What is the impact of wealth shocks on asset allocation?

I test the assumption of constant relative risk aversion using U.S. macroeconomic data and analyse the role of wealth shocks in generating transitory changes in asset portfolio composition. I show that the risky asset share exhibits cyclical behavior and it is significantly (and positively) affected by unexpected variation in wealth. Therefore, the empirical evidence suggests that risk aversion is counter-cyclical. I also find that the portfolio share of housing wealth falls when the agent is faced with a positive wealth shock, i.e. housing is a hedge against unfavorable wealth fluctuations. Finally, considering a variety of wealth definitions, the results show that: (i) wealth effects are stronger for direct holdings of risky assets than for indirect holdings, which highlights that investors do not typically trade some assets such as pension or mutual funds; (ii) although significant, wealth effects on asset allocation are mainly temporary as agents quickly rebalance the asset portfolio composition (i.e. there is weak evidence of inertia or slow adjustment in asset allocation); and (iii) changes in expected returns partially explain the variation in risky asset allocation.     

Liquidity Risk and the Dynamics of Arbitrage Capital

We develop a continuous‐time model of liquidity provision in which hedgers can trade multiple risky assets with arbitrageurs. Arbitrageurs have constant relative risk‐aversion (CRRA) utility, while hedgers' asset demand is independent of wealth. An increase in hedgers' risk aversion can make arbitrageurs endogenously more risk‐averse. Because arbitrageurs generate endogenous risk, an increase in their wealth or a reduction in their CRRA coefficient can raise risk premia despite Sharpe ratios declining. Arbitrageur wealth is a priced risk factor because assets held by arbitrageurs offer high expected returns but suffer the most when wealth drops. Aggregate illiquidity, which declines in wealth, captures that factor.     

Risk aversion under preference uncertainty

We show that if an agent is uncertain about the precise form of his utility function, his actual relative risk aversion may depend on wealth even if he knows his utility function lies in the class of constant relative risk aversion (CRRA) utility functions. We illustrate the consequences of this result for optimal asset allocation: poor agents that are uncertain about their risk aversion parameter invest less in risky assets than wealthy investors with identical risk aversion uncertainty.     

Algorithmic portfolio choice: lessons from panel survey data

Automated asset management offerings algorithmically assign risky portfolios to individual investors based on investor characteristics such as age, net income, or self-assessment of risk aversion. Using new German household panel data, we investigate the key household characteristics that drive private asset allocation decisions. This information allows us to assess which set of variables should be included in algorithmic portfolio advice. Using heavily cross-validated classification trees, we find that a combination of household balance sheet variables—describing the ability to take risks (e.g., net wealth)—and household personal characteristics—describing the willingness to take risks (e.g., risk aversion)—best explain the cross-sectional variation in household portfolio choice. Our empirical evidence is in line with models of portfolio choice under decreasing relative risk aversion and fixed investment costs. The results suggest the utility of a more holistic modeling of household characteristics. Including background risks in the form of household leverage not only makes investment sense, but is also the new regulatory reality under MIFID II rules. Robo-advisors are strongly advised to act accordingly.     

Asset pricing implications of benchmarking: a two-factor CAPM

The paper considers the equilibrium effects of an institutional investor whose performance is benchmarked to an index. In a partial equilibrium setting, the objective of the institutional investor is modelled as the maximization of expected utility (an increasing and concave function, in order to accommodate risk aversion) of final wealth minus a benchmark. In equilibrium this optimal strategy gives rise to the two-beta CAPM: together with the market beta a new risk-factor (termed active management risk) is brought into the analysis. This new beta is defined as the normalized (to the benchmark's variance) covariance between the asset excess return and the excess return of the market over the benchmark index. The empirical test supports the model's predictions. The cross-section return on the active management risk is positive and significant, especially after 1990, when institutional investors became the representative agent of the market.     

Whence GARCH? A Preference-Based Explanation for Conditional Volatility

We develop a preference-based equilibrium asset pricing modelthat explains low-frequency conditional volatility. Similarto Barberis, Huang, and Santos (2001), agents in our model careabout wealth changes, experience loss aversion, and keep a mentalscorecard that affects their level of risk aversion. A new featureof our model is that when perturbed by unexpected returns, investorsbecome temporarily more sensitive to news. Gradually investorsbecome accustomed to the new level of wealth, restoring priorlevels of risk aversion and news sensitivity. The state-dependentsensitivity to news creates the type of volatility clusteringfound in low-frequency stock returns. We find empirical supportfor our model's predictions that relate the scorecard to conditionalvolatility and skewness.     

Covariance complexity and rates of return on assets

This paper considers the estimation of the expected rate of return on a set of risky assets. The approach to estimation focuses on the covariance matrix for the returns. The structure in the covariance matrix determines shared information which is useful in estimating the mean return for each asset. An empirical Bayes estimator is developed using the covariance structure of the returns distribution. The estimator is an improvement on the maximum likelihood and Bayes–Stein estimators in terms of mean squared error. The effect of reduced estimation error on accumulated wealth is analyzed for the portfolio choice model with constant relative risk aversion utility.     

