Finance Essay

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Risk aversion is a concept in psychology, economics, and finance, based on the behavior of humans (especially consumers and investors) while exposed to uncertainty to attempt to reduce 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, a risk-averse investor might choose to put his or her money into a bank account with a low but guaranteed interest rate, rather than into a stock that may have high expected returns, but also involves a chance of losing value. ------------------------------------------------- Utility of money[edit source | editbeta] In expected utility theory, an agent has a utility function u(x) where x represents the value that he might receive in money or goods (in the above example x could be 0 or 100). Time does not come into this calculation, so inflation does not appear. (The utility function u(x) is defined only up to positive linear affine transformation - in other words a constant offset could be added to the value of u(x) for all x, and/or u(x) could be multiplied by a positive constant factor, without affecting the conclusions.) An agent possesses risk aversion if and only if the utility function is concave. 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% chance of receiving 0) is, , and if the person has the utility function with u(0)=0, u(40)=5, and u(100)=10 then the expected 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

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