Estimating Risk Aversion Research Articles

Properties of risk aversion estimated from portfolio weights

While risk tolerance is often elicited using questionnaire-based instruments, in this paper, we evaluate the merits of an inversion-based technique, wherein risk aversion parameters are inferred from an individual’s portfolio holdings and a sequence of realized returns. We obtain expressions for the finite sample and asymptotic variance of the estimated risk aversion parameter under the inversion approach with a single risky asset, demonstrating that confidence intervals for parameter estimates are relatively wide. Extending the analysis, we show that inferring risk aversion from multiple risky assets does not typically serve to reduce the estimated parameter variance, but rather propagates estimation error.

Time-varying risk aversion and international stock returns

We estimate aggregate, time-varying risk aversion inferred from options, stock returns and macroeconomic data for a panel of 8 countries. We document that, for most countries, the estimated risk aversion measure is counter-cyclical. Moreover, we show that estimated risk aversion forecasts monthly stock index returns up to 12 months ahead. This effect is statistically significant in panel regressions, and it survives the inclusion of additional control variables, such as an estimated of the variance risk premium, an investors’ sentiment index, and a measure of economic uncertainty. Finally, we show that risk aversion provides useful information to an investor who aims at timing the market. An investment strategy that uses the estimated time-varying risk aversion measure to solve a mean–variance asset allocation problem, delivers significantly positive returns.

Time varying risk aversion and its connectedness: evidence from cryptocurrencies

Changing patterns of risk aversion may follow a non-linear counter-cyclical process. However, the evidence so far has not considered developing cryptocurrency markets. Given some unique features of cryptocurrencies, it is interesting to distinguish how these assets differ from traditional products. This paper investigates the time effects of periodicity on risk aversion for a selection of major cryptocurrencies compared to major financial assets. Significant periodic time-varying patterns are identified when analysing risk aversion. Further, bilateral and bidirectional Granger causalities are identified within cryptocurrencies, as well as between cryptocurrencies and traditional financial assets. Bitcoin is identified as a leading information transmitter of the spillover of risk aversion upon other cryptocurrencies, while estimated risk aversion of traditional financial markets plays a dominant role in the spillover processes upon the cryptocurrency cluster. The latter finding presents further evidence of developing cryptocurrency market maturity. The COVID-19 pandemic is found to have significantly influenced the connectedness of risk aversion among cryptocurrency and traditional financial markets.

Does the Long-Run Risk Explain the Cross-Section of Corporate Bond Returns?

We test whether long-run consumption risk can explain the cross-section of corporate bond risk premiums. We find that a one-factor model with long-run consumption growth explains the risk premiums on bond portfolios sorted on credit spreads, maturity, credit rating, downside risk, idiosyncratic volatility, and the betas with respect to shocks to financial intermediary's capital of He, Kelly, and Manela (2017). Furthermore, the estimated risk aversion coefficient declines as we increase the horizon to measure consumption growth, and a model with relatively low values of risk-aversion can match the observed risk premiums if we use 24-month growth rate as a risk factor.

Export under Background Risk: A Mean-Variance Decision Analysis for Indian Manufacturing Firms

How would accessing foreign markets affect risk exposure of manufacturing firms? Producing for and selling specific goods to foreign markets (exports) require specialized attention. For example, manufacturing firms are exposed to idiosyncratic shocks in their global supply chains, such as exchange rate volatility, asset market frictions, transaction risks, credit tightening, and so on. Given this background, we probed production and exporting decision for a manufacturing firm (that serves both domestic and foreign markets) in the context of firm-specific and industry-specific shocks on trade, with a view of searching for optimality. These shocks are aggregated to form a type of risk that literature labels as ‘non-hedgeable’ background risk. We also propose that background risk is dependent on direct (endogenous) risk pertaining to fluctuations in the spot/nominal exchange rates. To test for potential optimal conditions, we employ a mean-variance decision-theoretic modelling approach. This approach was selected in order to trace out the comparative static responses of optimal export sales following the changes in the distribution of background risk or due to the dependence structure between the two sources of risks (i.e., background risk and exchange rate risk). Our contribution includes isolating all comparative static effects of these changes in the context of optimal production and exporting decisions. In particular, we consider the relative trade-offs between risks and returns, and offer intuitive economic theory based interpretations of our results. In order to demonstrate robustness of the key results in our model empirically, we utilised an unbalanced panel data of 1,273 exporting Indian manufacturing firms over the time period of 1996-2017 to perform a structural estimation of our theoretical model. This model is derived using a flexible utility function that incorporates all possible options of risk preferences. Through this approach, we are able to estimate risk aversion elasticities specific to our context.

