Relative Risk Aversion Research Articles

Portfolios of value and momentum: disappointment aversion and non-normalities

Professional money managers often combine value and momentum to benefit from diversification gains resulting from their negative return correlation. We go beyond the mean-variance and constant relative risk aversion environments to investigate this fundamental issue by assuming that investors exhibit disappointment aversion, and empirically account for the non-normalities and non-linear dependencies of the returns associated with these strategies. We perform an exploration exercise on the interplay of these two general sets of assumptions. In accordance with the literature, we find that disappointment preferences lead to optimal portfolio choices that are not attainable under the traditional constant relative risk aversion case. The findings reveal that higher disappointment aversion utility levels can be reached when non-normalities are introduced in the optimization process. The intensity of this phenomenon rises as disappointment aversion increases. However, taking advantage of these non-linearities and non-normalities requires higher portfolio turnovers. Therefore, when introducing transaction costs in the analysis, we find significant improvement in certainty equivalent returns only for investors having high disappointment aversion levels and facing low transaction costs.

Estimates of households consumer behavior in Russia

In this paper, the consumption profiles of households in the Russian Federation are constructed and, on their basis, the parameters of future discounting and relative risk aversion are evaluated. The paper demonstrates that the age profiles are hump-shaped, the peak consumption level is reached at 38—40 years. The important determinant of the hump shape is the composition of the household: when consumption is recalculated for the average individual in a household, the hump shape becomes less pronounced. On average, households have a high level of relative risk aversion and a low level of future discounting. This configuration of parameters indicates the important role of the precautionary motive in the consumer behavior of households. Estimates are presented for households with different levels of education and number of people.

Parental time preferences and educational choices: The role of children’s gender and of social origin

This paper contributes to the literature on Relative Risk Aversion theory in two ways: first, by considering that the effect of time preferences may differ according to both children’s gender and social origin; second, by exploring this possibility for different educational outcomes: upper secondary school choices and university enrollment. We use data of the Survey of Household Income and Wealth, which contains questions specifically addressed to capture an individual’s time discounting preference, to further explore the association between time discounting preference and the effect of social origin on educational outcomes in Italy. In line with prior research, we find that time preferences only have a meaningful effect among children of lowly educated parents. But such an effect, in turn, differs by gender: parental time preferences matter more for sons than for daughters of lowly educated parents. This gender effect is found both for upper secondary choices and for entry into higher education.

A Novel Model of Emergency Demand Response Program for Optimal Aggregators’ Strategy

Demand response (DR) programs have been used for a variety of purposes. In this study, Emergency Demand Response Program (EDRP), as an incentive-based program, is used for peak clipping, managing the volatility and the increase of the electricity prices, monetizing consumers’ involuntary electricity outage and controlling the price in the day-ahead market. A market-driven model in the form of a combination of Diamond’s over-lapping generations (OLG) and Price Elasticity (PE) formulations is proposed for the aggregates (AGGs) by which they can manage their consumers’ demand at the peak hours and maximize the profit. Furthermore, maximizing the profit of the AGGs was performed by determining the optimal amount of demand while three technical constraints such as demand ceiling, relative risk aversion and incentive limits were also included in the proposed model. The profit function of the AGGs is considered in the form of the difference between the revenue and the cost. The problem is solved with taking into consideration the different rate of time preference and PE over a 24-hour period. The simulation results showed a successful performance of the proposed model from the considered economical and technical viewpoints.

Banks’ liquidity provision and panic runs with recursive preferences

How important is it to distinguish relative risk aversion (RRA) from the intertemporal elasticity of substitution (IES) to study banks’ provision of liquidity insurance and the effectiveness of deposit freezes against depositors’ panic runs? To answer these questions, I develop a Diamond–Dybvig model of banking in which depositors feature recursive preferences. In equilibrium, banks provide liquidity insurance, and a time-consistent deposit freeze prevents panic runs, only if depositors’ preferences for an early resolution of uncertainty are sufficiently strong, i.e. if RRA is sufficiently larger than the inverse of IES.

The value and cost of more stages in stochastic programing: a statistical analysis on a set of portfolio choice problems

Sequential decision problems under uncertainty are commonly studied with stochastic programing. An important modeling choice is the number of stages. More stages allow additional information to be captured, but is associated with a coarser representation of uncertainty may worsen solution quality. In this paper, we study this trade-off, with the objective to advance the understanding of how the number of stages affect solution quality in stochastic programing. We show: (i) how the optimistic bounds from stochastic programing gradually suggest improved performance with more stages, while the real solution quality simultaneously deteriorates; and (ii) that real performance can be improved by adding stages, but only up to some point, after which more stages are detrimental. Further, we highlight the importance of understanding what creates the value of more stages in the problem of interest, and particularly if this can be captured in models with few stages. The numerical experiments are based on the classic portfolio choice problem of an investor with constant relative risk aversion preferences, maximizing the expected utility of terminal wealth. We study instances with proportional transaction costs and predictability in returns, which takes this problem into an inherently multi-stage nature.

