Risk Aversion Parameter Research Articles

An analysis of transaction costs in participating life insurance under mean–variance preferences

Transaction costs with respect to distribution and administration play a crucial role for the performance of participating life insurance products. The aim of this paper is to investigate the impact of such initial and annual transaction costs on policyholder mean–variance preferences depending on the contract features, comparing a point-to-point guarantee, a cliquet-style guarantee, and a money-back guarantee with annual surplus component. We extend previous work by deriving analytical solutions for the maximum allowed initial transaction costs as well as the risk aversion parameter that ensure a given customer preference level for different contract types. We further conduct simulation analyses to identify key factors in regard to transaction costs. One main finding is that in the present setting, insurers can indeed charge higher costs for more complex products with cliquet-style features, and that the difference in costs between the various product types increases considerably in a low interest-rate environment. However, these results are heavily impacted and even reversed depending on the risk–return asset characteristics, as insurers with a riskier asset management strategy may no longer be able to charge higher transaction costs for complex products with a strong annual cliquet-style surplus participation component without reducing their attractiveness to customers.

Optimal Multi-Asset Trading With Linear Costs: A Mean-Field Approach

Optimal multi-asset trading with Markovian predictors is well understood in the case of quadratic transaction costs, but remains intractable when these costs are L1. We present a mean-field approach that reduces the multi-asset problem to a single-asset problem, with an effective predictor that includes a risk averse component. We obtain a simple approximate solution in the case of Ornstein-Uhlenbeck predictors and maximum position constraints. The optimal strategy is of the bang-bang type similar to that obtained in [de Lataillade et al., 2012]. When the risk aversion parameter is small, we find that the trading threshold is an affine function of the instantaneous global position, with a slope coefficient that we compute exactly. We provide numerical simulations that support our analytical results.

Optimal Investment and Risk Control Strategies for an Insurance Fund in Stochastic Framework

This paper considers optimal investment and risk control problem under the Hull and White Stochastic Volatility (SV) model for an Insurer who aims to optimize the investment and risk control strategies. The surplus process of the insurer is assumed to follow the Brownian motion with drift. An Insurer can invest in the financial market consisting of risk-free and risky assets whose price process satisfies Hull-White SV model. By applying the stochastic dynamic programming approach, we derive closed-form expressions for the optimal strategies and the value function. We find that under the Hull and White model, the interest rate and risk aversion parameters both influence optimal strategies. Moreover, we provide a numerical example to illustrate the model’s economic implications.

Rescuing Rational Expectations from Undeserved Ridicule

Heterogeneity of risk aversion parameters of economic agents facilitates risk sharing, as such, is a necessary condition for economic viability of stock markets. This study finds price equilibriums that are outcome of conditioning of homogeneously received information on heterogeneous realizations of risk preferences Pareto dominate alternate comparable equilibriums that are conditioned on the `common' component of heterogeneously received information. Necessity of an information source that is not either of stock prices or stock returns, and that equally is visible to all for feasibility of homogeneously received information establishes necessity of a `market procedural mechanism' for conditioning of rational expectations equilibriums (REE). While stock return volatility has, in context of the `Intertemporal Capital Asset Pricing Model (ICAPM)', structure that is amenable to its characterization as a market procedural mechanism, expectations that are conditioned on stock return volatility explicitly are shown to have character of uninformed gambles. Implicitness of adoption of return volatility as market mechanism suffices then, for inducement of stock markets that are characterized by, `gambles over lotteries'; the `investors trade too much' phenomenon; and intermittency of market correction events. We arrive then at a rational explanation for seeming irrationality or proneness to bias of actions of investors in stock markets, namely absence of a robustly formulated market procedural mechanism for formation of rational expectations equilibriums. In aggregate, we arrive at rescue of concept of REE from undeserved ridicule, that is, infer failings of mechanism design as bane of current workings of stock markets.

