risk aversion (8522)

7/27/2019 Risk Aversion (8522)

1/6

Risk aversion is a concept in psychology, economics, and finance, based on the behavior ofhumans (especially consumers and investors) while exposed to uncertainty to attempt toreduce that uncertainty.

Risk aversion is the reluctance of a person to accept a bargain with an uncertain payoff rather

than another bargain with a more certain, but possibly lower, expected payoff. For example, arisk-averse investor might choose to put his or her money into a bank account with a low butguaranteed interest rate, rather than into a stock that may have high expected returns, but alsoinvolves a chance of losing value.

Utility of money

In expected utility theory, an agent has a utility function u(x) wherex represents the valuethat he might receive in money or goods (in the above examplex could be 0 or 100).

Time does not come into this calculation, so inflation does not appear. (The utility functionu(x) is defined onlyup topositive linearaffine transformation - in other words a constantoffset could be added to the value ofu(x) for allx, and/oru(x) could be multiplied by a

positive constant factor, without affecting the conclusions.) An agent possesses risk aversionif and only if the utility function isconcave. For instance u(0) could be 0, u(100) might be 10,u(40) might be 5, and for comparison u(50) might be 6.

The expected utility of the above bet (with a 50% chance of receiving 100 and a 50% chanceof receiving 0) is,

,

and if the person has the utility function with u(0)=0, u(40)=5, and u(100)=10 then theexpected utility of the bet equals 5, which is the same as the known utility of the amount 40.Hence the certainty equivalent is 40.

The risk premium is ($50 minus $40)=$10, or in proportional terms

or 25% (where $50 is the expected value of the risky bet: ( ). This risk premium

means that the person would be willing to sacrifice as much as $10 in expected value in orderto achieve perfect certainty about how much money will be received. In other words, the

person would be indifferent between the bet and a guarantee of $40, and would preferanything over $40 to the bet.

In the case of a wealthier individual, the risk of losing $100 would be less significant, and forsuch small amounts his utility function would be likely to be almost linear, for instance ifu(0) = 0 and u(100) = 10, then u(40) might be 4.0001 and u(50) might be 5.0001.

The utility function for perceived gains has two key properties: an upward slope, andconcavity. (i) The upward slope implies that the person feels that more is better: a largeramount received yields greater utility, and for risky bets the person would prefer a bet whichisfirst-order stochastically dominantover an alternative bet (that is, if the probability mass of
http://en.wikipedia.org/wiki/Up_tohttp://en.wikipedia.org/wiki/Up_tohttp://en.wikipedia.org/wiki/Up_tohttp://en.wikipedia.org/wiki/Concave_functionhttp://en.wikipedia.org/wiki/Concave_functionhttp://en.wikipedia.org/wiki/Concave_functionhttp://en.wikipedia.org/wiki/Stochastic_dominance#First-order_stochastic_dominancehttp://en.wikipedia.org/wiki/Stochastic_dominance#First-order_stochastic_dominancehttp://en.wikipedia.org/wiki/Stochastic_dominance#First-order_stochastic_dominancehttp://en.wikipedia.org/wiki/Stochastic_dominance#First-order_stochastic_dominancehttp://en.wikipedia.org/wiki/Concave_functionhttp://en.wikipedia.org/wiki/Up_to


2/6

the second bet is pushed to the right to form the first bet, then the first bet is preferred). (ii)The concavity of the utility function implies that the person is risk averse: a sure amountwould always be preferred over a risky bet having the same expected value; moreover, forrisky bets the person would prefer a bet which is amean-preserving contractionof analternative bet (that is, if some of the probability mass of the first bet is spread out without

altering the mean to form the second bet, then the first bet is preferred).

Measures of risk aversion

Absolute risk aversion

The higher the curvature of , the higher the risk aversion. However, since expectedutility functions are not uniquely defined (are defined only up toaffine transformations), ameasure that stays constant with respect to these transformations is needed. One suchmeasure is the Arrow-Pratt measure of absolute risk-aversion (ARA), after the economists

Kenneth ArrowandJohn W. Pratt,[1][2]also known as the coefficient of absolute riskaversion, defined as

.

The following expressions relate to this term:

Exponential utilityof the form is unique in exhibiting constantabsolute risk aversion (CARA): is constant with respect to c.