Significant Insights, Value Orientation and Differences Between the Mutual Fund Investment Flow and Indian Stock Market Returns – A Theoretical Assimilation

Researchers and academicians from all over the world have become interested in the study of the causal relationship between mutual fund investment flow and stock market returns in recent years. But there is currently a contradictory body of empirical data on this matter. Additionally, there are a few studies that take the case of India into account. In order to better understand the dynamics of the relationship between mutual fund investment flow and stock market returns in India from January 2000 to May 2010, the following article will do just that. The Granger causality tests are applied using the Toda and Yamamoto approach, which yields evidence of a one-way causal relationship between stock market returns and mutual fund investment flow. This suggests that the expansion of stock market activity in India draws mutual funds to the stock market. Therefore, the government and monetary authorities should take the necessary actions to reduce the volatility and increase the efficiency of the capital market. By gathering money from households and investing it in the stock and debt markets, mutual funds enable portfolio diversification and relative risk aversion. In India, a specific type of mutual fund called fixed-income funds invests in debt securities that have been issued by businesses, banks, or the government. In India, fixed-income funds are also referred to as debt funds and income funds. The goal of the current study is to assess the performance of a few selected debt or income mutual fund schemes in India based on their daily NAV using various statistical measures. In the past ten years, income schemes have become more and more popular. The securities that were purchased are referred to as the fund's portfolio. There may have been restrictions on rival products, which led to the emergence of money market and (short-term) bond funds. In this study, the performance of several mutual fund types in India was compared and studied. The results showed that equities funds outperformed income funds. The study also found that institutional fund managers can time their investments and that equity fund managers have significant market timing ability, but broker operated funds did not demonstrate this ability. Additionally, empirical research has shown that fund managers possess significant timing ability and can time their investments to match market conditions.

A Certainty Equivalent Merton Problem

The Merton problem is the well-known stochastic control problem of choosing consumption over time, as well as an investment mix, to maximize expected constant relative risk aversion (CRRA) utility of consumption. Merton formulated the problem and provided an analytical solution in 1970; since then a number of extensions of the original formulation have been solved. In this note we identify a certainty equivalent problem, i.e., a deterministic optimal control problem with the same optimal value function and optimal policy, for the base Merton problem, as well as a number of extensions. When time is discretized, the certainty equivalent problem becomes a second-order cone program (SOCP), readily formulated and solved using domain specific languages for convex optimization. This makes it a good starting point for model predictive control, a policy that can handle extensions that are either too cumbersome or impossible to handle exactly using standard dynamic programming methods.

Optimal Asset Allocation for CRRA and CARA Insurers under the Vasicek Interest Rate Model

This paper considers the reinsurance‐investment problem with interest rate risks under constant relative risk aversion and constant absolute risk aversion preferences, respectively. Stochastic control theory and dynamic programming principle are applied to investigate the optimal proportional reinsurance‐investment strategy for an insurer under the Vasicek stochastic interest rate model. Solving the corresponding Hamilton‐Jacobi‐Bellman equation via the Legendre transform approach, the optimal premium allocation strategies maximizing the expected utilities of terminal wealth are derived. In addition, several sensitivity analyses and numerical illustrations are given to analyze the impacts of different risk preferences and interest rate fluctuation on the optimal strategies. We find that the asset allocation and reinsurance ratio of the insurer are correlated with risk preference coefficient and interest rate fluctuation, and the insurance company may adjust the reinsurance‐investment strategy to deal with interest rate risk.

Optimal Investment and Consumption Problem with Stochastic Environments

Optimal investment and consumption problem for a CRRA investor or agent is solved in this study. An agent invests in the financial market with one risk-free security and one risky security. The stochastic interest rate dynamics of risk-free security follow a Ho-Lee model and the risky security is modeled as Heston’s model with its volatility parameter dynamics following a Cox-Ingersoll-Ross (CIR) model. Interest rates and volatility rates, in reality, are stochastic due to uncertain events such as the Coronavirus disease 2019 (COVID19) pandemic, climate change, etc. Our main goal is to allocate initial wealth x0 between risk-free security and risky security in order to maximize the discounted expected utility of consumption and terminal wealth over a finite horizon. Applying the Dynamic Programming Principle (DPP), the HJB PDE for the value function is established. The power utility function which belongs to the Constant Relative Risk Aversion (CRRA) class is employed for our analysis to obtain the value function and optimal policies. Finally, numerical examples and simulations are provided and discussed.