Asset pricing with beliefs-dependent risk aversion and learning

This paper studies equilibrium in a pure exchange economy with unobservable Markov switching growth regimes and beliefs-dependent risk aversion (BDRA). Risk aversion is stochastic and depends nonlinearly on consumption and beliefs. Equilibrium is obtained in closed form. The market price of risk, the interest rate, and the stock return volatility acquire new components tied to fluctuations in beliefs. A three-regime specification is estimated using the generalized method of moments (GMM). Model moments match their empirical counterparts for a variety of unconditional moments, including the equity premium, stock returns volatility, and the correlations between stock returns and consumption and dividends. Dynamic features of the data, such as the countercyclical behaviors of the equity premium and volatility, are also captured. Model volatility provides a good fit for realized volatility. A new factor, the information risk premium, is found to be a strong predictor of future excess returns. These results are obtained with an estimated risk aversion fluctuating between 1.44 and 1.93.

Household Production and the Elasticity of Marginal Utility of Consumption

Abstract The popular approach to estimating the elasticity of marginal utility of consumption (EMUC) (Chetty 2006, “A New Method of Estimating Risk Aversion.” American Economic Review 96 (5):1821–1834. doi:10.1257/aer.96.5.1821. http://www.aeaweb.org/articles.php?doi=10.1257/aer.96.5.1821) is here extended by including household production. It is shown that this generalization of the model is important as omission of household production may lead to bias, as demonstrated in a numerical sensitivity analysis. An extended model with household production is used to derive new EMUC formulas. Empirical estimates based on current evidence of the included parameters suggest a lower bound for EMUC of about 0.9.

A flexible approach to estimate the equity premium

ABSTRACTIn this article, we estimate the risk aversion for households accounting for their lifetime consumption risk. Households take into account the overall lifetime uninsured consumption risk when optimizing their resources, which based on micro data varies across households. Thus, representing households’ consumption by merging cross-sectional micro data into the single Euler equation (the common approach for estimating risk aversion based on consumption-based asset pricing theory) may be too rough an approximation, leading to biased results with respect to risk aversion. Our results suggest that consumption-based asset pricing models that were rejected in several studies do in fact fit the data when we account for households’ lifetime consumption risk. This finding also has implications for long-run aggregate consumption-based asset pricing models.

The Role of U.S. Market on International Risk-Return Tradeoff Relations

We study the intertemporal risk-return tradeoff relations based on returns from 18 international markets. We find striking new empirical evidence that the inclusion of U.S. market variables significantly changes the estimated risk-return tradeoff relationship in international markets. The estimated risk aversion coefficient switches from mostly negative to mostly positive after the inclusion of these U.S. market variables even when the conditional variance model specification remains the same. Our results are consistent with the state variable interpretation of the U.S. market variables in the sense of Merton's Intertemporal CAPM.