Mean-Variance Asset Liability Management with State-Dependent Risk Aversion

This article investigates the asset liability management problem with state-dependent risk aversion under the mean-variance criterion. The investor allocates the wealth among multiple assets including a risk-free asset and multiple risky assets governed by a system of geometric Brownian motion stochastic differential equations, and the investor faces the risk of paying uncontrollable random liabilities. The state-dependent risk aversion is taken into account in our model, linking the risk aversion to the current wealth held by the investor. An extended Hamilton-Jacobi-Bellman system is established for the optimization of asset liability management, and by solving the extended Hamilton-Jacobi-Bellman system, the analytical closed-form expressions for the time-inconsistent optimal investment strategies and the optimal value function are derived. Finally, numerical examples are presented to illustrate our results.     

Capital flows,investment, and exchange rates

This paper incorporates international capital flows into a two-country, monetary-general-equilibrium model of asset prices with investment and production. We calculate theoretical covariances between investment, the current account, the exchange rate, and the terms of trade. These covariances depend upon the coefficient of relative risk aversion, the magnitude and sign of a country's net international indebtedness, other properties of tastes and technologies, and the stochastic processes on disturbances to productivity and monetary growth rates. International capital flows arise from changes in world wealth and its relative composition in foreign and domestic assets.     

Decision making with Expected Shortfall and spectral risk measures: The problem of comparative risk aversion

We analyze spectral risk measures with respect to comparative risk aversion following Arrow (1965) and Pratt (1964) for deterministic wealth, and Ross (1981) for stochastic wealth. We argue that the Arrow–Pratt-concept per se well matches with economic intuition in standard financial decision problems, such as willingness to pay for insurance and simple portfolio problems. Different from the literature, we find that the widely-applied spectral Arrow–Pratt-measure is not a consistent measure of Arrow–Pratt-risk aversion. Instead, the difference between the antiderivatives of the corresponding risk spectra is valid. Within the framework of Ross, we show that the popular subclasses of Expected Shortfall, and exponential and power spectral risk measures cannot be completely ordered with respect to Ross-risk aversion. Thus, for all these subclasses, the concept of Ross-risk aversion is not generally compatible with Arrow–Pratt-risk aversion, but induces counter-intuitive comparative statics of its own. Compatibility can be achieved if asset returns are jointly normally distributed. The general lesson is that these restrictions have to be considered before spectral risk measures can be applied for the purpose of optimal decision making and regulatory issues.     

Risk aversion measures: comparing attitudes and asset allocation

Households' reported willingness to take financial risk is compared to the riskiness of their portfolios, measured as risky assets to wealth. Overall, their portfolio allocations are reliable indicators of attitudes toward risk, demonstrating an understanding of their relative level of risk taking. Multivariate regression analysis using multiply imputed data from the 1989 Survey of Consumer Finances indicates that households generally exhibit decreasing relative risk aversion. Further, investment in risky assets is significantly related to socioeconomic factors, attitude toward risk taking, desire to leave an estate and expectations about the adequacy of Social Security and pension income.     

HUMAN CAPITAL AND LIFE-CYCLE EFFECTS ON RISK AVERSION

This paper provides additional evidence on life-cycle patterns of relative risk aversion, using spline functions generated on Consumer Expenditure Survey data. Human capital is hypothesized to affect relative risk aversion; age has been used in previous work as a proxy for human capital. The objective of this study is to determine whether there is a life-cycle pattern that is independent of the effect of human capital. The results suggest an affirmative answer. Moreover, this independent life-cycle pattern is the opposite of that estimated in a previous study that used age as a proxy.     

Relative risk aversion once more: An analysis of Japanese households' financial asset holding pattern

It is widely accepted that as the total assets increse, households tend to diversify their portfolios. In other words, absolute risk aversion is decreasing. On the other hand, the proportion of risky assets may increase or decrease depending on whether relative risk aversion (RRA) is decreasing or increasing, and its direction is still left open as an empirical question. This study examines the constancy of RRA from Japanese individual households' financial asset holding data collected in 1984. Constant RRA implies that the proportion of risky assets in one's portfolio is constant regardless of the amount of total assets. A casual observation of household portfolio holding pattern suggests that this implication is clearly violated by the data, because there are substantial proportion of households which do not hold any risky assets. Zero-holding, however, may be interpreted as a result of fixed transaction cost incurred by individual investors when they hold risky assets. Then, we pose a question, ‘Do investors hold constant proportion of risky assets, when they decide to hold them?’ In order to explain a substantial number of zero risky asset holders in the sample, we propose a portfolio selection model with a transaction cost, and estimate the model using a variant of Heckman's two-step method. In estimation we control for individual investors' socioeconomic characteristics, as well as income and total assets. The construction of the model imposes nonlinear restrictions on the two estimators, from which we can test the specification of the model. The estimation results suggest that there is a statistically significant decreasing tendency linked to total assets but that its rate of change tapers off as total assets increase. Our results are consistent with the previous studies which tended to support constant RRA for the higher asset holders, and complement previous studies in explaining lower asset holders' investment behavior.     