The intertemporal risk-Return relation, investor behavior, and technical trading profits: evidence from the G-7 countries

ABSTRACTThe intertemporal risk-return relation and investor behavior are both important pricing factors that jointly determine the expected market risk premium. Using the price adjustment process as a control variable, we find that the intertemporal risk-return relation is positive conditional on bad market news, but is non-positive conditional on good market news. This implies that good (bad) market news weakens (strengthens) the positive risk-return relation. The pattern in the distortion of the risk-return relation is consistent with short-term mispricing in which investors overvalue (undervalue) the stock market in reaction to good (bad) market news. We also show that ignoring the price adjustment process in the estimation of the risk-return relation leads to model misspecification and induces an upward (downward) bias in estimates of the relative risk aversion parameter conditional on good (bad) news. Our model of the asymmetric risk-return relation along with the price adjustment process is capable of generating the return dynamics that is attributable to technical trading profits. We suggest that the profitability of technical trading rules is not a violation of market efficiency, but a consequence of trading rules exploiting the asymmetric effect of price changes on the risk-return relation, along with the persistence property of price changes.

Nash Equilibrium Strategy for a DC Pension Plan with State-Dependent Risk Aversion: A Multiperiod Mean-Variance Framework

This paper investigates a defined contribution (DC) pension plan investment problem during the accumulation phase under the multiperiod mean-variance criterion. Different from most studies in the literature, where the investor’s risk aversion attitude is state-independent, we choose a state-dependent risk aversion parameter, which is a fractional function of the current wealth level. Moreover, we incorporate the wage income factor into our model, which leads to a more complicated problem than the portfolio selection problems that appeared in relevant papers. Due to the time inconsistency of the resulting problem, we derive the explicit expressions for the equilibrium strategy and the corresponding equilibrium value function by adopting the game theoretic framework and using the extended Bellman equation. Further, two special cases are discussed. Finally, based on real data from the American market, some prominent features of the equilibrium strategy established in our theoretical derivations are provided by comparing them with the results in the existing literature.

Time-consistent mean–variance portfolio optimization: A numerical impulse control approach

We investigate the time-consistent mean–variance (MV) portfolio optimization problem, popular in investment–reinsurance and investment-only applications, under a realistic context that involves the simultaneous application of different types of investment constraints and modelling assumptions, for which a closed-form solution is not known to exist. We develop an efficient numerical partial differential equation method for determining the optimal control for this problem. Central to our method is a combination of (i) an impulse control formulation of the MV investment problem, and (ii) a discretized version of the dynamic programming principle enforcing a time-consistency constraint. We impose realistic investment constraints, such as no trading if insolvent, leverage restrictions and different interest rates for borrowing/lending. Our method requires solution of linear partial integro-differential equations between intervention times, which is numerically simple and computationally effective. The proposed method can handle both continuous and discrete rebalancings. We study the substantial effect and economic implications of realistic investment constraints and modelling assumptions on the MV efficient frontier and the resulting investment strategies. This includes (i) a comprehensive comparison study of the pre-commitment and time-consistent optimal strategies, and (ii) an investigation on the significant impact of a wealth-dependent risk aversion parameter on the optimal controls.

Risk-Return Trade-Off on the Currency Portfolios

Unconditional asset pricing models have generally found it challenging to identify evidence of risk aversion. This paper addresses this challenge by examining whether currency portfolios display an intertemporal risk-return relationship. We consider time-varying relations because investors' risk-aversion may change over time, based upon changing economic states. Moreover, we take into account a broad based measure of investors' expectation from a data rich environment and factor model. We identify that the relations between risk and return vary over time, and the risk-aversion parameters on momentum and value currency portfolios increased during the financial crisis. Those parameters can command both positive and negative values. Therefore traditional time-invariant models may not identify strong risk-return relations because state dependent evidence is washed out.

On the asymmetric impact of macro–variables on volatility

We extend the GARCH–MIDAS model to take into account possible different impacts from positive and negative macroeconomic variations on financial market volatility: a Monte Carlo simulation which shows good properties of the estimator with realistic sample sizes. The empirical application is performed on the daily S&P500 volatility dynamics with the U.S. monthly industrial production and national activity index as additional (signed) determinants. We estimate the Relative Marginal Effect of macro variable movements on volatility at different lags. In the out-of-sample analysis, our proposed GARCH–MIDAS model not only statistically outperforms the competing specifications (GARCH, GJR-GARCH and GARCH–MIDAS models), but shows significant utility gains for a mean-variance investor under different risk aversion parameters. Attention to robustness is given by choosing different samples and estimating the model in an international context (six different stock markets).

