scholarly journals Optimal Dynamic Portfolio Risk with First-Order and Second-Order Predictability

2004 ◽  
Vol 4 (1) ◽  
Author(s):  
Christian Gollier
Keyword(s):  
Relative Risk ◽  
Risk Aversion ◽  
Interest Rates ◽  
Stock Returns ◽  
Bayesian Learning ◽  
Absolute Risk ◽  
Second Order ◽  
Relative Risk Aversion ◽  
Portfolio Risk ◽  
First Order

We consider a two-period portfolio problem with predictable assets returns. First-order (second-order) predictability means that an increase in the first period returns yields a first-order (second-order) stochastically dominated shift in the distribution of the second period state prices. Mean reversion in stock returns, Bayesian learning, stochastic volatility and stochastic interest rates (bond portfolios) belong to one of these two types of predictability. We first show that a first-order stochastically dominated shift in the state price density reduces the marginal value of wealth if and only if relative risk aversion is uniformly larger than unity. This implies that first-order predictability generates a positive hedging demand for portfolio risk if this condition is met. A similar result is obtained with second-order predictability under the condition that absolute prudence be uniformly smaller than twice the absolute risk aversion. When relative risk aversion is constant, these two conditions are equivalent. We also examine the effect of exogenous predictability, i.e., when the information about the future opportunity set is conveyed by signals not contained in past asset prices.

scholarly journals The Investigation of a Wealth Distribution Model on Isolated Discrete Time Domains

2020 ◽  
Vol 2020 ◽  
pp. 1-21
Author(s):  
Chunhua Hu ◽  
Wenyi Huang ◽  
Tianhao Xie
Keyword(s):  
Relative Risk ◽  
Risk Aversion ◽  
Discrete Time ◽  
Rational Expectation ◽  
Absolute Risk ◽  
Wealth Distribution ◽  
Optimal Solution ◽  
Distribution Model ◽  
Relative Risk Aversion ◽  
Time Domains

A wealth distribution model on isolated discrete time domains, which allows the wealth to exchange at irregular time intervals, is used to describe the effect of agent’s trading behavior on wealth distribution. We assume that the agents have different degrees of risk aversion. The hyperbolic absolute risk aversion (HARA) utility function is employed to describe the degrees of risk aversion of agents, including decreasing relative risk aversion (DRRA), increasing relative risk aversion (IRRA), and constant relative risk aversion (CRRA). The effect of agent’s expectation on wealth distribution is taken into account in our wealth distribution model, in which the agents are allowed to adopt certain trading strategies to maximize their utility and improve their wealth status. The Euler equation and transversality condition for the model on isolated discrete time domains are given to prove the existence of the optimal solution of the model. The optimal solution of the wealth distribution model is obtained by using the method of solving the rational expectation model on isolated discrete time domains. A numerical example is given to highlight the advantages of the wealth distribution model.

Utility and Risk Aversion

2017 ◽  
Author(s):  
Kerry E. Back
Keyword(s):  
Relative Risk ◽  
Risk Aversion ◽  
Expected Utility ◽  
Absolute Risk ◽  
Risk Tolerance ◽  
Relative Risk Aversion ◽  
Absolute Risk Aversion ◽  
Certainty Equivalents ◽  
Conditional Expectations ◽  
Constant Absolute Risk Aversion

Expected utility is introduced. Risk aversion and its equivalence with concavity of the utility function (Jensen’s inequality) are explained. The concepts of relative risk aversion, absolute risk aversion, and risk tolerance are introduced. Certainty equivalents are defined. Expected utility is shown to imply second‐order risk aversion. Linear risk tolerance (hyperbolic absolute risk aversion), cautiousness parameters, constant relative risk aversion, and constant absolute risk aversion are described. Decreasing absolute risk aversion is shown to imply a preference for positive skewness. Preferences for kurtosis are discussed. Conditional expectations are introduced, and the law of iterated expectations is explained. Risk averse investors are shown to dislike mean‐independent noise.

scholarly journals Risk, Delay, and Convex Self-Control Costs

2011 ◽  
Vol 3 (3) ◽  
pp. 34-68 ◽  
Author(s):  
Drew Fudenberg ◽  
David K Levine
Keyword(s):  
Relative Risk ◽  
Risk Aversion ◽  
Interest Rates ◽  
Time Horizon ◽  
Self Control ◽  
Relative Risk Aversion ◽  
Allais Paradox ◽  
Macroeconomic Theory ◽  
Wide Range ◽  
Short Run