Risk Aversion and Wealth: Evidence from Person-to-Person Lending Portfolios

We estimate risk aversion from investors’ financial decisions in a person-to-person lending platform. We develop a method that obtains a risk-aversion parameter from each portfolio choice. Since the same individuals invest repeatedly, we construct a panel data set that we use to disentangle heterogeneity in attitudes toward risk across investors, from the elasticity of risk aversion to changes in wealth. We find that wealthier investors are more risk averse in the cross section and that investors become more risk averse after a negative housing wealth shock. Thus, investors exhibit preferences consistent with decreasing relative risk aversion and habit formation. Data, as supplemental material, are available at http://dx.doi.org/10.1287/mnsc.2015.2317 . This paper was accepted by Amit Seru, finance.

Uniform Confidence Bands for Pricing Kernels

Pricing kernels implicit in option prices play a key role in assessing the risk aversion over equity returns. We deal with non-parametric estimation of the pricing kernel (Empirical Pricing Kernel) given by the ratio of the risk-neutral density estimator and the subjective density estimator. The former density can be represented as the second derivative w.r.t. the European call option price function, which we estimate by non-parametric regression. The subjective density is estimated non-parametrically too. In this framework, we develop the asymptotic distribution theory of the EPK in the L1 sense. Particularly, to evaluate the overall variation of the pricing kernel, we develop a uniform confidence band of the EPK. Furthermore, as an alternative to the asymptotic approach, we propose a bootstrap confidence band. The developed theory is helpful for testing parametric specifications of pricing kernels and has a direct extension to estimating risk aversion patterns. The established results are assessed and compared in a Monte-Carlo study. As a real application, we test risk aversion over time induced by the EPK.

"Garbage as an Alternative Measure of Consumption: Evidence from Korea

We find that using garbage as an alternative measure of consumption allows the standard consumption-based asset pricing model to match the observed equity premium with a more reasonable relative risk aversion coefficient than using standard consumption expenditure in Korea. Structural GMM estimation of the risk aversion parameter shows that when garbage is used, the risk aversion estimate ranges from 4.44 to 6.92, and the implied risk-free rate ranges from 3% to 8%. In contrast, when standard consumption expenditure is used, the estimated risk aversion ranges from 12.89 to 18.34, and the implied risk-free rate ranges from 61% to 82%. Overall, our findings suggest that Savov’s (2011) novel idea of using garbage as an indirect measure of consumption is broadly supported by data in Korea.

Consumption Based Asset Pricing Adjusting for Measurement Error in Consumption

This paper presents a modification to the testable Euler equation in the form of an adjustment term due to additive measurement error in consumption data. The error in consumption data has the potential to magnify the equity premium puzzle in a CRRA framework and including the adjustment term leads to a reduction in the estimated risk aversion coefficient. The paper also empirically estimates a ballpark figure for the variance of measurement error and demonstrates a significant resolution of the puzzle by including measurement error in the model.

The long-run impact of a traumatic experience on risk aversion

We examine the long-run impact of exposure to a traumatic event on risk attitudes. We estimate risk aversion of those who experienced the Korean War at different ages to identify a sensitive period for risk attitude formation. This major war broke out suddenly, and the impact of the war on civilians was substantial but limited to a brief period of time. The results reveal that individuals who were 4–8 years old during the peak of the war are more risk averse about five decades later. Furthermore, within the affected cohorts, those who resided in more severely damaged provinces are more risk averse.

What drives stochastic risk aversion?

This paper examines determinants of stochastic relative risk aversion in conditional asset pricing models. Novel time-series specification tests are proposed as direct extensions of Guo, Wang, and Yang (2013, JMCB)'s model using nonlinear state-space models with heteroskedasticity. I then establish the following facts. First, the surplus consumption ratio implied by the external habit formation model is the most important determinant of relative risk aversion. Second, the CAY of Lettau and Ludvigson (2001a) without a look-ahead bias and the short term interest rate explain part of relative risk aversion. Third, the estimated risk aversion from 1957Q2 to 2010Q3 is countercyclical and positive. Finally, the selected models explain part of the momentum and the financial distress premiums.

