Relative Risk Tolerance Research Articles

Optimal investment strategies under the relative performance in jump-diffusion markets

AbstractWe work on a portfolio management problem for one agent and a large group of agents under relative performance concerns in jump-diffusion markets with the CRRA utility function. Herein, we define two wealth dynamics: the agent’s and the group’s wealth. We measure the performances of both the agent and the group with preferences linked to the group performance. Therefore, we have stochastic optimal control problems for both the representative agent and the group to determine what the group does and the agent’s optimal proportion in the portfolio relative to the group’s performance. Further, our framework assumes that the agent’s performance does not affect the group, while the group affects the agent’s utility. Moreover, we investigate special cases where all agents in the market are homogeneous in their risk aversion and relative performances. We explore the qualitative behavior of the agent and show some numerical results depending on her relative performance consideration and risk tolerance degree.

The influence of CEO risk tolerance on initial pay packages

AbstractResearch SummaryBased on agency theory, CEOs with greater risk aversion should be given greater incentive‐based compensation to motivate risk taking. We explore whether new CEOs receive initial pay packages that follow this recommendation, or instead receive pay packages that mirror their risk preferences. Rather than finding support for the agency theory perspective, we find that new CEOs are compensated in the way that reinforces their existing risk preferences. Specifically, using a CEO's political orientation to capture relative risk tolerance, we find that conservative‐leaning CEOs receive relatively less performance‐based pay than their liberal‐leaning counterparts. Supplemental analyses suggest this occurs through both a matching and tailoring process, whereby boards offer similar pay packages from CEO‐to‐CEO, but modify them based on differences in risk tolerances.Managerial SummaryWhen designing a new CEO's pay contract, what proportion of the total compensation should be guaranteed versus performance based? To encourage risk taking, most researchers suggest that CEOs with greater risk aversion should have a pay mix that is more heavily weighted toward performance‐based pay. We find that the opposite occurs; new CEOs who are more risk averse tend to receive relatively less performance‐based pay than new CEOs who are more risk tolerant. This appears to occur because CEOs are attracted to firms that offered the prior CEO a pay package that appeals to the new CEO's risk tolerance. Our results also suggest that risk‐seeking CEOs' strategic actions are more strongly influenced by performance‐based pay, while more risk‐averse CEOs seem relatively unaffected by pay mix.

A test of traditional and psychometric relative risk tolerance measures on household financial risk taking

This article provides a comparative test of two ways in which individual relative risk tolerance is commonly measured in research and practice. Results suggest that the popular method of measuring gambles across lifetime income provides less insight into household investment behavior than the psychometric approach that is often used to derive a risk profile measure.

The Influence of CEO Risk Tolerance on Initial Pay Packages and Strategic Change

We explore whether new CEOs receive initial pay packages that a) align with their risk preferences or b) are calibrated to offset their natural tendencies. Specifically, we examine the initial pay structures of CEOs in relation to their relative risk tolerance, which we measure using a CEO’s political orientation, and find that more conservative-leaning CEOs receive less performance-based pay than their more liberal-leaning counterparts. Supplemental analyses indicate that both a matching and adjustment process appear to occur, whereby boards offer similar pay packages from CEO-to-CEO, but modify them based on differences in risk tolerances. Moreover, our results suggest that a CEO’s relative risk tolerance also influences the relationship between performance-based pay and strategic change. Liberal CEOs are more sensitive to performance-based pay, while conservative CEOs are relatively intolerant to pay mix. Overall, these findings suggest that contrary to typical recommendations based on agency theory, CEOs often receive pay packages that reinforce their personal risk propensity.

