Measures of Risk Aversion

Satisfactory Essays
Topics: Risk aversion, Risk
Measures of Risk Aversion
Financial Economics
Martín Solá

October 2010

Martín Solá (FE)

Measures of Risk Aversion

08/10

1 / 41

Introduction

In this …rst stage we will study the individual decisions of optimal portfolio choice under uncertainty and its consequences in the valuation of risky assets. In short, the Financial Theory rests on the no-arbitrage principle. The idea behind this principle is that it is not possible to make pro…ts without risk, without initial investment.

Martín Solá (FE)

Measures of Risk Aversion

08/10

2 / 41

Risk Aversion (Jensen’ Inequality) s
Consider the following situation: given an initial wealth wo , there is a lottery where the possible results are h1 < 0 with probability p, h2 > 0 with probability (1-p ). A lottery is actuarially fair if the expected payo¤ is 0, h1 p + h2 (1-p ) = 0.

De…nition
An agent is risk averse if this agent is not willing to take an actuarially fair lottery.

Martín Solá (FE)

Measures of Risk Aversion

08/10

3 / 41

Risk Aversion (Jensen’ Inequality) s

So, we have the following inequality U ( wo ) U (wo + h1 )p + U (wo + h2 )(1-p ).

Since, by de…nition, an actuarially fair lottery satis…es wo = (wo + h1 )p + (wo + h2 )(1-p ), we can rewrite the inequality as U ((wo + h1 )p + (w0 + h2 )(1-p )) U (w0 + h1 )p + U (w0 + h2 )(1-p )

This relation proves that the risk aversion implies that the agent’ s utility function to be concave, and a concave utility function implies risk aversion.

Martín Solá (FE)

Measures of Risk Aversion

08/10

4 / 41

Risk Aversion (Jensen’ Inequality) s

If we de…ne the (ex-ante) wealth as a random variable w = wo + h, b where h is the random variable previously de…ned, the Jensen’ s Inequality can be expressed as U (E (w )) b E (U (w )). b

Remember that concavity implies that the marginal utility of wealth is decreasing. For a risk averse agent is worthless to take a fair lottery.

Martín Solá (FE)

You May Also Find These Documents Helpful

  • Good Essays

    Risk Aversion

    • 4064 Words
    • 17 Pages

    Lecture 1: Risk and Risk Aversion • This should mostly be review given your Microeconomics courses • Readings: ▪ Ingersoll – Chapter 1 ▪ Leroy and Werner Chapters 8 & 9 ▪ Ross – “Stronger Measures of Risk Aversion” The most interesting aspect of Asset Pricing, the focus of this course, considers how securities markets price risk (the time dimension alone is largely mechanical although there are interesting interactions between the two). For this question to…

    • 4064 Words
    • 17 Pages
    Good Essays
  • Good Essays

    measure risk

    • 1626 Words
    • 13 Pages

    EVALUATION OF RISK How does we Measure Risk? Understanding the nature of the risk is not adequate unless the investor or analyst is capable of expressing it in some quantitative terms. Expressing the risk of a stock in quantitative terms makes it comparable with other stocks. Measurement cannot be assures of percent accuracy because risk is caused by numerous factors as discussed above. Measurement provides an approximate quantification of risk. The statistical tool often used to measure is the standard…

    • 1626 Words
    • 13 Pages
    Good Essays
  • Satisfactory Essays

    of Sparky's Kerosene Company (SKC) face a variety of risks in holding SKC shares. If SKC purchases fire insurance for their factories, their shareholders will face lower Your Answer Score Explanation Systematic/Market Risk. Specific/Idiosyncratic Risk. Correct 5.00 Correct. You have a good intuition for fundamental types of risk. Total 5.00 / 5.00 Question Explanation A fundamental question about different types of risks. Question 2 (5 points) Suppose there are three securities…

    • 1303 Words
    • 9 Pages
    Satisfactory Essays
  • Powerful Essays

    Expected Utility Theory and Risk Aversion Seminar Paper 1 Contents S.no. Topic Page No. 1. Acknowledgment 2 2. Introduction 3 3. Is this theory Empirically true? 8 4. 5. How do different people with different levels of risk aversion behave, under the EUT? Major Criticism: Coherence of Large & Small Stake gambles 13 16 6. Conclusion 20 7. References 21 2 Acknowledgement I would like to thank Mr. because without…

    • 5372 Words
    • 22 Pages
    Powerful Essays
  • Good Essays

    Regulation and Decision Making Under Risk and Uncertainty” by Mircea Miclea, Andrei C. Miu, Renata M. Heilman, Liviu G. Crisan from Babes-Bolyai University, in Cluj-Napoca, Romania and Daniel Houser from George Mason University in Virginia, USA. The study was published in the American Psychological Association, 2010, Vol. 10, No. 2. It deals with emotion regulation (ER) tactics such as cognitive reappraisal and expression suppression and their effects on risk aversion and decision making. Reappraisal…

    • 1099 Words
    • 5 Pages
    Good Essays
  • Satisfactory Essays

    that all investors prefer more wealth to less : U’(W)>0 – Investors will always seek to maximize their expected utility of wealth. – All investors will use it as their objective function. 3 3-C-Establishing a definition of risk aversion • Utility functions are specific to individuals • Every individual has his own subjective utility function (that embodies his preferences) • It follows that group utility functions, such as the utility function of a firm makes…

    • 1146 Words
    • 5 Pages
    Satisfactory Essays
  • Good Essays

    Taste Aversion

    • 660 Words
    • 2 Pages

    Conditioned taste aversion is a phenomenon in which one would associate a certain taste with an uncomfortable symptom such as nausea, dizziness, sickness, or vomiting. One ingesting a certain substance that causes symptoms such as nausea, vomiting, and other sicknesses, which then an individual learns to avoid, usually causes taste aversion. Dr. Garcia whom is a researcher that had realized rats had associated their sickness from the radiation to the food they had ingested prior to the treatment…

    • 660 Words
    • 2 Pages
    Good Essays
  • Good Essays

    Loss Aversion

    • 550 Words
    • 3 Pages

    “A Behavioral Study Of The Impact Of Loss Aversion on the Decision Making Of Individual Investors: In Context of Madhya Pradesh” Decision-making is a complex activity. Decision-making can be defined as the process of choosing a particular alternative from a number of alternatives. Choosing from the alternatives is the most crucial challenge faced by the investors is in the area of investment. The principal objective of an investment is to make money. Investment decision making involves the process…

    • 550 Words
    • 3 Pages
    Good Essays
  • Good Essays

    ‘The concept of risk aversion is fundamental to investment analyses’ – A statement evaluation Risk is almost always present when an investment is taken; the evaluation of risk begins immediately with analysts asking questions about the level of risk associated with an investment, performing calculations to measure the risk involved, also diversifications may be considered to minimise risk. This clear focus and proactive approach to risk minimisation implies risk aversion plays a major role in…

    • 527 Words
    • 2 Pages
    Good Essays
  • Satisfactory Essays

    The Aversion Project

    • 284 Words
    • 2 Pages

    HESI Fundamentals: Pain 1. Wrenda's younger child is an infant, who needs feed every 3 hours 2. What word best describes the pain you are experiencing 3. Frequent guarding 4. Continue the interview with the client 5. Client reports pain of 1 on a 0-10 scale 6. Discuss the plan of care with the client 7. Tylenol does not have an antiinflammatory effect 8. All aspirin products should be avoided in children unless specifically prescribed 9. The dry heat provided by your heating pad…

    • 284 Words
    • 2 Pages
    Satisfactory Essays