On a special case of non-symmetric resource extraction games with unbounded payoffs

The game of resource extraction/capital accumulation is a stochastic infinite-horizon game, which models a joint utilization of a productive asset over time. The paper complements the available results on pure Markov perfect equilibrium existence in the non-symmetric game setting with an arbitrary number of agents. Moreover, we allow that the players have unbounded utilities and relax the assumption that the stochastic kernels of the transition probability must depend only on the amount of resource before consumption. This class of the game has not been examined beforehand. However, we could prove the Markov perfect equilibrium existence only in the specific case of interest. Namely, when the players have constant relative risk aversion (CRRA) power utilities and the transition law follows a geometric random walk in relation to the joint investment. The setup with the chosen characteristics is motivated by economic considerations, which makes it relevant to a certain range of real-word problems.

Time Inconsistent Preferences with Time Dependent Relative Risk Aversion: A Model with Some Macroeconomic Applications

Time Inconsistent Preferences with Time Dependent Relative Risk Aversion: A Model with Some Macroeconomic Applications

Closed-form portfolio optimization under GARCH models

This paper develops an approximate closed-form optimal portfolio allocation formula for a spot asset whose variance follows a GARCH(1,1) process. We consider an investor with constant relative risk aversion (CRRA) utility who wants to maximize the expected utility from terminal wealth under a Heston and Nandi (2000) GARCH (HN-GARCH) model. Based on an approximation of the log returns from Campbell and Viceira (1999), we obtain closed formulas for the optimal investment strategy, the value function and the optimal terminal wealth. We find the optimal strategy is independent of the development of the risky asset, and the solution converges to that of a continuous-time Heston stochastic volatility model (Kraft, 2005), albeit under additional conditions. For a daily trading scenario, the optimal solutions are quite robust to variations in the parameters, while the numerical wealth equivalent loss (WEL) analysis shows good performance of the Heston solution, with a quite inferior performance of the Merton solution.The solution is extended to two dimensions under the multivariate affine GARCH in Escobar-Anel et al. (2020).

Currency substitution as an automatic stabilizer

AbstractIn the presence of frictions, the existing literature shows that currency substitution is detrimental for domestic aggregate stability. This paper singles out the role of currency substitution and shows that diversified currency holdings operate as an automatic stabilizer that mitigates belief-driven cyclical fluctuations in Farmer’s (1997) indeterminate monetary economy. When the foreign inflation rate is lower than the domestic inflation rate, the model’s steady state always displays saddle-path stability. Hence, equilibrium indeterminacy originally present in the domestic country is entirely removed in the presence of diversified currency holdings. When the foreign inflation rate is higher than the domestic inflation rate, then depending on the degrees of currency substitution and relative risk aversion, indeterminacy is either impossible or the requisite level of the foreign inflation rate for indeterminacy is too high to square with data. The stabilizing effect of diversified currency holdings on domestic aggregate stability is robust to whether domestic and foreign currencies display as Edgeworth substitutes or complements, or are additively separable in the household’s preferences.

Countercyclical Labor Income Risk and Portfolio Choices over the Life Cycle

Abstract I estimate a life cycle model of portfolio choices that incorporates the relationship between market returns and the skewness of idiosyncratic income shocks. The cyclicality of skewness can explain (a) low stock market participation among young households, (b) why the equity share of participants slightly increases until retirement, and (c) why renters invest less in stocks than do homeowners. With a relative risk aversion of 6 and yearly participation cost of $250, the model matches the evolution of wealth, participation, and conditional equity shares over the life cycle. Nevertheless, cyclical skewness increases the equity premium by at most 0.5 percentage points. Authors have furnished an Internet Appendix, which is available on the Oxford University Press Web site next to the link to the final published paper online.

Polynomial affine approach to HARA utility maximization with applications to OrnsteinUhlenbeck [formula omitted] models.