Geospatial Risk Assessment of Marine Terminal Infrastructure to Storm Surge Inundation and Sea Level Rise

Planning resiliency and sustainability of port operations and critical infrastructure requires risk assessment of storm surge exposure and potential sea level rise. An approach for rapid, screening-level assessment is developed to estimate the current and future risk of exposure to severe storm surges posed to marine terminal facilities in Norfolk, Virginia. The approach estimates the vertical elevation of local mean sea level fifty years into the future and attendant increases in potential storm surge heights. Inundation models are designed for baseline water levels and storm surges for category 1–3 hurricanes across five precautionary future sea level rise scenarios. In addition, tidal flooding poses an emerging threat because sea level rise will also force tides to higher elevations, suggesting that today’s extreme high tides may be the future mean high tide and today’s “nuisance” tidal flooding may in the future recur with chronic regularity. Potential tidal flooding levels are also modeled for each sea level scenario. This approach allows a port to assess relative risk tolerance across the range from lesser to more severe flooding events. Maps and tabular information in linked scenarios are used to summarize the extent, pattern, and depth of potential flooding. The methodology and data developed in this study may be applied to inform the timing and placement of planned assets and can be leveraged in the broader pursuit of optimization in support of long-term master planning at marine terminals.

Understanding dynamic mean variance asset allocation

We provide a new portfolio decomposition formula that sheds light on the economics of portfolio choice for investors following the mean-variance (MV) criterion. We show that the number of components of a dynamic portfolio strategy can be reduced to two: the first is preference free and hedges the risk of a discount bond maturing at the investor’s horizon while the second hedges the time variation in pseudo relative risk tolerance. Both components entail strong horizon effects in the dynamic asset allocation as a result of time-varying risk tolerance and investment opportunity sets. We also provide closed-form solutions for the optimal portfolio strategy in the presence of market return predictability. The model parameters are estimated over the period 1963 to 2012 for the U.S. market. We show that (i) intertemporal hedging can be very large, (ii) the MV criterion hugely understates the true extent of risk aversion for high values of the risk aversion parameter, and the more so the shorter the investment horizon, and (iii) the efficient frontiers seem problematic for investment horizons shorter than one year but satisfactory for large horizons. Overall, adopting the MV model leads to acceptable results for medium and long term investors endowed with medium or high risk tolerance, but to very problematic ones otherwise.

Understanding Dynamic Mean Variance Asset Allocation

We provide a new portfolio decomposition formula that sheds light on the economics of portfolio choice for investors following the mean-variance (MV) criterion. We show that the number of components of a dynamic portfolio strategy can be reduced to two: the first is preference free and hedges the risk of a discount bond maturing at the investor's horizon while the second hedges the time variation in pseudo relative risk tolerance. Both components entail strong horizon effects in the dynamic asset allocation as a result of time-varying risk tolerance and investment opportunity sets. We also provide closed-form solutions for the optimal portfolio strategy in the presence of market return predictability. The model parameters are estimated over the period 1963 to 2012 for the U.S. market. We show that:(i) intertemporal hedging can be very large, (ii) the MV criterion hugely understates the true extent of risk aversion for high values of the risk aversion parameter, and the more so the shorter the investment horizon and, (iii) the efficient frontiers seem problematic for investment horizons shorter than one year but satisfactory for large horizons. Overall, adopting the MV model leads to acceptable results for medium and long term investors endowed with medium or high risk tolerance, but to very problematic ones otherwise.

Ventromedial prefrontal cortex damage alters relative risk tolerance for prospective gains and losses

One paradigmatic example of “irrational” bias in human economic decision-making—known as the “reflection effect”—is a tendency to prefer sure amounts over risky gambles in situations involving potential gain, but to prefer risky gambles over sure amounts in situations involving potential loss. To date, there is no causal evidence regarding the neural basis of the reflection effect. The ventromedial prefrontal cortex (vmPFC) is believed to play a critical role in mediating value-based decision-making. In this study, we administered a behavioral test of the reflection effect to three groups of subjects: neurosurgical patients with focal bilateral vmPFC lesions, neurosurgical patients with lesions outside vmPFC, and neurologically healthy adults. Subjects made a series of choices between a sure amount (e.g., gain of $50) and a gamble (e.g., 50% chance of gaining $100, 50% chance of gaining $0). Half the trials featured potential gains while the other half featured potential losses. The sure amounts varied across trials. Relative to the two comparison groups, the vmPFC lesion patients exhibited a significantly greater reflection effect; more gambles selected in the loss condition and fewer gambles selected in the gain condition. This finding demonstrates a critical role for vmPFC in governing susceptibility to bias in decision-making.