The Effect of Income-Dependent Mortality on Withdrawal Strategies

Recent literature documented significant dependency between individual lifetime earnings and life expectancy. In light of this phenomenon, we examine the effect of using salary-fitted mortality tables on optimized withdrawal strategies. We find that although earnings rank meaningfully affects expected retirement length, the impact of modeling salary-fitted mortality is more nuanced and depends on the investor’s risk-aversion parameter. In the base case, a risk-neutral investor is willing to adjust her optimal withdrawal strategy roughly in proportion to the change in expected retirement length and can therefore experience a substantially larger misallocation of withdrawals. In contrast, for a risk-averse investor, a 10% income-related difference in expected retirement length does not necessitate a sizable adjustment of an optimized withdrawal strategy; the unconditional mortality assumption causes annual withdrawal misallocation of only about 1% to 3% of pre-retirement consumption. Given this difference in results, we stress the need for a comprehensive and cohesive framework when analyzing the full implications of a retirement horizon assumption.

Is Liquidity Risk Priced? Theory and Evidence

This study studies a recently proposed measure of liquidity premium (or discount). Specifically, the liquidity premium we utilize is defined as a function of a time discount factor, a relative risk aversion parameter, and the expected return and volatility of the asset, given the risk-free rate. Using U.S. stock market data, our empirical results confirm that the proposed liquidity premium measure is largely comparable to that commonly used in existing studies. Our results also imply that a risk factor based on the liquidity premium measure not only explains cross-sectional stock returns, but also time-series excess returns on portfolios sorted on the commonly used liquidity measure. In addition, our study suggests that better understanding the liquidity risk leads to sustainable trading for investors.

Effect of Income-Dependent Mortality on Withdrawal Strategies

Recent literature documented significant dependency between individual’s lifetime earnings and life expectancy. In light of this phenomenon, we examine the effect of using salary-fitted mortality tables on optimized withdrawal strategies. We find that while earnings rank meaningfully affects expected retirement length, the impact of modeling salary-fitted mortality is more nuanced and depends on investor’s risk aversion parameter. For a risk-averse investor, a 10% income-related difference in expected retirement length does not necessitate a sizable adjustment of an optimized withdrawal strategy: the unconditional mortality assumption causes annual withdrawals misallocation of only about 1-3% of pre-retirement consumption. In contrast, a risk-neutral investor is willing to adjust her optimal withdrawal strategy roughly in proportion to the change in expected retirement length and can experience a substantially larger withdrawals misallocation. Given this difference in results, we stress the need for a comprehensive and cohesive framework when analyzing full implications of a retirement horizon assumption.

Risk-Based Two-Stage Stochastic Optimization Problem of Micro-Grid Operation with Renewables and Incentive-Based Demand Response Programs

The operation problem of a micro-grid (MG) in grid-connected mode is an optimization one in which the main objective of the MG operator (MGO) is to minimize the operation cost with optimal scheduling of resources and optimal trading energy with the main grid. The MGO can use incentive-based demand response programs (DRPs) to pay an incentive to the consumers to change their demands in the peak hours. Moreover, the MGO forecasts the output power of renewable energy resources (RERs) and models their uncertainties in its problem. In this paper, the operation problem of an MGO is modeled as a risk-based two-stage stochastic optimization problem. To model the uncertainties of RERs, two-stage stochastic programming is considered and conditional value at risk (CVaR) index is used to manage the MGO’s risk-level. Moreover, the non-linear economic models of incentive-based DRPs are used by the MGO to change the peak load. The numerical studies are done to investigate the effect of incentive-based DRPs on the operation problem of the MGO. Moreover, to show the effect of the risk-averse parameter on MGO decisions, a sensitivity analysis is carried out.