We develop a dual-self model of self-control that is compatible with modern dynamic macroeconomic theory and evidence. We show that a convex cost of self-control explains a wide range of behavioral anomalies concerning risk, including the Allais paradox, and also explains the observed interaction between risk and delay. We calibrate the model to obtain a quantitative fit. We find that most of the data can be explained with subjective interest rates in the range of 1–7 percent, short-run relative risk aversion of about two, and a time horizon of one day for the short-run self. (JEL D11, D44, D81)

Relative Risk Aversion and Portfolio Choice

2005 ◽  
Author(s):  
Pablo Muñoz Ceballos ◽  
Esteban Flores Díaz
Keyword(s):  
Relative Risk ◽  
Risk Aversion ◽  
Portfolio Choice ◽  
Relative Risk Aversion

scholarly journals Relative risk aversion models: How plausible are their assumptions?

2021 ◽  
pp. 104346312199408
Author(s):  
Carlo Barone ◽  
Katherin Barg ◽  
Mathieu Ichou
Keyword(s):  
Relative Risk ◽  
Risk Aversion ◽  
Loss Aversion ◽  
Educational Inequality ◽  
Risky Choice ◽  
Relative Risk Aversion ◽  
Downward Mobility ◽  
Educational Decisions ◽  
Empirically Supported ◽  
Occupational Risks

This work examines the validity of the two main assumptions of relative risk-aversion models of educational inequality. We compare the Breen-Goldthorpe (BG) and the Breen-Yaish (BY) models in terms of their assumptions about status maintenance motives and beliefs about the occupational risks associated with educational decisions. Concerning the first assumption, our contribution is threefold. First, we criticise the assumption of the BG model that families aim only at avoiding downward mobility and are insensitive to the prospects of upward mobility. We argue that the loss-aversion assumption proposed by BY is a more realistic formulation of status-maintenance motives. Second, we propose and implement a novel empirical approach to assess the validity of the loss-aversion assumption. Third, we present empirical results based on a sample of families of lower secondary school leavers indicating that families are sensitive to the prospects of both upward and downward mobility, and that the loss-aversion hypothesis of BY is empirically supported. As regards the risky choice assumption, we argue that families may not believe that more ambitious educational options entail occupational risks relative to less ambitious ones. We present empirical evidence indicating that, in France, the academic path is not perceived as a risky option. We conclude that, if the restrictive assumptions of the BG model are removed, relative-risk aversion needs not drive educational inequalities.

scholarly journals The Burden of the Nondiversifiable Risk of Entrepreneurship

2010 ◽  
Vol 100 (3) ◽  
pp. 1163-1194 ◽  
Author(s):  
Robert E Hall ◽  
Susan E Woodward
Keyword(s):  
Relative Risk ◽  
Risk Aversion ◽  
Venture Capital ◽  
Dynamic Program ◽  
Certainty Equivalent ◽  
Important Class ◽  
Relative Risk Aversion ◽  
The Past ◽  
Equity Value ◽  
The Difference

Entrepreneurship is risky. We study the risk facing a well-documented and important class of entrepreneurs, those backed by venture capital. Using a dynamic program, we calculate the certainty-equivalent of the difference between the cash rewards that entrepreneurs actually received over the past 20 years and the cash that entrepreneurs would have received from a risk-free salaried job. The payoff to a venture-backed entrepreneur comprises a below-market salary and a share of the equity value of the company when it goes public or is acquired. We find that the typical venture-backed entrepreneur received an average of $5.8 million in exit cash. Almost three-quarters of entrepreneurs receive nothing at exit and a few receive over a billion dollars. Because of the extreme dispersion of payoffs, an entrepreneur with a coefficient of relative risk aversion of two places a certainty equivalent value only slightly greater than zero on the distribution of outcomes she faces at the time of her company's launch. (JEL G24, G32, L26, M13)

Relative Risk Aversion Revisited

1982 ◽  
Vol 64 (3) ◽  
pp. 481 ◽  
Author(s):  
Frederick W. Siegel ◽  
James P. Hoban
Keyword(s):  
Relative Risk ◽  
Risk Aversion ◽  
Relative Risk Aversion
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