfolio optimization with a generalized expected utility model under ambiguity

This paper proposes a robust approach maximizing worst-case utility when both the distributions underlying the uncertain vector of returns are exactly unknown and the estimates of the structure of returns are unreliable. We introduce concave convex utility function measuring the utility of investors under model uncertainty and uncertainty structure describing the moments of returns and all possible distributions and show that the robust portfolio optimization problem corresponding to the uncertainty structure can be reformulated as a parametric quadratic programming problem, enabling to obtain explicit formula solutions, an efficient frontier and equilibrium price system. We would like to thank Prof. Zengjing Chen from School of Mathematics and System Sciences, Shandong University for helpful suggestions, and to thank the anonymous referee for valuable comments.     

Using Generalized Method of Moments to Test Mean-Variance Efficiency

This paper develops tests of unconditional mean-variance efflciency under weak distributional assumptions using a Generalized Method of Moments framework. These tests are potentially more robust than commonly employed tests which rely on the assumption that asset returns are normally distributed and temporarily i.i.d. Using returns for size-based portfolios from 1926 to 1988 we show that the conclusion concerning the mean-variance effilciency of market indexes can be sensitive to the test considered.     

State uncertainty in stock markets: How big is the impact on the cost of equity?

We propose a novel Bayesian framework to incorporate uncertainty about the state of the market. Among others, one advantage of the framework is the ability to model a large collection of time-varying parameters simultaneously. When we apply the framework to estimate the cost of equity we find economically significant effects of state uncertainty. A state-independent pricing model overestimates the cost of equity by about 4% per annum for a utility firm and by as much as 3% for industries. We also observe that the expected return, volatility, risk loading, and pricing error all display state-dependent dynamics that coincide with the business cycle. More interestingly, the forecasted market and Fama–French factor risk premiums can predict the future real GDP growth rate even though the model does not use any macroeconomic variables, which suggests that the proposed Bayesian framework captures the state-dependent dynamics well.     

Background Risk, Demand for Insurance, and Choquet Expected Utility Preferences

This article deals with demand for insurance with a background risk in a nonprobabilized uncertainty framework, where preferences are represented by a nonadditive model of decision making. The Choquet expected utility model that we use generalizes expected utility and allows for a separation of the attitude towards uncertainty and the attitude towards wealth. When the insurable and the background risk are comonotone, the impact of the background risk on the demand for insurance is related to the attitude towards wealth. In contrast, when the two risks are anticomonotone, the attitude towards uncertainty is determinant. In this case, some of the resulting behaviors cannot be explained by the standard expected utility model.     

The Economic Value of Volatility Timing

Numerous studies report that standard volatility models have low explanatory power, leading some researchers to question whether these models have economic value. We examine this question by using conditional mean-variance analysis to assess the value of volatility timing to short-horizon investors. We find that the volatility timing strategies outperform the unconditionally efficient static portfolios that have the same target expected return and volatility. This finding is robust to estimation risk and transaction costs.     

Optimal investment of an insurer with regime-switching and risk constraint

We investigate an optimal investment problem of an insurance company in the presence of risk constraint and regime-switching using a game theoretic approach. A dynamic risk constraint is considered where we constrain the uncertainty aversion to the ‘true’ model for financial risk at a given level. We describe the surplus of an insurance company using a general jump process, namely, a Markov-modulated random measure. The insurance company invests the surplus in a risky financial asset whose dynamics are modeled by a regime-switching geometric Brownian motion. To incorporate model uncertainty, we consider a robust approach, where a family of probability measures is cosidered and the insurance company maximizes the expected utility of terminal wealth in the ‘worst-case’ probability scenario. The optimal investment problem is then formulated as a constrained two-player, zero-sum, stochastic differential game between the insurance company and the market. Different from the other works in the literature, our technique is to transform the problem into a deterministic differential game first, in order to obtain the optimal strategy of the game problem explicitly.     

Optimal investment strategies for general utilities under dynamic elasticity of variance models

This paper studies the optimal investment strategies under the dynamic elasticity of variance (DEV) model which maximize the expected utility of terminal wealth. The DEV model is an extension of the constant elasticity of variance model, in which the volatility term is a power function of stock prices with the power being a nonparametric time function. It is not possible to find the explicit solution to the utility maximization problem under the DEV model. In this paper, a dual-control Monte-Carlo method is developed to compute the optimal investment strategies for a variety of utility functions, including power, non-hyperbolic absolute risk aversion and symmetric asymptotic hyperbolic absolute risk aversion utilities. Numerical examples show that this dual-control Monte-Carlo method is quite efficient.     

Energy price uncertainty and the value premium

This paper examines the impact of energy price uncertainty on a range of value anomalies. We demonstrate that the value premium is substantially stronger in periods of heightened energy price uncertainty. Energy price uncertainty exerts an asymmetric effect on the value anomalies, whereby downside energy price uncertainty accentuates the return differences between value and growth stocks compared to upside energy uncertainty. These findings are consistent with the argument that value firms possess a larger amount of inflexible assets than growth firms. Therefore, they struggle more to adjust in periods of elevated energy price uncertainty. We also demonstrate that energy price uncertainty has predictive power on the value premium one-month ahead. Using the Feasible Generalized Least Squares predictive model, energy price uncertainty can help mean-variance investors to obtain a positive annual utility gain across the value anomalies for up to 16.71%.