Hyperbolic absolute risk aversion(HARA) is the most general class of utilityfunctions that are usually used in practice (specifically, CRRA (constant relative riskaversion, see below), CARA (constant absolute risk aversion), and quadratic utility allexhibit HARA and are often used because of their mathematical tractability). A utilityfunction exhibits HARA if its absolute risk aversion is ahyperbolic function, namely

.

The solution to this differential equation (omitting additive and multiplicative constant terms,which do not affect the behavior implied by the utility function) is:

where and . Note that when , this is CARA, as

, and when , this is CRRA (see below), as

. See[3]
http://en.wikipedia.org/wiki/Mean-preserving_spreadhttp://en.wikipedia.org/wiki/Mean-preserving_spreadhttp://en.wikipedia.org/wiki/Mean-preserving_spreadhttp://en.wikipedia.org/wiki/Affine_transformationshttp://en.wikipedia.org/wiki/Affine_transformationshttp://en.wikipedia.org/wiki/Affine_transformationshttp://en.wikipedia.org/wiki/Kenneth_Arrowhttp://en.wikipedia.org/wiki/Kenneth_Arrowhttp://en.wikipedia.org/wiki/John_W._Pratthttp://en.wikipedia.org/wiki/John_W._Pratthttp://en.wikipedia.org/wiki/Risk_aversion#cite_note-Arrow-1http://en.wikipedia.org/wiki/Risk_aversion#cite_note-Arrow-1http://en.wikipedia.org/wiki/Risk_aversion#cite_note-Arrow-1http://en.wikipedia.org/wiki/Exponential_utilityhttp://en.wikipedia.org/wiki/Exponential_utilityhttp://en.wikipedia.org/wiki/Hyperbolic_absolute_risk_aversionhttp://en.wikipedia.org/wiki/Hyperbolic_absolute_risk_aversionhttp://en.wikipedia.org/wiki/Hyperbolic_functionhttp://en.wikipedia.org/wiki/Hyperbolic_functionhttp://en.wikipedia.org/wiki/Hyperbolic_functionhttp://en.wikipedia.org/wiki/Risk_aversion#cite_note-3http://en.wikipedia.org/wiki/Risk_aversion#cite_note-3http://en.wikipedia.org/wiki/Risk_aversion#cite_note-3http://en.wikipedia.org/wiki/Risk_aversion#cite_note-3http://en.wikipedia.org/wiki/Hyperbolic_functionhttp://en.wikipedia.org/wiki/Hyperbolic_absolute_risk_aversionhttp://en.wikipedia.org/wiki/Exponential_utilityhttp://en.wikipedia.org/wiki/Risk_aversion#cite_note-Arrow-1http://en.wikipedia.org/wiki/Risk_aversion#cite_note-Arrow-1http://en.wikipedia.org/wiki/John_W._Pratthttp://en.wikipedia.org/wiki/Kenneth_Arrowhttp://en.wikipedia.org/wiki/Affine_transformationshttp://en.wikipedia.org/wiki/Mean-preserving_spread


3/6

Decreasing/increasing absolute risk aversion (DARA/IARA) is present if isdecreasing/increasing. Using the above definition of ARA, the following inequalityholds for DARA:

and this can hold only if . Therefore, DARA implies that the utility function is

positively skewed; that is, .[4]Analogously, IARA can be derived with theopposite directions of inequalities, which permits but does not require a negatively skewed

utility function ( ). An example of a DARA utility function is ,

with , while , withwould represent a quadratic utility function exhibiting IARA.

Experimental and empirical evidence is mostly consistent with decreasing absoluterisk aversion.[5]

Contrary to what several empirical studies have assumed, wealth is not a good proxyfor risk aversion when studying risk sharing in a principal-agent setting. Although

is monotonic in wealth under either DARA or IARA and constantin wealth under CARA, tests of contractual risk sharing relying on wealth as a proxyfor absolute risk aversion are usually not identified.[6]

Relative risk aversion

TheArrow-Pratt-De Finetti measure of relative risk-aversion (RRA) orcoefficient of relativerisk aversion is defined as

.