Optimal portfolios when volatility can jump

We consider an asset allocation problem in a continuous-time model with stochastic volatility and jumps in both the asset price and its volatility. First, we derive the optimal portfolio for an investor with constant relative risk aversion. The demand for jump risk includes a hedging component, which is not present in models without volatility jumps. We further show that the introduction of derivative contracts can have substantial economic value. We also analyze the distribution of terminal wealth for an investor who uses the wrong model, either by ignoring volatility jumps or by falsely including such jumps, or who is subject to estimation risk. Whenever a model different from the true one is used, the terminal wealth distribution exhibits fatter tails and (in some cases) significant default risk.     

Optimal excess-of-loss reinsurance contract with ambiguity aversion in the principal-agent model

ABSTRACT

We discuss an optimal excess-of-loss reinsurance contract in a continuous-time principal-agent framework where the surplus of the insurer (agent/he) is described by a classical Cramér-Lundberg (C-L) model. In addition to reinsurance, the insurer and the reinsurer (principal/she) are both allowed to invest their surpluses into a financial market containing one risk-free asset (e.g. a short-rate account) and one risky asset (e.g. a market index). In this paper, the insurer and the reinsurer are ambiguity averse and have specific modeling risk aversion preferences for the insurance claims (this relates to the jump term in the stochastic models) and the financial market's risk (this encompasses the models' diffusion term). The reinsurer designs a reinsurance contract that maximizes the exponential utility of her terminal wealth under a worst-case scenario which depends on the retention level of the insurer. By employing the dynamic programming approach, we derive the optimal robust reinsurance contract, and the value functions for the reinsurer and the insurer under this contract. In order to provide a more explicit reinsurance contract and to facilitate our quantitative analysis, we discuss the case when the claims follow an exponential distribution; it is then possible to show explicitly the impact of ambiguity aversion on the optimal reinsurance.     

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.     

Generalized Disappointment Aversion and Asset Prices

We characterize generalized disappointment aversion (GDA) risk preferences that can overweight lower‐tail outcomes relative to expected utility. We show in an endowment economy that recursive utility with GDA risk preferences generates effective risk aversion that is countercyclical. This feature comes from endogenous variation in the probability of disappointment in the representative agent's intertemporal consumption‐saving problem that underlies the asset pricing model. The variation in effective risk aversion produces a large equity premium and a risk‐free rate that is procyclical and has low volatility in an economy with a simple autoregressive endowment‐growth process.     

MEASURING RISK AVERSION: ALLOCATION,LEVERAGE, AND ACCUMULATION

The risk-asset ratio that measures Arrow-Pratt relative risk aversion reflects a multidimensional risk behavior. The risk-asset ratio is decomposed into the product of ratios that measure portfolio allocation between riskless and risk assets, use of financial leverage, and accumulation of wealth in marketable form. The three dimensions are less sensitive to the definition of wealth than is the composite risk-asset ratio. Constant relative risk aversion can be characterized by offsetting changes in the three dimensions as wealth changes.     

Dynamic portfolio choice without cash

We consider the dynamic mean–variance portfolio choice without cash under a game theoretic framework. The mean–variance criterion is investigated in the situation where an investor allocates the wealth among risky assets while keeping no cash in a bank account. The problem is solved explicitly up to solutions of ordinary differential equations by applying the extended Hamilton–Jacobi–Bellman equation system. Given a constant risk aversion coefficient, the optimal allocation without a risk-free asset depends linearly on the current wealth, while that with a risk-free asset turns out to be independent of the current wealth. We also study the minimum-variance criterion, which can be viewed as an extension of the mean–variance model when the risk aversion coefficient tends to infinity. Calibration exercises demonstrate that for large investments, the mean–variance model without cash yields the highest certainty equivalent return for both short-term and long-term investments. Furthermore, the mean–variance portfolio choices with and without cash yield almost the same Sharpe ratio for an investment with large initial wealth.     

Derivative Pricing with Liquidity Risk: Theory and Evidence from the Credit Default Swap Market

We derive an equilibrium asset pricing model incorporating liquidity risk, derivatives, and short‐selling due to hedging of nontraded risk. We show that illiquid assets can have lower expected returns if the short‐sellers have more wealth, lower risk aversion, or shorter horizon. The pricing of liquidity risk is different for derivatives than for positive‐net‐supply assets, and depends on investors' net nontraded risk exposure. We estimate this model for the credit default swap market. We find strong evidence for an expected liquidity premium earned by the credit protection seller. The effect of liquidity risk is significant but economically small.