Are Imputation Credits Capitalized Into Stock Returns?

This paper develops an equilibrium model demonstrating that: firstly, imputation credits are negatively capitalized into stock returns; and secondly, the extent of capitalization is a function of domestic investors’ relative risk tolerance. Using Australian data, it shows that imputation credits lead to lower required returns on stocks, which is consistent with the model’s predictions. The negative capitalization of imputation credits is stronger for stocks with larger size, smaller return volatility and smaller idiosyncratic risk. Overall, the theoretical and empirical evidence suggests that imputation credit capitalization is determined by all investors and does not support the marginal investor hypothesis.

Two-stage financial risk tolerance assessment using data envelopment analysis

Typical questionnaires administered by financial advisors to assess financial risk tolerance mostly contain stereotypes of people, have seemingly unscientific scoring approaches and often treat risk as a one-dimensional concept. In this work, a mathematical tool was developed to assess relative risk tolerance using Data Envelopment Analysis (DEA). At its core, it is a novel questionnaire that characterizes risk by its four distinct elements: propensity, attitude, capacity, and knowledge. Over 180 individuals were surveyed and their responses were analyzed using the Slacks-based measure type of DEA efficiency model. Results show that the multidimensionality of risk must be considered for complete assessment of risk tolerance. This approach also provides insight into the relationship between risk, its elements and other variables. Specifically, the perception of risk varies by gender as men are generally less risk averse than women. In fact, risk attitude and knowledge scores are consistently lower for women, while there is no statistical difference in their risk capacity and propensity compared to men. The tool can also serve as a “risk calculator” for an appropriate and defensible method to meet legal compliance requirements, known as the “Know Your Client” rule, that exist for Canadian financial institutions and their advisors.

Sharing Rules for Common-Pool Resources When Self-Insurance is Available

When a group of users who share a common-pool resource through a system of licenses is exposed to the risk of shortage, there is a need to establish a sharing rule. Such sharing rule is likely to impact the individual decisions to self-insure, i.e., to rely on a secure but costly resource instead of the free but uncertain common-pool resource. We determine the optimal sharing rule and the optimal diversification between the common-pool resource and the safe resource as a function of the agents’ individual characteristics, the distribution of the common-pool resource availability, and the cost of the safe resource. We find that, for a group of agents with heterogenous risk preferences, a perfectly informed regulator can obtain the optimal diversification level by imposing a rationing rule which shares the resource between agents proportionally to their relative risk tolerance. We illustrate and interpret our results in the context of water management in France.

Divorce as risky behavior.

Given that divorce often represents a high-stakes income gamble, we ask how individual levels of risk tolerance affect the decision to divorce. We extend the orthodox divorce model by assuming that individuals are risk averse, that marriage is risky, and that divorce is even riskier. The model predicts that conditional on the expected gains to marriage and divorce, the probability of divorce increases with relative risk tolerance because risk averse individuals require compensation for the additional risk that is inherent in divorce. To implement the model empirically, we use data for first-married women and men from the 1979 National Longitudinal Survey of Youth to estimate a probit model of divorce in which a measure of risk tolerance is among the covariates. The estimates reveal that a 1-point increase in risk tolerance raises the predicted probability of divorce by 4.3% for a representative man and by 11.4% for a representative woman. These findings are consistent with the notion that divorce entails a greater income gamble for women than for men.

Imputing Risk Tolerance From Survey Responses

Economic theory assigns a central role to risk preferences. This article develops a measure of relative risk tolerance using responses to hypothetical income gambles in the Health and Retirement Study. In contrast to most survey measures that produce an ordinal metric, this article shows how to construct a cardinal proxy for the risk tolerance of each survey respondent. The article also shows how to account for measurement error in estimating this proxy and how to obtain consistent regression estimates despite the measurement error. The risk tolerance proxy is shown to explain differences in asset allocation across households.

