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Questions tagged [risk-aversion]

A property of preferences that causes an agent to prefer alternatives whose outcomes are relatively certain, even when the associated expected payoff is lower.

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Relative Risk Aversion and elasticities [on hold]

I am trying to prove the following theorem (Danthine and Donaldson- Intermediate Financial Theory 3rd edition, p. 121) but haven't been successful. Theorem 5.5 (Arrow, 1971): If, for all wealth ...
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116 views

Investor's optimization problem with risk aversion

Consider an investor with initial wealth $w$ and has to decide how to invest it. There is a riskless asset with rate of return $r$. The risky asset has return $x_i$ with probability $\pi_i$ for $i=1,2,...
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Relation between Epstein Zin and Power Utility

I found this graph in Campbell and Viceira 2001 at page 35-36 (https://faculty.fuqua.duke.edu/~charvey/Teaching/BA453_2006/Campbell_Viceira.pdf) which is used to explain the relation between Epstein-...
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1answer
39 views

Construct utility function for a risk-averse agent

I am trying to construct utility function for an agent who can be risk-seeking or risk-averse. We have an agent $i$ who has an ideal point $x$ in a policy space $X = [0,1]$. There is a policy (option) ...
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1answer
67 views

Relative risk aversion, a property of period or lifetime utility

This question is to be understood in the context of consumption based asset pricing. I'm wondering whether relative risk aversion is a property of the period utility function, which is simply a ...
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1answer
26 views

Value of Statistical Life and Risk

I have been reading a paper by Bove & Elia (2011), where they quote a definition of the value of statistical life from Bellavance, Dionne & Lebeau (2009). I have tried making my peace with the ...
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1answer
168 views

Why is the Marginal Utility of losses deminishing in Prospect Theory?

This is Kahneman's value-plot on prospect theory: QUESTION: Why is the Marginal Utility of losses deminishing? CONTEXT: I fully understand that the Marginal Utility of gains deminishes: 100 dollar ...
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CRRA Utility Function with more than three goods

I've been searching for how to set up a CRRA utility function when there are more than three goods but couldn't find some materials to reference. The typical example from textbooks or class materials ...
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2answers
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a risk lover agent preferences and the preference of risk natural agent may be the same

Consider two lotteries $N$ and $M$. Agent $i$ is risk-averse and prefers $N$. Agent $j$ is risk-neutral and prefers $M$. Would any risk-loving agent $k$ also prefer $M$? That is, would $j$ and $k$ ...
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1answer
58 views

Entrepreneurs and risk aversion

The are various opinion whether entrepreneurs are more or less risk-averse than the general population. The commonly held belief is that they are less so, but the contrary opinion exists as well. ...
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43 views

Analyse empirical data with Prospect Theory and Expected Utility Theory

I would like to compare the preference function of Prospect Theory against classical Expected Utility Theory, using empirical data representing gains and losses. What utility should I choose for ...
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1answer
35 views

Is there a natural intuitive interpretation of the **numerical value** of the coefficients of risk aversion?

We can write down the coefficient of absolute risk aversion $R_a$, or the coefficient of relative risk aversion $R_r$. Are there intuitive interpretations of the numerical values of these ...
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1answer
265 views

Proving that constant absolute risk aversion and relative risk aversion implies independence of initial wealth

I was able to prove that for a portfolio with one risk-free asset and one risky asset, if the Arrow-Pratt measure of absolute risk aversion is constant (i.e., constant absolute risk aversion, CARA), ...
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Terminology for separability in price and value

Take an agent with mean-variance utility over something that is uncertain: $$ U(x) = \mu_x^\theta - \sigma_x^\lambda $$ $A\in \{0,1\}$ happens if $U(x)>0$, and $x$ is a random variable $$ A = \...
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1answer
53 views

CARA Coefficient Calculation

Consider the following scenario: A consumer with CARA (constant absolute risk aversion) claims that she is indifferent between "getting $2400 for sure" and "getting $5000 or $0, each with 50% ...
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1answer
2k views

von-Neumann-Morgenstern v. Bernoulli Utility Function

A great deal of time is spent distinguishing the big $U$ (von-Neumann-Morgenstern)v. small $u$ (Bernoulli Utility Function). The v.NM function maps from the space of lotteries to real number as it ...
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How a utility function which is both DARA and CRRA can be explained?

I'm studying risk aversion and I cannot make a intuitive explain about the utility function which is DARA and CRRA. for instance, let's say, $\ln W$, where $W$ stands for one's wealth. by the ...
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1answer
61 views

Testing if one regressor is a proxy for another

I'm reading Guiso, Sapienza and Zingales: "Trusting the Stock Market" The Journal of Finance, Vol. 63, No. 6, 2008 and have a question about how they test whether trust is a proxy for risk aversion. ...
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1answer
105 views

Is car accident/theft a fair bet? [closed]

A person with a current wealth of 100,000 who faces the prospect of a 25% chance of losing his or her 20,000 automobile through theft during the next year. Since there is no upside to this event and E(...
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413 views

Certainty Equivalents and Risk Premiums in Expected Utility Theory for Asymmetric Distributions

I want to calculte risk-premiums in order to assess how much risk-averse customers would be willing to pay for an insurance against an uncertain loss modeled by a random variable $X$. How would a risk-...
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2answers
299 views

Why should the statistical value of life exist?

