Understanding saving and portfolio choices with predictable changes in assets returns

We consider an expected-utility-maximizing consumer living two periods who can invest in two assets, one of which is risk free. We do not restrict relative risk aversion to be constant. We first examine the effect that a change in the opportunity set in the second period has on the optimal saving in the first period. We show that an increase in the future risk free rate (keeping the equity premium unchanged) reduces savings if relative risk aversion is uniformly larger than unity. An increase in the equity premium or a reduction in the volatility of the risky asset raises savings if the index of cautiousness, i.e., the derivative of absolute risk tolerance, is smaller than unity. In a second stage, we use these results to determine the sign of the hedging demand for the risky asset for the following three types of predictability: predictable changes in the interest rate, mean-reversion in stock returns, and predictable changes in volatility. Depending upon the type of predictability under scrutiny, what matters to sign the hedging demand is whether relative risk aversion or cautiousness is smaller or larger than unity.     

Is insurance normal or inferior? -A regret theoretical approach-

This study considers how changes in wealth affect insurance demand when individuals suffer disutility from regret. Anticipated regret stems from a comparison between the ex-post maximum and actual wealth. We consider a situation wherein individuals maximize their expected utility incorporating anticipated regret. The wealth effect on insurance demand can be classified into the risk and the regret effects. These effects are determined by the properties of the utility function and the regret function. We show that insurance can be normal when individuals place weight on anticipated regret, even though the utility function exhibit decreasing absolute risk aversion. This result indicates that regret theory is a possible explanation to the wealth effect puzzle, in which insurance is normal from empirical observation, but it should be inferior by theoretical prediction under expected utility theory.     

Prevention incentives in long‐term insurance contracts

Long‐term insurance contracts are widespread, particularly in public health and the labor market. Such contracts typically involve monthly or annual premia which are related to the insured's risk profile. A given profile may change, based on observed outcomes which depend on the insured's prevention efforts. The aim of this paper is to analyze the latter relationship. In a two‐period optimal insurance contract in which the insured's risk profile is partly governed by her effort on prevention, we find that both the insured's risk aversion and prudence play a crucial role. If absolute prudence is greater than twice absolute risk aversion, moral hazard justifies setting a higher premium in the first period but also greater premium discrimination in the second period. This result provides insights on the trade‐offs between long‐term insurance and the incentives arising from risk classification, as well as between inter‐ and intragenerational insurance.     

Optimal Two‐Part Pricing under Demand Uncertainty

This paper examines the pricing behavior of a risk‐averse monopolistic firm under demand uncertainty. The firm produces a single good at a constant marginal cost. To facilitate sales, the firm uses a two‐part pricing contract that includes a membership fee and a selling price per unit. The good is sold to a continuum of heterogeneous consumers who are subject to a common demand shock. We show that the global and marginal effects of risk aversion are to push the unit price closer to the constant marginal cost and to shrink the market coverage so as to limit the firm’s risk exposure to the demand uncertainty. The more risk‐averse firm as such charges a higher membership fee to consumers. We further show that an increase in the fixed cost of production induces the firm to lower (raise) the unit price, to raise (lower) the membership fee, and to shrink (enlarge) the market coverage under decreasing (increasing) absolute risk aversion. The firm’s optimal two‐part pricing contract, however, is unaffected by changes in the fixed cost under constant absolute risk aversion. Finally, we show that a mean‐preserving‐spread increase in the demand uncertainty induces the firm to lower the unit price, to raise the membership fee, and to shrink the market coverage under either decreasing or constant absolute risk aversion. The firm’s risk preferences as such play a pivotal role in determining the optimal two‐part pricing under demand uncertainty. Copyright © 2013 John Wiley & Sons, Ltd.     