Evaluation of reliability in risk‐constrained scheduling of autonomous microgrids with demand response and renewable resources

Uncertainties in renewable energy resources and electricity demand have introduced new challenges to energy and reserve scheduling of microgrids, particularly in autonomous mode. In this study, a risk-constrained stochastic framework is presented to maximise the expected profit of a microgrid operator under uncertainties of renewable resources, demand load and electricity price. In the proposed model, the trade-off between maximising the operator's expected profit and the risk of getting low profits in undesired scenarios is modelled by using the conditional value-at-risk (CVaR) method. The influence of consumers’ participation in demand response (DR) programs and their emergency load shedding for different values of lost load (VOLL) are then investigated on the expected profit of the operator, CVaR, expected energy not served and scheduled reserves of the microgrid. Moreover, the impacts of different VOLL and risk aversion parameters are illustrated on the system reliability. Extensive simulation results are also presented to illustrate the impact of risk aversion on system security issues with and without DR. Numerical results demonstrate the advantages of customers’ participation in the DR program on the expected profit of the microgrid operator and the reliability indices.

Investment behavior of Canada egg producers

PurposeThe purpose of this paper is to document the level of risk in the Québec egg sector (conventional and specialty eggs) and analyze the optimal choices of Québec egg producers that must allocate limited resources to production of different types of eggs.Design/methodology/approachA quadratic programming approach applied to expected mean-variance models is used to analyze the impact of risk on decision to invest when the resources must be allocated to different type of production that have different risk levels. The model is calibrated using monthly data from 2009 to 2016.FindingsResults indicated multiple uncertainty sources (technological, cost of production, price of eggs) that vary according to the types of eggs. Given risk aversion parameters, producer would favor production modes with the lowest producers’ price variance, which correspond to free-run eggs. Results also indicated that in response to a greater intensity of risk aversion, the course of action producers may choose is to increase the relative production of free-run eggs.Research limitations/implicationsThe empirical limits of this research are found in the lack of quality data on producer prices and costs for specialty eggs. Future research could explore the relationship between the growing impact of egg for processing, which price is based on the US price, and its relationship with specialty eggs.Practical implicationsThe findings of the study will be useful for policy makers and managers of eggs supply chain. This is important, given the recent announcement by Canadian’s large retailers and fast food companies to increase cage free eggs offering and, in some cases, eventually only selling these types of eggs.Originality/valueThis study adds to the understanding of the role of risk and uncertainty in the investment decision of egg producers and different mode of production, as well as in the development of the growing production of specialty eggs in Canada. It fills a gap in the literature regarding the impact of risk in Canadian egg production. This gap is likely explained by the perception of a lack of risk in this supply managed sector in Canada and its small size relative to other supply managed sector.

Valuation Risk Revalued

The recent asset pricing literature finds valuation risk is an important determinant of key asset pricing moments. Valuation risk is modelled as a time preference shock within Epstein-Zin recursive utility preferences. While this form of valuation risk appears to fit the data extremely well, we show the preference specification violates an economically meaningful restriction on the weights in the Epstein-Zin time-aggregator. The same model with the corrected preference specification performs nearly as well at matching asset pricing moments, but only if the risk aversion parameter is well above the accepted range of values used in the literature. When the corrected preference specification is combined with Bansal-Yaron long-run risk, the estimated model significantly downgrades the role of valuation risk in determining asset prices. The only significant contribution of valuation risk is to help match the volatility of the risk-free rate.

Time-Consistent Mean-Variance Portfolio Optimization: A Numerical 2 Impulse Control Approach

We investigate the time-consistent mean-variance (MV) portfolio optimization problem under a realistic context that involves the simultaneous application of different types of investment constraints and modelling assumptions, for which a closed-form solution is not known to exist. We develop an efficient numerical partial differential equation method for determining the optimal control for this problem. Central to our method is a combination of (i) an impulse control formulation of the MV investment problem, and (ii) a discretized version of the dynamic programming principle enforcing a time-consistency constraint. We impose realistic investment constraints, such as no trading if insolvent, leverage restrictions and different interest rates for borrowing/lending. Our method requires solution of linear partial integro-differential equations between intervention times, which is numerically simple and computationally effective. The proposed method can handle both continuous and discrete rebalancings.We study the substantial effect and economic implications of realistic investment constraints and modelling assumptions on the MV efficient frontier and the resulting investment strategies. This includes (i) a comprehensive comparison study of the pre-commitment and time-consistent optimal strategies, and (ii) an investigation on the significant impact of a wealth-dependent risk aversion parameter on the optimal controls.