Like for absolute risk aversion, the corresponding terms constant relative risk aversion(CRRA) and decreasing/increasing relative risk aversion (DRRA/IRRA) are used. This

measure has the advantage that it is still a valid measure of risk aversion, even if the utilityfunction changes from risk-averse to risk-loving as c varies, i.e. utility is not strictlyconvex/concave over all c. A constant RRA implies a decreasing ARA, but the reverse is not

always true. As a specific example, the expected utility function impliesRRA = 1.

Inintertemporal choiceproblems, theelasticity of intertemporal substitutionis often unableto be disentangled from the coefficient of relative risk aversion. Theisoelastic utilityfunction
http://en.wikipedia.org/wiki/Risk_aversion#cite_note-4http://en.wikipedia.org/wiki/Risk_aversion#cite_note-4http://en.wikipedia.org/wiki/Risk_aversion#cite_note-4http://en.wikipedia.org/wiki/Risk_aversion#cite_note-5http://en.wikipedia.org/wiki/Risk_aversion#cite_note-5http://en.wikipedia.org/wiki/Risk_aversion#cite_note-5http://en.wikipedia.org/wiki/Risk_aversion#cite_note-6http://en.wikipedia.org/wiki/Risk_aversion#cite_note-6http://en.wikipedia.org/wiki/Risk_aversion#cite_note-6http://en.wikipedia.org/wiki/Intertemporal_choicehttp://en.wikipedia.org/wiki/Intertemporal_choicehttp://en.wikipedia.org/wiki/Intertemporal_choicehttp://en.wikipedia.org/wiki/Elasticity_of_intertemporal_substitutionhttp://en.wikipedia.org/wiki/Elasticity_of_intertemporal_substitutionhttp://en.wikipedia.org/wiki/Elasticity_of_intertemporal_substitutionhttp://en.wikipedia.org/wiki/Isoelastic_utilityhttp://en.wikipedia.org/wiki/Isoelastic_utilityhttp://en.wikipedia.org/wiki/Isoelastic_utilityhttp://en.wikipedia.org/wiki/Isoelastic_utilityhttp://en.wikipedia.org/wiki/Elasticity_of_intertemporal_substitutionhttp://en.wikipedia.org/wiki/Intertemporal_choicehttp://en.wikipedia.org/wiki/Risk_aversion#cite_note-6http://en.wikipedia.org/wiki/Risk_aversion#cite_note-5http://en.wikipedia.org/wiki/Risk_aversion#cite_note-4


4/6

exhibits constant relative risk aversion with and the elasticity of inter temporalsubstitution. However, a time varying relative risk aversion can be considered.[7]When andone is subtracted in the numerator (facilitating the use ofl'Hpital's rule), this simplifies tothe case oflog utility, and theincome effectandsubstitution effecton saving exactly offset.

Implications of increasing/decreasing absolute and relative risk aversion

The most straightforward implications of increasing or decreasing absolute or relative riskaversion, and the ones that motivate a focus on these concepts, occur in the context offorming a portfolio with one risky asset and one risk-free asset.[1][2]If the person experiencesan increase in wealth, he/she will choose to increase (or keep unchanged, or decrease) thenumber of dollars of the risky asset held in the portfolio ifabsolute risk aversion isdecreasing (or constant, or increasing). Thus economists avoid using utility functions, such asthe quadratic, which exhibit increasing absolute risk aversion, because they have anunrealistic behavioral implication.

Similarly, if the person experiences an increase in wealth, he/she will choose to increase (orkeep unchanged, or decrease) thefraction of the portfolio held in the risky asset ifrelativerisk aversion is decreasing (or constant, or increasing).

Portfolio theory

Inmodern portfolio theory, risk aversion is measured as the additional marginal reward aninvestor requires to accept additional risk. In modern portfolio theory, risk is being measuredasstandard deviationof the return on investment, i.e. thesquare rootof itsvariance. Inadvanced portfolio theory, different kinds of risk are taken into consideration. They are being

measured as then-th radicalof the n-thcentral moment. The symbol used for risk aversion isA or An.

