Economics
Risk Aversion
Risk aversion refers to the tendency of individuals to prefer certainty over uncertainty when making decisions involving risk. In economic terms, it means that people are willing to accept a lower expected return in exchange for a reduction in the variability of that return. This behavior is a key concept in understanding decision-making under uncertainty.
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8 Key excerpts on "Risk Aversion"
- Mark Machina, W. Kip Viscusi(Authors)
- 2013(Publication Date)
- North Holland(Publisher)
Handbook of the Economics of Risk and Uncertainity, Volume 1 © 2014 Elsevier B.V. ISSN 2211-7547, All rights reserved. http://dx.doi.org/10.1016/B978-0-444-53685-3.00003-9 99 CHAPTER The Theory of Risk and Risk Aversion Jack Meyer Department of Economics, Michigan State University, USA Abstract Risk and Risk Aversion are important concepts when modeling how to choose from or rank a set of random variables. This chapter reviews and summarizes the definitions and related findings concern-ing Risk Aversion and risk in both a mean-variance and an expected utility decision model context. Keywords Risk Aversion, Increases in Risk, Stochastic Dominance JEL Classification Codes D81 3.1 INTRODUCTION Risk and Risk Aversion have been recognized and included in the scientific discussion of decision making under uncertainty for hundreds of years. The St. Petersburg Paradox presented by mathematician Daniel Bernoulli (1954) in 1738 is often mentioned when first introducing the topic. Bernoulli identifies a gamble that most persons would pay only a small sum to be allowed to participate in, but whose expected value is infinite. Bernoulli suggests diminishing marginal utility as a reason why this is the case. Bernoulli describes the following gamble. Suppose a person receives an outcome of size 2 if flipping a fair coin results in heads on the first toss. The gamble ends if this occurs. Should a tail occur on the first toss, the gamble continues. When the coin is flipped a second time, if heads is observed, the payment is increased to 4, and the gamble ends. Should a tail occur on each of the first two tosses, the gamble continues 3 Contents 3.1 Introduction 99 3.2 The Mean-Variance Approach to Risk and Risk Aversion 100 3.3 The Expected Utility Approach 104 3.4 Risk Aversion 106 3.5 Increases in Risk and Stochastic Dominance 122 3.6 Mean Variance Analysis and Expected Utility 129 References 131
eBook - ePub- Nicholas L. Georgakopoulos(Author)
- 2018(Publication Date)
- Palgrave Macmillan(Publisher)
© The Author(s) 2018 Nicholas L. Georgakopoulos Illustrating Finance Policy with Mathematica Quantitative Perspectives on Behavioral Economics and Finance https://doi.org/10.1007/978-3-319-95372-4_10Begin Abstract10. Aversion to Risk
End AbstractNicholas L. Georgakopoulos1(1) Indiana University, Indianapolis, IN, USA1 Risk Aversion
Attitudes toward risk are central to the choices people make. Therefore, attitudes toward risk are important for the incentive scheme that law and policy produce as well as for the assessment of values that finance studies. In this chapter, we enter the mathematical understanding of aversion to risk when it applies to money. Attitudes toward risk outside monetary choices are still not well understood. Also, attitudes toward risk about money do not seem closely related to those about unrelated activities. We see little paradoxical about a solo ice-climber, for example, who would pay for a mistake half-way up a frozen waterfall with the ice-climber’s own life, in taking no financial risk and only investing in treasuries. Vice versa, a venture capitalist, most of whose investments are destined to fail, would not be seen as strange if the venture capitalist takes very few physical risks, driving exceedingly cautiously and exercising only in the safest ways. Aversion to physical risk has little relation to aversion to financial risk, and our economic models only deal with financial risk. From here, risk refers only to financial risk.The road to comprehending risk begins at simple gambles. Someone faces a choice between receiving a certain amount and two risky amounts. For example, the risky amounts may be $100 and $900, say, depending on the toss of a coin. If the coin comes heads, take $900, if tails then $100. The uncertainty, thus, is the $100 or $900 outcome. This example will be the foundation for understanding reactions to risk. The first step is to recognize the subjectivity of the correspondence between the risk and a certain amount.