Risk-Based Bi-Level Model for Simultaneous Profit Maximization of a Smart Distribution Company and Electric Vehicle Parking Lot Owner

In this paper, the effect of renewable energy resources (RERs), demand response (DR) programs and electric vehicles (EVs) is evaluated on the optimal operation of a smart distribution company (SDISCO) in the form of a new bi-level model. According to the existence of private electric vehicle parking lots (PLs) in the network, the aim of both levels is to maximize the profits of SDISCO and the PL owners. Furthermore, due to the uncertainty of RERs and EVs, the conditional value-at-risk (CVaR) method is applied in order to limit the risk of expected profit. The model is transformed into a linear single-level model by the Karush–Kuhn–Tucker (KKT) conditions and tested on the IEEE 33-bus distribution system over a 24-h period. The results show that by using a proper charging/discharging schedule, as well as a time of use program, SDISCO gains more profit. Furthermore, by increasing the risk aversion parameter, this profit is reduced.

Risk Attitude Optimization and Heterogeneous Stock Market Participation

This paper studies equilibrium portfolio choice and asset returns using a new model of recursive preferences called optimal risk attitude utility. Our model is an extension of recursive expected utility that allows an individual to optimally select her risk aversion parameter in response to the uncertainty that she faces. Choosing a lower level of risk aversion comes at a cognitive cost, and therefore is only undertaken in response to sufficiently large risk exposure. In addition to separating risk aversion from the elasticity of intertemporal substitution, our model can also separate risk attitudes toward small and large risks. We solve the dynamic stochastic general equilibrium of a calibrated economy and show that optimal risk attitude utility can provide a partial resolution to both the stock market participation puzzle and the equity premium puzzle. Our model generates a moderate premium for equity as well as endogenous heterogeneity in risk exposure, with one segment of the population holding minimal risk while the other holds a disproportionate share of aggregate risk, even when consumers have identical preferences and even among wealthy households. Using simple binary gambles as a rationality check for our model, we demonstrate that the preference parameters used in our calibration exhibit descriptively accurate levels of risk aversion for gambles ranging from one hundred dollars up to ten percent of wealth.

A Very Simple Goals - and Risk-Based Asset Pricing Model (or Asset Pricing with Heterogeneous Investors)

Prof, Andre Perold has shown how the Capital Asset Pricing Model (with implications for asset pricing and risk-adjusted performance) can be derived from maximizing the Sharpe ratio as opposed to the traditional approach of assuming that investors maximize the utility of wealth. More recently, Goals-based Investing (GBI) is becoming the norm for investors and Prof. Robert Merton has suggested that theory needs to accommodate the fact that investors maximize relative (wealth divided by the present value of the goal) and not absolute wealth. Individuals save for a range of goals (e.g., retirement, a child’s college expenses) and each has a unique set of cash flows. The paper first argues for the creation of a new class of relative risk-free fixed income securities for each goal as proposed for a number of countries by Prof. Merton. These instruments will typically be interest-only real bonds (linked to the appropriate inflation index), with a forward start date, and pay coupons for the period required for the respective goal. The second contribution of this paper is to use the Perold approach and show that with two such goals/instruments and the traditional risk-free asset, all risky assets can be priced and optimal asset allocation recommendations derived, without requiring a formal utility function, risk aversion parameter or market portfolio. All that is needed is the assumption that investors maximize risk-adjusted returns relative to the goal-replicating asset and specify risk goals much like traditional investors would specify. The asset pricing model is derived from the simple idea that a relatively risk-free asset for one goal is a risky asset for another, and hence these two assets, plus the absolute risk-free rate allow us to triangulate to establish returns for all other assets. This approach also lends itself easily to an asset pricing model with heterogeneous investors and effective risk-adjusted performance measures.