Uniform Confidence Bands for Pricing Kernels

Pricing kernels implicit in option prices play a key role in assessing the risk aversion over equity returns. We deal with nonparametric estimation of the pricing kernel (Empirical Pricing Kernel) given by the ratio of the risk-neutral density estimator and the subjective density estimator. The former density can be represented as the second derivative w.r.t. the European call option price function, which we estimate by nonparametric regression. The subjective density is estimated nonparametrically too. In this framework, we develop the asymptotic distribution theory of the EPK in the L1 sense. Particularly, to evaluate the overall variation of the pricing kernel, we develop a uniform confidence band of the EPK. Furthermore, as an alternative to the asymptotic approach, we propose a bootstrap confidence band. The developed theory is helpful for testing parametric specifications of pricing kernels and has a direct extension to estimating risk aversion patterns. The established results are assessed and compared in a Monte-Carlo study. As a real application, we test risk aversion over time induced by the EPK.

CAPM Intertemporal: um teste empírico utilizando dados brasileiros

O artigo examina a validade empírica do Inter-temporal Capital Asset Pricing Model (ICAPM) com o uso de dados do mercado brasileiro. É empregada a metodologia de Bali e Engle (2010), com a estimação de covariâncias condicionais entre retornos de carteiras de ações e fatores de precificação. As covariâncias são a seguir utilizadas como variáveis explicativas na equação de precificação. Os resultados confirmam o modelo para o período de 1988 a 2012. O coeficiente de aversão a risco é positivo e significante, e os fatores relevantes são taxas de juros e de inflação, além do preço do ouro. O oposto ocorre com a taxa de câmbio. A quebra do período de estudo em subperíodos indica que eventos importantes, como mudanças de regime econômico e a crise de 2008 têm o poder de modificar as associações encontradas e enfraquecer a validade do modelo.

Risk Attitude and Housing Wealth Effect

This paper examines whether the housing wealth effect—the consumption change induced by house price appreciation is dependent upon households’ attitudes toward risk. A simple theoretical model is introduced to highlight a negative relationship between the wealth effect and risk aversion. The paper empirically tests for this negative relationship, using data from the U.S. Consumer Expenditure Survey. The investigation involves two steps. In the first step, we make use of households’ demographics and their risky and liquid asset holdings to estimate risk aversion. The Heckman correction model is applied to address the issue of limited stock market participation. For the second step, we construct pseudo panel data through grouping households by their birth years and their predicted values of risk aversion, and then, we estimate the responses of households’ consumption changes to house price fluctuations by risk-attitude group. Consistent with the prediction of the theoretical model, the estimation results suggest a significant negative relationship between the housing wealth effect and households’ risk attitudes. Households, who are less risk averse, experience greater consumption changes in response to house price appreciation.

A Theoretical and Experimental Appraisal of Five Risk Elicitation Methods

We perform a comparative analysis of five incentivized tasks used to elicit risk preferences. Theoretically, we compare the elicitation methods in terms of completeness of the range of the estimates as well as their precision, the likelihood of triggering loss aversion, and problems arising when multiple choices are required. Using original data from a homogeneous population, we experimentally investigate the distribution of estimated risk preferences, whether they differ by gender, and the complexity of the tasks. We do so using both non-parametric tests and a structural model estimated with maximum likelihood. We find that the estimated risk aversion parameters vary greatly across tasks and that gender differences appear only when the task is more likely to trigger loss aversion.

A Theoretical and Experimental Appraisal of Five Risk Elicitation Methods

We perform a comparative analysis of five incentivized tasks used to elicit risk preferences. Theoretically, we compare the elicitation methods in terms of completeness of the range of the estimates as well as their precision, the likelihood of triggering loss aversion, and problems arising when multiple choices are required. Using original data from a homogeneous population, we experimentally investigate the distribution of estimated risk preferences, whether they differ by gender, and the complexity of the tasks. We do so using both non-parametric tests and a structural model estimated with maximum likelihood. We find that the estimated risk aversion parameters vary greatly across tasks and that gender differences appear only when the task is more likely to trigger loss aversion.