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Managing Risks

Managing Risks - Managing Risks Prelims… • Attitudes...

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Unformatted text preview: Managing Risks: Prelims… • Attitudes towards risk • Risk neutral: indifferent between uncertain outcome and the average outcome • Risk averse: prefers the average outcome to an uncertain outcome • Risk taker: prefers the uncertain outcome (i.e, prefers the gamble) • Note: not the same as different beliefs Risk attitudes: Examples • Suppose individual has $10 • Gamble: bet $x and win $20 or $0 w/ probability (1/2;1/2) • Find the amount $x willing to pay to participate: • If (a) utility U(w)=w (i.e, risk neutral) • If (b) utility U(w)=w 1/2 (i.e., risk averse) • If (c) utility U(w)=w 2 (i.e., risk taker) Risk neutral:… • u 10-x 30-x 20-x 20-x U(w)=w 30-x 10-x Risk neutral: maximum bet If bet $x, the final wealth will be: • For risk-neutral, U=w, expected utility is: • Since individual gets utility u=10 if doesn’t not participate, then $x is such that: w x prob x prob =-- 30 0 5 10 0 5 . . EU x x x [ ] ( . )( ) ( . )( ) = - + - = - 05 30 05 10 20 U EU x x ( ) [ ] 10 10 10 20 10 = = ⇒ =- ⇒ = Risk neutral: Discussion • The risk neutral investor is indifferent between the expected utility and the utility from consuming the average wealth, $10. • Alternatively, risk neutral individual is not willing to pay a premium to avoid the gamble Risk averse: maximum bet If bet $x, the final wealth will be: • For risk-averse guy, U=w...
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Managing Risks - Managing Risks Prelims… • Attitudes...

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