File Name: risk aversion in the small and in the large kindle.zip
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Variance Aversion in the Small and the Large - Economics Variance Aversion in the Small and the Large. A direct l in k is established between the se measures and. Implications for problems of choice under uncerta in ty. This paper establishes the equivalence of two measures of risk aversion for a general. It fur the r derives implications for decision mak in g. Variance Aversion in the Small and the Large 2. I in troduce two measures of variance aversion, and analyze the ir connection to.
And f in ally, equivalence is established between. It is closely related to the Arrow-Pratt coefficient. The second measure, the partial variance compensation, is the. The ma in the orem establishes an equivalence of the in troduced measures of variance. I describe the general framework and def in e the measures of variance aversion in. Section 3 is the ma in the orem. In section 4, I analyze the relationship of the. Section 5 is dedicated to. Variance Aversion in the Small and the Large 3.
Consider two agents 1 and 2 with mean-variance utility functions u 1 and u 2 ,. Now in troduce the follow in g two measures of variance aversion:. That is twice the. To formalize this, I use the follow in g. Variance Aversion in the Small and the Large 4. We are now ready to prove the ma in the orem, which establishes that the in troduced. Theorem 5 If A1 , A2 are satisfied, the follow in g are equivalent:. Whenever mean and variance are sufficient to characterize expected utility preferences.
That is,. Variance Aversion in the Small and the Large 5. Note that 1 is equivalent to. Thus, the ma in the orem provides a near equivalence relationship of the in troduced. In particular, the the orem fails if one restricts attention to normally.
In particular, for the class. Variance Aversion in the Small and the Large 6. Epste in shows that under decreas in g-absolute-risk-aversion conditions nonexpected. Thus, our ma in. See Kusuda for fur the r analysis of relations between various measures of. In this section, I follow the approach of Wang and Werner Variance Aversion in the Small and the Large 7.
Theorem 5 has direct implication to problems of choice under uncerta in ty with. To formalize the above statement I need to in troduce the follow in g relationship. Theorem 7 If A1 , A2 are satisfied, the follow in g are equivalent:. Everyth in g I have established so far in this section can also be applied to a less.
Variance Aversion in the Small and the Large 8. Def in ition 8 Portfolio choice problem PCP with short-sales constra in ts and 2.
Theorem 9 If A1 , A2 are satisfied, the follow in g are equivalent:. This the orem not only demonstrates that our measures of variance aversion have. Variance Aversion in the Small and the Large 9. Also by cont in uity of u 2 , we can parameterize the in difference curve of agent 2 go in g. Variance Aversion in the Small and the Large This follows immediately from the previous the orem.
Suppose not. Take R such. Epste in , L. Kusuda, K. Mach in a, M. Pratt, J. Ross, S. Wang Z. No tags were found A direct l in k is established between the se measures and st and ard measures of risk aversion. Implications for problems of choice under uncerta in ty such as portfolio choice problems are derived. Introduction This paper establishes the equivalence of two measures of risk aversion for a general class of mean-variance preferences.
Variance Aversion in the Small and the Large 2 I in troduce two measures of variance aversion, and analyze the ir connection to exist in g measures of risk aversion. And f in ally, equivalence is established between compar in g the se measures and compar in g choices that agents make under uncerta in ty. The second measure, the partial variance compensation, is the mean-variance counterpart of partial risk compensation in troduced by Ross for expected utility preferences; and thus l in ks the result of this paper to the stronger notion of risk aversion of Ross.
The ma in the orem establishes an equivalence of the in troduced measures of variance aversion. I describe the general framework and def in e the measures of variance aversion in section 2. In section 4, I analyze the relationship of the in troduced measures to exist in g measures of risk aversion.
Section 5 is dedicated to implications for choice under uncerta in ty, and in particular, portfolio choice problem. That is, agent 1 is weakly more variance averse than agent 2 if 1 rejects a prospect with higher variance and higher mean whenever 2 rejects it. We are now ready to prove the ma in the orem, which establishes that the in troduced measures capture our notion of variance aversion and are equivalent. Theorem 5 If A1 , A2 are satisfied, the follow in g are equivalent: 1.
Agent 1 is weakly more variance averse than agent 2. See Appendix 4. Relation to Exist in g Measures of Risk Aversion 4. Expected Utility Framework Whenever mean and variance are sufficient to characterize expected utility preferences over risky prospects for example, when one restricts attention only to quadratic von Neumann-Morgenstern utility functions or only to normally distributed r and om variables , variance fully characterizes risk, and partial variance compensation co in cides with partial risk compensation, in troduced by Ross Thus whenever preferences over a given class of distributions have both an expected utility representation and a mean-variance representation, 2.
In particular, the the orem fails if one restricts attention to normally distributed r and om variables. See Kusuda for fur the r analysis of relations between various measures of risk aversion.
Variance Aversion in the Small and the Large 7 Theorem 5 has direct implication to problems of choice under uncerta in ty with mean-variance preferences CAPM, etc.
Theorem 7 If A1 , A2 are satisfied, the follow in g are equivalent: 3. Agent 1 is weakly more variance averse than agent 2; 4. See Appendix 5. Implications for Portfolio Choice Everyth in g I have established so far in this section can also be applied to a less general, but more economically in terest in g class of problems - portfolio choice problems. Theorem 9 If A1 , A2 are satisfied, the follow in g are equivalent: 3. See Appendix This the orem not only demonstrates that our measures of variance aversion have direct implications for portfolio choice problems, but also allows portfolio characterization of variance aversion see Wang and Werner Appendix: Proofs Proof.
Theorem 5. The proof is by contradiction, us in g Lemma 4. The proof is by contradiction. But we have a. Theorem 7. Theorem 9. Short-link Link Embed. Share from cover. Share from page:. More magazines by this user. Close Flag as Inappropriate. You have already flagged this document. Thank you, for helping us keep this platform clean.
Nevertheless, this relationship became only a topic of interest in modern economic studies since the last quarter of the twentieth century, when Ehrenberg and Azzi developed a utility-maximizing model taking into account both lifetime and afterlife utility see, for example, Iannaccone, ; Jackson and Fleischer, Hence, studies investigate both microand macroeconomic effects of religiosity 2 , while some recent papers specifically address the relationship between religion and financial decisions: risk aversion and speculative behavior in particular are believed to depend on religious adherence. Not only have studies linked religiosity with a higher level of pure risk aversion in corporate decision making Hilary and Hui, , but also suggests current research that religious beliefs spill over in investment decisions due to different notions of gambling. For instance, Kumar found Catholics to be more willing to take on speculative risk by investing more in risky stocks than Protestants do. This paper aims to critically review Kumar, Page, and Spalt and structures as follows: firstly the theoretical framework of gambling in economics will be presented with a focus on cumulative prospect theory and its implications for asset pricing. The subsequent section discusses the hypotheses of Kumar, Page, and Spalt
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Variance Aversion in the Small and the Large - Economics Variance Aversion in the Small and the Large. A direct l in k is established between the se measures and.
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