This paper designs a numerical methodology, named PAMH, to approximate an investor’s optimal portfolio strategy in the contexts of expected utility theory (EUT) and mean-variance theory (MVT). Thanks to the use of hyperbolic absolute risk aversion utilities (HARA), the approach produces optimal solutions for decreasing relative risk aversion (DRRA) investors, as well as for increasing relative risk aversion (IRRA) agents. The accuracy and efficiency of the approximation is examined in a comparison to known closed-form solutions for a one dimensional (n=1) geometric Brownian motion with a CIR stochastic volatility model (i.e. GBM 1/2 or Heston model), and a high dimensional (up to n=35) stochastic covariance model. The former confirms the method works even when the theoretical candidate is not well-defined, while the latter illustrates low errors (up to 8% in certainty equivalent rate (CER)) and feasible computational time (less than one hour in a PC).Given the potential of this method, we investigate a relevant practical setting with no closed-form solution, namely when assets follow an OrnsteinUhlenbeck 4/2 stochastic volatility (SV, i.e. OU 4/2) model. We conduct sensitivity analyses of the optimal strategies for DRRA and IRRA investors with respect to key parameters; (e.g. risk aversion, minimum capital guarantee and 4/2’s parameters). In particular, the efficient frontier for the IRRA case is presented. A comparison to important sub-optimal strategies in terms of CER is performed, indicating low CER performances due to ignorance of stochastic volatility for CRRA investors, i.e. a myopic strategy would be even better than ignoring SV. The analyses highlight the importance of efficient and precise numerical methods to obtain substantially higher CERs.

Portfolio optimization and intergenerational risk sharing for a collective defined contribution pension plan

Abstract In this paper, we use a continuous time stochastic model to study a collective defined contribution pension plan when the interest rate is stochastic, and where the benefit levels are adjusted depending on the performance of the plan, and with risk sharing between different generations. The nominal interest rate is characterized by the Vasicek model, and the pension fund is invested in a financial market consisting of three assets: one risk-free asset, one bond and one risky asset. The participants of the pension plan are the risk bearers, and the plan seeks optimal investment and risk-sharing arrangements for plan sponsors and participants that maximize the expected accumulated discount utility of intermediate benefit adjustments and terminal wealth. Closed-form solutions are derived via the stochastic optimal control approach under constant relative risk aversion utility function. Numerical results show the effects of financial market parameters on the optimal investment strategy and how the optimal benefit changes with respect to different risk aversions and wage increase rates.

Vocational School Students' Aspirations for Higher Education and Selected Social Background Characteristics

This study examines the association between vocational school students' aspirations for higher education and different factors that may be related to their social background. Using cultural reproduction and relative risk aversion (RRA) theories, the study draws on data from 7060 students of four-year vocational upper secondary school programmes in Croatia. A multinomial logistic model with a random intercept was applied, in which students' aspirations for pursuing higher education served as the outcome variable. Apart from indicators of socio-economic status (SES), vocational school students' characteristics related to cultural habits and behaviours, as well as their concerns with downward mobility, were used as regressor variables in the analysis. All three constructs showed independent effects on aspirations for higher education, controlling for vocational sector, gender, school achievement, and school year. Further, a moderation effect was identified, indicating that the association between cultural capital and aspirations for higher education was stronger among students with more educated parents. In contrast to previous studies, the findings point to the potential complementarity of cultural capital and RRA concerning educational aspirations. We discuss the implications of the study and directions for future research.

Social background and school track choice: An analysis informed by the rational choice framework

We investigate social inequalities based on social background in the choice of the academic track among equally performing students, and how indicators derived from the rational choice framework contribute to account for such inequalities. We discuss the main theoretical concepts underpinning rational choice theory as applied to educational decisions: perceived costs, benefits, and risks of failure; relative risk aversion; and time-discounting preferences. In the empirical section, we use a unique dataset concerning the transition to different tracks in upper secondary school in a large Southern Italian region. By using various regression methods and the Karlson/Holm/Breen decomposition technique, we show that social inequalities in access to the academic track are considerable, even in recent cohorts, and that they are largely not explained by previous academic performance. Indicators linked to key concepts proposed by the rational choice theory—as measured in this study—account, as a whole, for 31% of the gap based on parental education, and for 40% of the gap based on parental occupation. The most important sources of inequalities among those this study examines are the expected benefits associated with the educational alternatives and the time-discounting preferences, while relative risk aversion and the perceived chances of success play negligible roles.

Portfolio optimization with optimal expected utility risk measures

The purpose of this article is to evaluate optimal expected utility risk measures (OEU) in a risk-constrained portfolio optimization context where the expected portfolio return is maximized. We compare the portfolio optimization with OEU constraint to a portfolio selection model using value at risk as constraint. The former is a coherent risk measure for utility functions with constant relative risk aversion and allows individual specifications to the investor’s risk attitude and time preference. In a case study with three indices, we investigate how these theoretical differences influence the performance of the portfolio selection strategies. A copula approach with univariate ARMA-GARCH models is used in a rolling forecast to simulate monthly future returns and calculate the derived measures for the optimization. The results of this study illustrate that both optimization strategies perform considerably better than an equally weighted portfolio and a buy and hold portfolio. Moreover, our results illustrate that portfolio optimization with OEU constraint experiences individualized effects, e.g., less risk-averse investors lose more portfolio value in the financial crises but outperform their more risk-averse counterparts in bull markets.