Uncertainty and risk premium puzzle

This paper provides a theory and evidence that the risk premium puzzle may be viewed mainly as a phenomenon pertaining to the unstable foreign exchange market. In an unstable market, errors uncompensated by an initial risk premium accrue due to consumer expectation revision about the ex ante uncertainty of the exchange rate. These revision errors are different from the forecasting errors, depending on the frequency of the consumer expectation revision and the degree of risk aversion. A simulation was discussed on how the risk premium actually deviates from an initial premium in the unstable market. Using the monthly data of the U.K., Japan, Australia, Korea, Malaysia, and Thailand from January 1994 to December 2008, it is shown that revision errors for risk premium were statistically significant and were non-trivial in magnitude and that the degree of absolute risk aversion went up during the Asian currency crisis as well as the recent financial crisis periods.     

Risk aversion and business cycles: An empirical analysis

Unlike investors, who tend to maintain highly-diversified portfolios, private entrepreneurs usually lack access to complete risk-pooling for idiosyncratic risks, thus more directly internalize the cost of volatility. Risk aversion, however, modifies the optimal contract between entrepreneurs and lenders by incorporating the risk premium that entrepreneurs demand for the uninsurable risk: the private equity premium. Consequently, real shocks tend to be amplified as changes in entrepreneurs’ net worth affect the private equity premium and so the rental rate of capital, investment and output. This theoretical framework suggests that economies where the private entrepreneurial sector is a relatively larger, and therefore more vulnerable to uninsurable risk, all else equal, should present higher volatility. I test this prediction by (1) conducting a simple reduced-form analysis that shows that output volatility is negatively associated with the relative importance of the corporate vs. the privately-held sector; and (2) estimating the model's structural parameters. Intuitively, countries where private entrepreneurs are predominant and so risk aversion is likely to impose stronger impacts, positive risk aversion coefficients should be found. Results suggest that risk aversion is empirically more relevant for economies like Argentina, Brazil, Chile, Korea, Mexico and Thailand than for Canada, France, Germany, the U.K. and the U.S.     

FLEXIBLE RETIREMENT

Flexible retirement – that is, the opportunity to choose one's own personal retirement age – is a hedge against pension risk and provides insurance to workers facing health or productivity shocks. Flexible retirement and flexible pension schemes are in practice closely linked because of imperfect capital markets and institutional restrictions. I discuss three necessary conditions to provide insurance through flexible retirement. First, it should be possible to adjust the pension starting date at limited cost. This condition is gradually being fulfilled, as many countries are moving toward more actuarially neutral pension schemes. Second, individuals should be willing to adjust their labor supply in case of a wealth shock. This condition seems largely fulfilled, although the available empirical evidence suggests that the ‘standard retirement age’ is at least as important as the income effect. Third, the labor market should be able to deal with flexible individual retirement decisions. This condition is gaining importance, but has not yet received much attention in the literature. Institutions often hamper employment past the ‘standard retirement age’. Moreover, the hiring rates of older workers are low and their unemployment duration is high. Institutional reforms facilitating flexible retirement opportunities are desirable from an insurance perspective.     

Attitude towards risk,uncertainty, and fixed investment

We explore the relevance of the risk attitude of managers to the investment-uncertainty relation. Higher moments of the distribution of net profits are used to measure the risk premium of the firm, from which we derive a proxy for the risk aversion of managers. Using an unbalanced panel of Dutch listed firms, we find that in general a low degree of risk aversion coincides with a positive impact of demand uncertainty on investment. More specifically, we find that risk-averse firms respond to demand uncertainty by cutting investment, while the investment undertaken by risk-taking firms responds to demand uncertainty positively.     