Risk Tolerance and its Relation to Important Life Events

We study panel data on three birth-year cohorts to understand the changes in risk tolerance across different age groups. Interval regression models on cross-sectional data for each birth cohort are constructed to investigate how time-invariant factors and macroeconomic events such as September 11, 2001, might influence individuals' risk tolerance. Well-established maximum likelihood estimation procedure is followed to obtain a parametric distribution of logarithm of relative risk tolerance that is potentially subject to noise, and to assess how this distribution shifts with time. Finally, we conduct interval regressions on first difference models to capture the reasons for change in the risk tolerance in each cohort. The main differences in the results as compared to previous studies are that risk tolerance does decrease with age, but there is much more within-subject heterogeneity among younger individuals, and that income lowers risk tolerance among younger Americans, whereas wealth increases risk tolerance among older Americans. The risk tolerance of the oldest cohort is negatively affected by late-life marriage and widowhood, whereas risk tolerance increases with greater wealth, and somewhat due to retirement. An increase in family size through marriage and more children lowers the risk tolerance of the youngest cohort, whereas unemployment has a positive association with tolerance.

Option Bounds and Second Order Arbitrage Opportunities

In this paper we investigate the relationship between risk aversion and cautiousness, two important risk preference measures. We show how high cautiousness is associated with low risk aversion and how bounds and limits of cautiousness imply bounds and limits of relative risk aversion respectively. We also show how the monotonicity of cautiousness implies the monotonicity of risk aversion. Interestingly, we find that decreasing cautiousness implies standard risk aversion. We also reveal a close relationship between cautiousness and relative risk tolerance. These results help us better understand various conditions concerning risk aversion and cautiousness. They may also shed light on how investors' investment decisions in the equity and options markets are related.

The adoption of electronic banking technologies by US consumers

Is there an electronic banking (e‐banking) revolution in the USA? Millions of Americans are currently using a variety of e‐banking technologies and millions more are expected to come “online.” However, millions of others have not or will not. This paper explores factors that affect the of adoption or intention to adopt three e‐banking technologies and changes in these factors over time. Using a Federal Reserve Board commissioned data set, the paper finds that relative advantage, complexity/simplicity, compatibility, observability, risk tolerance, and product involvement are associated with adoption. Income, assets, education, gender and marital status, and age also affect adoption. Adoption changed over time, but the impacts of other factors on adoption have not changed. Implications for both the banking industry and public policy are discussed.

Capital flows and net international investment

This paper analyzes the effect of stochastic terms of trade and commodity preferences on international capital flows and the net asset position of a country. Investors hold foreign assets if excess return from foreign bonds is positive. The demand for foreign assets to hedge against the unanticipated changes in terms of trade is an increasing function of expenditure on imports, if the product of relative risk tolerance and consumption expenditure elasticity of imports is less than the price elasticity of imports. The paper also shows that the net international investment in a country is a decreasing function of the excess return from foreign industry and the rate of change of the terms of trade but an increasing function of their variances, cross-price elasticity of domestic good, price elasticity and consumption expenditure elasticity of imports. An increase in the expenditure on imports may result in a decrease or increase in the net international investment depending on whether the product of relative risk tolerance and consumption expenditure elasticity of imports is less or greater than the price elasticity of imports. JEL: F36, G15.

The demand for foreign bonds

This paper derives the demand for foreign bonds in a simple general equilibrium model in which the exchange rate is perfectly correlated with the terms of trade. A necessary condition for the demand for foreign bonds to be an increasing function of the domestic currency value of imports is derived. Earlier work shows that the demand for foreign bonds is an increasing function of imports if the domestic investor's degree of relative risk tolerance is smaller than one. The present paper shows that the demand for foreign bonds can be a decreasing function of imports if the degree of relative risk tolerance is smaller than one when the consumption expenditure elasticity of imports exceeds one.