Risk aversion in the brain[edit source|editbeta]

Attitudes towards risk have attracted the interest of the field ofneuroeconomicsandbehavioral economics. A study by researchers at the University of Cambridge[8]suggestedthat the activity of a specific brain area (right inferior frontal gyrus) correlates with riskaversion, with more risk averse participants (i.e. those having higher risk premia) also havinghigher responses to safer options. This result coincides with other studies,[9][10]that show thatneuromodulation of the same area results in participants making more or less risk aversechoices, depending on whether the modulation increases or decreases the activity of the targetarea.
http://en.wikipedia.org/wiki/Risk_aversion#cite_note-7http://en.wikipedia.org/wiki/Risk_aversion#cite_note-7http://en.wikipedia.org/wiki/Risk_aversion#cite_note-7http://en.wikipedia.org/wiki/L%27H%C3%B4pital%27s_rulehttp://en.wikipedia.org/wiki/L%27H%C3%B4pital%27s_rulehttp://en.wikipedia.org/wiki/L%27H%C3%B4pital%27s_rulehttp://en.wikipedia.org/wiki/Income_effecthttp://en.wikipedia.org/wiki/Income_effecthttp://en.wikipedia.org/wiki/Income_effecthttp://en.wikipedia.org/wiki/Substitution_effecthttp://en.wikipedia.org/wiki/Substitution_effecthttp://en.wikipedia.org/wiki/Substitution_effecthttp://en.wikipedia.org/wiki/Risk_aversion#cite_note-Arrow-1http://en.wikipedia.org/wiki/Risk_aversion#cite_note-Arrow-1http://en.wikipedia.org/wiki/Risk_aversion#cite_note-Arrow-1http://en.wikipedia.org/wiki/Modern_portfolio_theoryhttp://en.wikipedia.org/wiki/Modern_portfolio_theoryhttp://en.wikipedia.org/wiki/Modern_portfolio_theoryhttp://en.wikipedia.org/wiki/Standard_deviationhttp://en.wikipedia.org/wiki/Standard_deviationhttp://en.wikipedia.org/wiki/Standard_deviationhttp://en.wikipedia.org/wiki/Square_roothttp://en.wikipedia.org/wiki/Square_roothttp://en.wikipedia.org/wiki/Square_roothttp://en.wikipedia.org/wiki/Variancehttp://en.wikipedia.org/wiki/Variancehttp://en.wikipedia.org/wiki/Variancehttp://en.wikipedia.org/wiki/N-th_roothttp://en.wikipedia.org/wiki/N-th_roothttp://en.wikipedia.org/wiki/N-th_roothttp://en.wikipedia.org/wiki/Central_momenthttp://en.wikipedia.org/wiki/Central_momenthttp://en.wikipedia.org/wiki/Central_momenthttp://en.wikipedia.org/w/index.php?title=Risk_aversion&action=edit&section=9http://en.wikipedia.org/w/index.php?title=Risk_aversion&action=edit&section=9http://en.wikipedia.org/w/index.php?title=Risk_aversion&action=edit&section=9http://en.wikipedia.org/w/index.php?title=Risk_aversion&veaction=edit&section=9http://en.wikipedia.org/w/index.php?title=Risk_aversion&veaction=edit&section=9http://en.wikipedia.org/wiki/Neuroeconomicshttp://en.wikipedia.org/wiki/Neuroeconomicshttp://en.wikipedia.org/wiki/Neuroeconomicshttp://en.wikipedia.org/wiki/Behavioral_economicshttp://en.wikipedia.org/wiki/Behavioral_economicshttp://en.wikipedia.org/wiki/Risk_aversion#cite_note-8http://en.wikipedia.org/wiki/Risk_aversion#cite_note-8http://en.wikipedia.org/wiki/Risk_aversion#cite_note-8http://en.wikipedia.org/wiki/Risk_aversion#cite_note-9http://en.wikipedia.org/wiki/Risk_aversion#cite_note-9http://en.wikipedia.org/wiki/Risk_aversion#cite_note-9http://en.wikipedia.org/wiki/Risk_aversion#cite_note-9http://en.wikipedia.org/wiki/Risk_aversion#cite_note-9http://en.wikipedia.org/wiki/Risk_aversion#cite_note-8http://en.wikipedia.org/wiki/Behavioral_economicshttp://en.wikipedia.org/wiki/Neuroeconomicshttp://en.wikipedia.org/w/index.php?title=Risk_aversion&veaction=edit&section=9http://en.wikipedia.org/w/index.php?title=Risk_aversion&action=edit&section=9http://en.wikipedia.org/wiki/Central_momenthttp://en.wikipedia.org/wiki/N-th_roothttp://en.wikipedia.org/wiki/Variancehttp://en.wikipedia.org/wiki/Square_roothttp://en.wikipedia.org/wiki/Standard_deviationhttp://en.wikipedia.org/wiki/Modern_portfolio_theoryhttp://en.wikipedia.org/wiki/Risk_aversion#cite_note-Arrow-1http://en.wikipedia.org/wiki/Risk_aversion#cite_note-Arrow-1http://en.wikipedia.org/wiki/Substitution_effecthttp://en.wikipedia.org/wiki/Income_effecthttp://en.wikipedia.org/wiki/L%27H%C3%B4pital%27s_rulehttp://en.wikipedia.org/wiki/Risk_aversion#cite_note-7