Risk aversion in a model of endogenous growth

Despite the evidence on incomplete financial markets and substantial risk being borne by innovators, current models of growth through creative destruction predominantly model innovators’ as risk neutral. Risk aversion is expected to reduce the incentive to innovate and we might fear that without insurance innovation completely disappears in the long run. The present paper introduces risk averse agents into an occupational choice model of endogenous growth in which insurance against failure to innovate is not available. We derive a clear negative relationship between the level of risk aversion and long run growth. Surprisingly, we show that in an equilibrium there exists a cut-off value of risk aversion below which the growth rate of the mass of innovators tends to a strictly positive constant. In this case, innovation persists on the long run and consumption per capita grows at a strictly positive rate. On the other hand, for levels of risk aversion above the cut-off value, the economy eventually stagnates.     

A Housing Career Perspective on Risk

The main question analyzed in the article is how uncertainty in the asset price of owner-occupied housing capital affects user costs and consequently housing demand. The analysis is performed within the framework of a dynamic model of planned housing careers. Owner-occupied housing has a dual role as both an asset and a consumption good—a consumption good both now and in the future. By holding owner-occupied housing capital, the risk associated with future purchase of housing can be reduced. Taking account of this, it is shown that the risk premium in the user cost is negative for consumers on a sufficient increasing path of future housing consumption. Hence, the demand for owner-occupied housing of a risk-averse consumer can be increasing in asset price volatility. This result is contrary to the “conventional wisdom” in housing economics and can be identified only within an analytical framework that takes account of the dynamic aspects of housing market behavior.     

An intertemporal CAPM with higher-order moments

We propose an intertemporal asset pricing model that incorporates both preference for higher-order moments and stochastic investment opportunities and encompasses a wide range of existing models. We provide supporting evidence from the U.S. stock market and find that, not only is systematic skewness negatively priced, an extra return premium is also required for accepting high systematic risk associated with a rise in risk aversion. Our findings suggest that considering both skewness preference and intertemporal hedging demands improves the estimated risk-return trade-off, and that cross-sectional anomalies such as value, momentum, and failure probability puzzles can be partially explained by our model.     

THE RELATIONSHIP BETWEEN RELATIVE RISK AVERSION AND THE LEVEL OF EDUCATION: A SURVEY AND IMPLICATIONS FOR THE DEMAND FOR LIFE INSURANCE

The expected utility hypothesis has been widely used in the construction of economic models and numerous difficulties are encountered in attempting to take into account preferences toward risk in a real‐world setting. More recently, attention has focused on comparative studies in economics and business in an international framework and problems related to the hypothesis of relative risk aversion (RRA). One ambiguous hypothesis is the relationship between the level of RRA and the level of education, which has been found either positive or negative. From a causality point of view, it may be argued that investors with a high level of education are less risk averse, but it may also be argued that less risk‐averse individuals choose to pursue a higher level of education. The purpose of this paper is to survey the empirical literature on this subject. It provides evidence that risk aversion is negatively correlated with higher education and human development. The results have important implications for macroeconomic empirical studies and the demand for financial assets and more specifically on the demand for life insurance. Assuming the same degree of RRA for utility‐maximizing consumers should be limited to homogeneous samples.     

Substitution,risk aversion,taste shocks and equity premia

This paper gauges the relative contribution of risk aversion, inter-temporal substitution and taste shocks on postwar monthly US equity premia. The time-varying consumption, market, and taste risks involved in the Euler equations are recovered from a common factor GARCH process and the MLE are obtained by applying the Kalman filter. Empirically, (1) the market risk is the only source of risk that does not statistically affect the equity premia, and thus, the hypothesis that the coefficient of relative risk aversion corresponds to the reciprocal of the elasticity of inter-temporal substitution is not rejected; (2) the estimates are reasonable, so that the equity premium puzzle is circumvented; and (3) taste risks are quantitatively important in capturing excess returns movements. © 1998 John Wiley & Sons, Ltd.     

Risk premia in general equilibrium

This paper shows that non-linearities from a neoclassical production function alone can generate time-varying, asymmetric risk premia and predictability over the business cycle. These empirical key features become relevant when we allow for non-normalities in the form of rare disasters. We employ analytical solutions of dynamic stochastic general equilibrium models, including a novel solution with endogenous labor supply, to obtain closed-form expressions for the risk premium in production economies. In contrast to an endowment economy with constant investment opportunities, the curvature of the consumption function affects the risk premium in production economies through controlling the individual's effective risk aversion.     