In areas such as insurance pricing and government policy analysis, it is often necessary to assign human life a monetary amount in order to compare it with other monetary amounts. So economists have ...
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557 views

Negative expected value; risk neutral choice

Suppose there are two options: (1) take a gamble with 50% chance you win \$100 and 50% chance you lose \$110 or (2) don't take the gamble at all and win/lose nothing. Would the risk-neutral take the ...
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1answer
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given someone's past investing history, is there a way to calculate his risk aversion?

given someone's past investing history, is there a way to calculate his risk aversion? Say, we know this client's investment history for example his past return, is there a way to calculate his risk ...
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2answers
1k views

Is DARA utility implying CRRA most of the time?

The Wikipedia page on risk aversion states that a "Constant Relative Risk Aversion implies a Decreasing Absolute Risk Aversion, but the reverse is not always true". Let me decompose this statement in ...
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How do I compute the relative risk aversion of Epstein-Zin preferences?

$$ \newcommand{\E}{\mathbb{E}} $$ Preface This question is related to this one about the elasticity of intertemporal substitution and this one about the definition of absolute risk aversion. (It's ...
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2answers
844 views

Risk Premium in the Expected Utility Theory

Consider an agent with utility function $u$, initial wealth $\omega$, and a random variable $x$. By definition of the risk premium $R$, we have $$ Eu(w+x) = u(w+E(x)-R). $$ The classical derivation ...
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1answer
103 views

What behaviour do different values of Relative Risk Aversion imply?

What behaviour does it imply that Relative Risk Aversion of consumption, say R(c) is less than 1, equal to 1 or greater than 1? I am reading an article of Diamond & Dybvig (1983), about Bank ...
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1answer
268 views

Does vNM rationality depend on the good chosen?

The von Neumann-Morgenstern theorem states that, assuming a person's preferences under risk satisfy certain rationality axioms, then there exists a utility function u, the von Neumann utility function,...
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1answer
180 views

Relative risk aversion and lotteries exercise

Given a consumer with a utility function, $u(w)$, and a wealth of $w>1000$. Assuming that the consumers relative risk aversion is constant and equal to 1, that is $R_r(w)=1$ for $w>0$, the ...
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1answer
2k views

Derivation of Arrow-Pratt risk aversion measure

This is a question about the derivation of Arrow-Pratt relative risk aversion measure $R(w)=-\dfrac{U^{''}(w)}{wU^{'}(w)}$. I have an own way to derive it, but I really want how did the authors ...
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3answers
849 views

Question about the Ellsberg Paradox in Expected Utility Theory

The von Neumann-Morgenstern theorem states that, assuming a person's preferences under risk satisfy certain rationality axioms, then there exists a utility function u, the von Neumann utility function,...
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3answers
740 views

Does risk aversion cause diminishing marginal utility, or vice versa?

Let $A$ be the set of possible states of the world, or possible preferences a person could have. Let $G(A)$ be the set of "gambles" or "lotteries", i.e. the set of probability distributions over $A$. ...
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2answers
469 views

Can a risk-averse agent's Certainty Equivalent be lower than the lowest possible outcome of a gamble?

Suppose there is an agent who faces the following gamble g: 50\$ with probability 1/3 100\$ with probability 1/3 150\$ with probability 1/3 Clearly, the E[g] = 100\$. Since agent is risk averse, we ...
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2answers
261 views

Does risk aversion of utility function cause the existence of positive interest rate?

In standard macro model, it is usually time preference that causes positive interest rate. But is there anything to do with risk aversion of utility function that causes existence of positive interest ...
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0answers
211 views

Calculating the optimal portfolio for an investor with quadratic utility

The problem is from Asset Pricing and Portfolio Theory by Back and can be found here. The relevant info from section 2.5 can be found here. Given that we have the Expected value and the variance of ...
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1answer
547 views

Portfolio choice problem of a CARA investor with n risky assets

Ok, I am working on a problem that consists of the following: I am looking to solve the portfolio choice optimization problem (maximizing utility with a known utility function) in the case where all ...
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1answer
257 views

Question about constant relative risk aversion

The question: Consider a person with constant relative risk aversion $p$. (a) Suppose the person has wealth of $100,000$ and faces a gamble in which he wins or loses $x$ with equal probabilities. ...
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2answers
2k views

Intuition behind risk premium

In Lecture 20 of MIT's Microeconomics course, a situation is proposed where a 50/50 bet will either result in losing \$100 or gaining \$125 with a starting wealth of \$100. It is stated that a person ...
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2answers
2k views

Empirical estimates of CRRA and CARA utility

I am working on macroeconomic model and I need to calibrate it. I am looking primarily for a statistically-founded estimate for the coefficient of relative risk aversion in the CRRA utility function ...