5/6

Public understanding and risk in social activities

In the real world, many government agencies, e.g.Health and Safety Executive, arefundamentally risk-averse in their mandate. This often means that they demand (with the

power of legal enforcement) that risks be minimized, even at the cost of losing the utility ofthe risky activity. It is important to consider theopportunity costwhen mitigating a risk; thecost of not taking the risky action. Writing laws focused on the risk without the balance of theutility may misrepresent society's goals. The public understanding of risk, which influences

political decisions, is an area which has recently been recognised as deserving focus.DavidSpiegelhalteris theWinton Professor of the Public Understanding of RiskatCambridgeUniversity; a role he describes as "outreach".[11]

Avaccineto protect children against the three common diseases measles, mumps and rubellawas developed and recommended for all children in several countries including the UK.However, acontroversyarose around allegations that it caused autism. This alleged causal

link was thoroughly disproved,

[12]

and the doctor who made the claims was expelled from theGeneral Medical Council. Even years after the claims were disproved, some parents wantedto avert the risk of causing autism in their own children. They chose to spend significantamounts of their own money on alternatives from private doctors. These alternatives carriedtheir own risks which were not balanced fairly; most often that the children were not properlyimmunised against the more common diseases of measles, mumps and rubella.

Mobile phonesmay carry some small[13][14]health risk. While most people would accept thatunproven risk to gain the benefit of improved communication, others remain so risk aversethat they do not. (TheCOSMOS cohort studycontinues to study the actual risks of mobile

phones.)

Risk aversion theory can be applied to many aspects of life and its challenges, for example:

Briberyandcorruption- whether the risk of being implicated or caught outweighs thepotential personal or professional rewards

Drugs- whether the risk of having abad tripoutweighs the benefits of possibletransformative one; whether the risk of defyingsocial bansis worth the experience ofalteration. See "Harm reduction".

Sex- judgement whether an experience that goes againstsocial convention,ethicalmoresor common healthprescriptionsis worth the risk.

Extreme sports- weighing the risk of physical injury or death against theadrenalinerushandbragging rights.

Playby children in playgrounds or beyond the reach of their parents.Limitations

The notion of (constant) risk aversion has come under criticism from behavioral economics.

According to Matthew Rabin of UC Berkeley, a consumer who, from any initial wealth level [...] turns

down gambles where he loses $100 or gains $110, each with 50% probability [...] will turn down 50-