Comparative Ross risk aversion in the presence of mean dependent risks

This paper studies comparative risk aversion between risk averse agents in the presence of a background risk. Our contribution differs from most of the literature in two respects. First, background risk does not need to be additive or multiplicative. Second, the two risks are not necessarily mean independent, and may be conditional expectation increasing or decreasing. We show that our order of cross Ross risk aversion is equivalent to the order of partial risk premium, while our index of decreasing cross Ross risk aversion is equivalent to decreasing partial risk premium. These results generalize the comparative risk aversion model developed by Ross for mean independent risks. Our theoretical results are related to utility functions having the n-switch independence property.     

What drives equity market non-participation?

This paper produces endogenous equity market non-participation in an economy with uninsurable labor income risk and heterogeneous skill levels. Prudence and impatience generate stationary household wealth levels that depend on income. Skill, and therefore labor income, heterogeneity leads to wealth heterogeneity, with high skill households accumulating high wealth and low skill households accumulating low wealth. A HARA class utility with subsistence consumption requirement generates decreasing RRA with respect to household wealth. Consequently, low skill households also have significantly higher local RRA. In addition low skill households have less human capital and therefore have lower diversification demand for stocks. Low wealth, high RRA and low diversification demand predicts that low skill households do not hold stocks in the face of a moderate ownership cost. In addition, the model predicts a humped lifecycle wealth accumulation pattern and a humped lifecycle stock allocation pattern. I also find that stockholders exhibit a greater aggregate willingness to supply risky capital during the expansion phase of a business cycle, despite the lower conditional equity premium.     

Risk sharing and counter-cyclical variation in market correlations

I present a consumption-based dynamic asset pricing model in which international market correlations vary counter-cyclically over time. The driving force in the model is the time-varying effective risk aversion induced by external habit formation. Market returns are driven by fundamental outputs and discount rates. When risk aversion is high, the effect of discount rates on market returns rises with the market price of risk. To the extent that countries share risk, the cross-country correlation of discount rates exceeds the cross-country correlation of fundamental outputs. In bad times, market correlations rise as returns are mostly driven by discount rates. Thus, consistent with the empirical evidence, periods of high risk aversion are associated with high market correlations and high market volatility. After calibration, my model is consistent with the observed variation in market correlations, as well as other features of asset prices including the equity premium and market volatility.     

中国无风险利率之谜与股权溢价

按照传统的消费资本资产定价理论,中国股市的高股权溢价只能由投资者的高相对风险厌恶系数来解释。但是这又会产生所谓的无风险利率之谜,因为投资者相对风险厌恶系数高时,其时间偏好率为负,明显不合情理。     

Inventory management under uncertainty: A financial theory for the transactions motive

This paper examines the effects of risk aversion and output market uncertainty on optimal inventory policy decisions for a transactions demand for inventory using the capital asset pricing theory. The paper shows that (1) the optimal order quantity of the risk-adjusted value-maximizing firm is smaller than that of the expected-profit-maximizing one and (2) the greater the firm's output market uncertainty, the smaller its optimal order quantity, where the output market uncertainty is defined as the relative volatility of the demand for the firm's output.     

The firm's insurance decision. Some questions raised by the capital asset pricing model

Using the capital asset pricing model it is shown that the firm will be indifferent towards insurance against specific risks. Insurance against systematic risks involves a transfer of these non-diversifiable risks from the firm to the insurance company, and will thus only be available at a price which reflects the ‘market price of risk’. Again the firm will be indifferent towards insurance. This then leads to the investigation of alternative motivations for a firm purchasing insurance — the costs of financial distress, human capital considerations, asymmetry of information and tax laws.