eBook - PDF- RICHARD WATT(Author)
- 2017(Publication Date)
- Red Globe Press(Publisher)
Curiously, the result that some risk will always be purchased is independent of exactly how risk averse the individual is, and how slight might be the expected value advantage of the risky asset. 3.3 Measures of Risk Aversion Now that the concept of Risk Aversion has been formally introduced, it makes sense to analyse it in greater detail. One of the most interesting question about Risk Aversion is whether or not we can characterise different individuals according to their Risk Aversion. That is, if any two individuals can be ranked, or ordered, according to who is more risk averse. In order to do this, consider Figure 3.9, in which we represent the situation of an individual with an initial situation of pure risk-free wealth of w 0 . The initial wealth endowment is given by the point w 0 = ( w 0 1 , w 0 2 ) = ( w 0 , w 0 ). The indifference curve that passes through this point cuts the contingent claims space into two separate parts; the points that lie below the endowed indifference curve (lotteries that are less preferred to the endowment point w 0 , i.e. w : w 0 w ) and points that are on or above the endowed indifference curve (lotteries that are at least as preferred as w 0 , i.e., w : w w 0 ). We shall refer to the set A ( w 0 ) = { w : w w 0 } as the acceptance set , since it indicates all the lotteries that the individual would accept, voluntarily, in exchange for his endowment. 50 3. Risk Aversion w 2 w 1 w 1 = w 2 w 0 w 0 A ( w 0 ) Figure 3.9 – An acceptance set Absolute Risk Aversion Now, consider two individuals who are identical in all but their utility function. In particular, the two individuals share the same endowment point, and the same probabilities of the two states of nature.
eBook - PDFMarkets, Games, and Strategic Behavior
An Introduction to Experimental Economics (Second Edition)
- Charles A. Holt, Charles Holt(Authors)
- 2019(Publication Date)
- Princeton University Press(Publisher)
In any case, it is important to keep the diminishing- marginal-utility intuition for Risk Aversion in mind, since this factor plays such a prominent role in investments, insurance, and other types of economic decisions. There is a large literature on risk preferences, and many issues have been passed over here, e.g., whether utility should be a function of final wealth or of income (gains or losses from current wealth). In this chapter, we treat the util-ity as a function of income (gains and losses) instead of final wealth. There is experimental and theoretical evidence for this (Rabin, 2000; Cox and Vjollca, 2001). Appropriate reference points that separate gains from losses will be dis-cussed in the next chapter. In a provocative book entitled Risky Curves: On the Empirical Failure of Expected Utility Theory , Friedman et al. (2014) argue that different measures of risk aver-sion are not strongly correlated and are not very predictive of behavior in risky situations. The reader may also wish to peruse Eckel’s (2016) thoughtful and nu-anced review of this book. Friedman et al. note that risk of low or negative payoffs is considered to be much more serious than risk associated with high payoffs, a topic that will be revisited in the context of “upside” and “downside” risk in the next chapter. Deck et al. (2013) did find a significant ( p = 0.01) within-subjects Risk and Decision Making 57 correlation between Holt-Laury (tabular) and Eckel-Grossman (investment task) measures of Risk Aversion, with a correlation of 0.27, although there is no corre-lation between either of those measures and two more dynamic (“balloon” and “deal-or-no-deal”) tasks. One takeaway is that risk preferences may be multi-dimensional in a way that existing measurement tasks do not pick up. Sometimes one gets the impression that other emotions can dominate risk preferences, e.g., the urge to speculate during an asset price surge may dimin-ish natural caution.
eBook - ePubCoping with Risk in Agriculture
Applied Decision Analysis
- J Brian Hardaker, Ruud B M Huirne, Jock R Anderson, Gudbrand Lien(Authors)
- 2015(Publication Date)
- CAB International(Publisher)
Experience suggests that choice of exact form of a utility function is seldom important for decision analysis provided the degree of Risk Aversion (absolute, relative or partial, as appropriate) is consistently represented. So risk-aversion coefficients derived as described can be used with reasonable confidence in a function of any convenient form. In the work of research stations and extension agencies estimates of the range in Risk Aversion, derived consistently with the above methods and relationships for some target group of farmers, can be used in risk analysis for such specific contexts. Appropriate methods for such analyses are described in Chapter 7, this volume. Rationalizing Risk Aversion In Chapters 3 and 4 we argued that a rational person would want to achieve consistency in subjective probability judgements. We suggest that it is also rational to strive for consistency in attitudes to risk – a view supported by Meyer (2001). It makes no sense, for example, to be much more risk averse to a risky prospect expressed in terms of losses and gain compared with the assessment of the same prospect expressed in terms of wealth. Moreover, we also argued earlier in this chapter that extreme aversion to small losses, found by Rabin (2000) to be common behaviour, is irrational. We therefore suggest that it will usually be best to elicit a utility function (or to estimate a coefficient of Risk Aversion) for wealth, then to use this as a basis for assessing the appropriate risk attitude for risky prospects expressed in terms of income or losses and gains. To apply this approach we need to understand the logical relationships between risk-aversion measures when payoffs are expressed in different but related ways. Consistency of Risk Aversion across payoff measures We start by considering the case of a decision problem with payoffs expressed as losses and gains