50 bets of losing $1,000 or gaining any sum of money.
http://en.wikipedia.org/wiki/Health_and_Safety_Executivehttp://en.wikipedia.org/wiki/Health_and_Safety_Executivehttp://en.wikipedia.org/wiki/Health_and_Safety_Executivehttp://en.wikipedia.org/wiki/Opportunity_costhttp://en.wikipedia.org/wiki/Opportunity_costhttp://en.wikipedia.org/wiki/Opportunity_costhttp://en.wikipedia.org/wiki/David_Spiegelhalterhttp://en.wikipedia.org/wiki/David_Spiegelhalterhttp://en.wikipedia.org/wiki/David_Spiegelhalterhttp://en.wikipedia.org/wiki/David_Spiegelhalterhttp://en.wikipedia.org/wiki/Winton_Professorship_of_the_Public_Understanding_of_Riskhttp://en.wikipedia.org/wiki/Winton_Professorship_of_the_Public_Understanding_of_Riskhttp://en.wikipedia.org/wiki/Winton_Professorship_of_the_Public_Understanding_of_Riskhttp://en.wikipedia.org/wiki/Cambridge_Universityhttp://en.wikipedia.org/wiki/Cambridge_Universityhttp://en.wikipedia.org/wiki/Cambridge_Universityhttp://en.wikipedia.org/wiki/Cambridge_Universityhttp://en.wikipedia.org/wiki/Risk_aversion#cite_note-11http://en.wikipedia.org/wiki/Risk_aversion#cite_note-11http://en.wikipedia.org/wiki/Risk_aversion#cite_note-11http://en.wikipedia.org/wiki/MMR_vaccinehttp://en.wikipedia.org/wiki/MMR_vaccinehttp://en.wikipedia.org/wiki/MMR_vaccinehttp://en.wikipedia.org/wiki/MMR_vaccine_controversyhttp://en.wikipedia.org/wiki/MMR_vaccine_controversyhttp://en.wikipedia.org/wiki/MMR_vaccine_controversyhttp://en.wikipedia.org/wiki/Risk_aversion#cite_note-12http://en.wikipedia.org/wiki/Risk_aversion#cite_note-12http://en.wikipedia.org/wiki/Risk_aversion#cite_note-12http://en.wikipedia.org/wiki/General_Medical_Councilhttp://en.wikipedia.org/wiki/General_Medical_Councilhttp://en.wikipedia.org/wiki/Mobile_phonehttp://en.wikipedia.org/wiki/Mobile_phonehttp://en.wikipedia.org/wiki/Risk_aversion#cite_note-13http://en.wikipedia.org/wiki/Risk_aversion#cite_note-13http://en.wikipedia.org/wiki/Mobile_phone_radiation_and_healthhttp://en.wikipedia.org/wiki/Mobile_phone_radiation_and_healthhttp://en.wikipedia.org/wiki/Mobile_phone_radiation_and_healthhttp://en.wikipedia.org/wiki/COSMOS_cohort_studyhttp://en.wikipedia.org/wiki/COSMOS_cohort_studyhttp://en.wikipedia.org/wiki/COSMOS_cohort_studyhttp://en.wikipedia.org/wiki/Briberyhttp://en.wikipedia.org/wiki/Briberyhttp://en.wikipedia.org/wiki/Political_corruptionhttp://en.wikipedia.org/wiki/Political_corruptionhttp://en.wikipedia.org/wiki/Political_corruptionhttp://en.wikipedia.org/wiki/Drugshttp://en.wikipedia.org/wiki/Drugshttp://en.wikipedia.org/wiki/Bad_triphttp://en.wikipedia.org/wiki/Bad_triphttp://en.wikipedia.org/wiki/Bad_triphttp://en.wikipedia.org/wiki/Spiritual_transformationhttp://en.wikipedia.org/wiki/Spiritual_transformationhttp://en.wikipedia.org/wiki/Social_banshttp://en.wikipedia.org/wiki/Social_banshttp://en.wikipedia.org/wiki/Social_banshttp://en.wikipedia.org/wiki/Harm_reductionhttp://en.wikipedia.org/wiki/Harm_reductionhttp://en.wikipedia.org/wiki/Harm_reductionhttp://en.wikipedia.org/wiki/Sexhttp://en.wikipedia.org/wiki/Sexhttp://en.wikipedia.org/wiki/Social_conventionhttp://en.wikipedia.org/wiki/Social_conventionhttp://en.wikipedia.org/wiki/Social_conventionhttp://en.wikipedia.org/wiki/Ethicshttp://en.wikipedia.org/wiki/Ethicshttp://en.wikipedia.org/wiki/Ethicshttp://en.wikipedia.org/wiki/Ethicshttp://en.wikipedia.org/wiki/Medical_prescriptionhttp://en.wikipedia.org/wiki/Medical_prescriptionhttp://en.wikipedia.org/wiki/Medical_prescriptionhttp://en.wikipedia.org/wiki/Extreme_sportshttp://en.wikipedia.org/wiki/Extreme_sportshttp://en.wikipedia.org/wiki/Adrenaline_rushhttp://en.wikipedia.org/wiki/Adrenaline_rushhttp://en.wikipedia.org/wiki/Adrenaline_rushhttp://en.wikipedia.org/wiki/Adrenaline_rushhttp://en.wikipedia.org/wiki/Bragging_rightshttp://en.wikipedia.org/wiki/Bragging_rightshttp://en.wikipedia.org/wiki/Bragging_rightshttp://en.wikipedia.org/wiki/Play_(activity)http://en.wikipedia.org/wiki/Play_(activity)http://en.wikipedia.org/wiki/Play_(activity)http://en.wikipedia.org/wiki/Bragging_rightshttp://en.wikipedia.org/wiki/Adrenaline_rushhttp://en.wikipedia.org/wiki/Adrenaline_rushhttp://en.wikipedia.org/wiki/Extreme_sportshttp://en.wikipedia.org/wiki/Medical_prescriptionhttp://en.wikipedia.org/wiki/Ethicshttp://en.wikipedia.org/wiki/Ethicshttp://en.wikipedia.org/wiki/Social_conventionhttp://en.wikipedia.org/wiki/Sexhttp://en.wikipedia.org/wiki/Harm_reductionhttp://en.wikipedia.org/wiki/Social_banshttp://en.wikipedia.org/wiki/Spiritual_transformationhttp://en.wikipedia.org/wiki/Bad_triphttp://en.wikipedia.org/wiki/Drugshttp://en.wikipedia.org/wiki/Political_corruptionhttp://en.wikipedia.org/wiki/Briberyhttp://en.wikipedia.org/wiki/COSMOS_cohort_studyhttp://en.wikipedia.org/wiki/Mobile_phone_radiation_and_healthhttp://en.wikipedia.org/wiki/Risk_aversion#cite_note-13http://en.wikipedia.org/wiki/Risk_aversion#cite_note-13http://en.wikipedia.org/wiki/Mobile_phonehttp://en.wikipedia.org/wiki/General_Medical_Councilhttp://en.wikipedia.org/wiki/Risk_aversion#cite_note-12http://en.wikipedia.org/wiki/MMR_vaccine_controversyhttp://en.wikipedia.org/wiki/MMR_vaccinehttp://en.wikipedia.org/wiki/Risk_aversion#cite_note-11http://en.wikipedia.org/wiki/Cambridge_Universityhttp://en.wikipedia.org/wiki/Cambridge_Universityhttp://en.wikipedia.org/wiki/Winton_Professorship_of_the_Public_Understanding_of_Riskhttp://en.wikipedia.org/wiki/David_Spiegelhalterhttp://en.wikipedia.org/wiki/David_Spiegelhalterhttp://en.wikipedia.org/wiki/Opportunity_costhttp://en.wikipedia.org/wiki/Health_and_Safety_Executive