eBook - ePub- Chris Jones(Author)
- 2008(Publication Date)
- Routledge(Publisher)
consumption-based pricing model (CBPM) from the ADPM in (3.11).3.2.2 Measuring Risk Aversion
Risk Aversion plays a key role in determining the equilibrium risk premium in security returns, and there is evidence that it changes with wealth; consumers with relatively more wealth are likely to be marginally less risk-averse. In project evaluation analysts include a risk premium in discount factors on risky net cash flows, and the task is less complex when consumers measure and price risk in the same way. In effect, Risk Aversion measures the degree of concavity in the utility function over uncertain consumption expenditure. An example is shown in Figure 3.5 where income can vary between I1 and I2 with probabilities π1 and π2 , respectively. To simplify the analysis we assume there is one future time period. With state-independent preferences we can map utility from consumption in each state using the function U(Ĩ), where the loss in utility from facing the variance in income is for In monetary terms the consumer is prepared to forgo income to receive Î with certainty. Clearly, this difference rises with the degree of concavity of the utility function.Arrow (1971) and Pratt (1964) define a number of widely used measures of Risk Aversion. The first of them is:Definition 3.6 The coefficient of absolute Risk Aversion (ARA) measures the curvature of the utility function as(3.14)For a strictly concave utility function, such as the one illustrated in Figure 3.5 , a negative second derivative makes ARA positive. One way of isolating this measure of Risk Aversion is to take a second-order Taylor series expansion around Ī for the relationship that defines the risk premium (RP) in Figure 3.5 , where
eBook - PDF- Dana L. Hoag(Author)
- 2009(Publication Date)
- CRC Press(Publisher)
There are three main attitudes a person can have toward risk (Hardaker et al., 2004). An individual who is afraid of taking risks is known as risk averse. This individual prefers an investment with a lower, but certain, expected payoff to an investment with a higher, but uncertain, payoff. An individual is said to be risk neutral if he or she cares only about the expected payoff of an investment and not the risk that must be taken to achieve the investment goal. Such an individual will neither actively take risks nor pay to avoid them. This individual would self-insure against loss, for example. An individual who actively engages in risky investments is referred to as risk seeking or risk loving. We can use a decision tree of Aaron’s preferences to further explain this concept (see Chapter 9 for a formal discussion about decision trees). Aaron has an opportunity to store some of his corn crop when he harvests it, with the hope that the future price 94 Applied Risk Management in Agriculture goes up. The alternative choice is to sell the crop on the cash market at harvest for an expected $275,000. There is a chance that prices will go up if there is a short U.S. crop, and he could increase his revenue to $350,000 if he stores his corn. However, there is an equal chance that there will be a normal U.S. crop and that he would have to sell for $250,000—less than he could have received at harvest. As shown in Figure 6.1, there is one decision (sell later vs. sell at harvest), and three possible financial outcomes, a certain $275,000 or a risk between $250,000 and $350,000. Based upon Aaron’s risk preferences and the concept of expected value (EV), we can project at what point he should sell his crop. The EV is the sum of the probability of each possible outcome multiplied by its payoff (see Chapter 10 for more details about probability). In this case, the EV is ($350,000 × 0.5) + ($250,000 × 0.5), which equals $300,000.
eBook - PDFA Course in Monetary Economics
Sequential Trade, Money, and Uncertainty
- Benjamin Eden(Author)
- 2008(Publication Date)
- Wiley-Blackwell(Publisher)
PART II An Introduction to the Economics of Uncertainty 11 Preliminaries 12 Does Insurance Require Risk Aversion? 13 Asset Prices and the Lucas “Tree Model” 181 We review some of the material that is typically covered in microeconomic classes and then introduce some additional topics. We start with the expected utility hypothesis and the attitude towards risk. We then exposit the idea of trade in contingent contracts and apply it to problems of insurance, gambling and portfolio selection. Finally, we talk about efficient risk allocation and asset prices. The analysis is relevant for monetary economics because of the debate about the importance of Risk Aversion for business cycle analysis. Lucas (1987) has argued quite convincingly that eliminating the business cycle is not important if Risk Aversion is the only reason that agents are averse to cycles. This is related to the debate about the importance of Risk Aversion in general. Most economists think that there is overwhelming evidence about the importance of Risk Aversion. Gambling is quantitatively important but it is often discarded as primarily a game of “fun”. Agents can also get “fun” by betting on stocks where the odds are in their favor. Why do agents get “fun” by gambling rather than more efficiently by investing in stocks? We will elaborate on this issue after we are done with the standard background material. CHAPTER 11 Preliminaries In this book we will use the expected utility hypothesis. This is a theory about the behavior of agents under uncertainty. Rather than following the axiomatic approach, we use here a version of the exposition in Friedman (1976) and Becker (1971). It is assumed that the agent chooses among alternative lotteries, where a lottery is a probab-ility distribution of income (or consumption). A typical lottery promises the realization I s with probability P s , where s is an index that runs over all possible realizations.
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