6/6

Risk AversionCopyright 1999-2001 Samuel L. Baker

The interactive tutorial onriskcalculated the expected values of somegames and securities. It made a connection between the expected valueof a security and its market price. This use of the expected value is basedon the Law of Large Numbers, which is a statement about what happenswhen a game is repeated over and over and over again. If a game can berepeated many times, good luck and bad luck tend to wash out.

Risk averse means being willing to pay money to avoid playing a risky

game, even when the expected value of the game is in your favor.

Insurance and Risk Aversion

Enough fun and games. Back to something serious -- insurance.

The theory of risk aversion was developed largely to explain why peoplebuy insurance.

Buying insurance is hard to justify using the theory of expected value.That's because buying insurance is a gamble with a negative expected

value, in dollar terms.

Regular indemnity insurance specifies that you get money if certain thingshappen. If those things don't happen, you don't get any money. So far,that's just like playing roulette.

In return for the chance to get some money, you bet some money bypaying the insurance company a "premium." The insurance companykeeps your premium if you don't have a claim. So far, that's still just likeplaying roulette.

Over the large number of people who sign up for insurance, the insurancecompany pays out less money in claims than it takes in. If it doesn't, itcan't stay in business. Your expected payoff is therefore less than yourpremium, unless you can fool (or legally force) the insurance companyinto selling you a policy with odds are in your favor. Buying insurance hasa negative expected value. Still just like playing roulette.
http://hspm.sph.sc.edu/courses/econ/Risk/Risk.htmlhttp://hspm.sph.sc.edu/courses/econ/Risk/Risk.htmlhttp://hspm.sph.sc.edu/courses/econ/Risk/Risk.htmlhttp://hspm.sph.sc.edu/courses/econ/Risk/Risk.html

risk aversion (8522)

Documents