风险回避

nullRisk Aversion(风险回避）Risk Aversion(风险回避）Author(s): Matthew Rabin and Richard H. ThalerCase Case suppose we know that Johnny is a risk-averse expected utility maximizer, and that he will always turn down the 50-50 gamble of losing $10 or gaining $11. From the description above, what is the biggest Y such that we know Johnny will turn down a 50-50 lose $100/win $Y bet? nulla) $110 b) $221 c) $2,000 d) $20,242 e) $1.1 million f) $2.5 billion g) Johnny will reject the bet no matter what Y is. h) We can't say without more information about Johnny's utility function. nullDid you guess a, b, or c? If so, you are wrong. Guess again. Did you guess d? Maybe you figured we wouldn‘t be asking if the answer weren’t shocking, so you made a ridiculous guess like e, or maybe even f. If so, again you are wrong. Perhaps you guessed h, thinking that the question is impossible to answer with so little to go on. Wrong again. nullThe correct answer is g. Johnny will turn down any bet with a 50 percent risk of losing at least $100, no matter how high the upside risk. Johnny's risk aversion over the small bet means, therefore, that his marginal utility for wealth must diminish incredibly rapidly. nullThis means, in turn, that even the chance for staggering gains in wealth provide him with so little marginal utility that he would be unwilling to risk anything significant to get these gains.explainsexplains Suppose you have initial wealth of W, and you reject a 50-50 lose $10/gain $11 gamble because of diminishing marginal utility of wealth. Then it must be that U(W + 11) - U(W) ≤U(W) - U(W-10)nullHence, on average you value each of the dollars between Wand W + 11 by at most 10/11 as much as you, on average, value each of the dollars between W-10 and W . this implies that you value the dollar W + 11 at most 10/11 as much as you value the dollar W-10. null Iterating this observation, if you have the same aversion to the lose $10/gain $11 bet at wealth level W+ 21, then you value dollar W+ 21 + 11 = W+ 32 by at most 10/11 as you value dollar W+ 21 -10 = W+ 11,which means you value dollar W+ 32 by at most 10/11 X 10/11 ≈5/6 as much as dollar W-10. You will value the W + 210th dollar by at most 40 percent as much as dollar W-10, and the W + 900th dollar by at most 2 percent as much as dollar W-10.nullIn words, rejecting the 50-50 lose $10/gain $11 gamble implies a 10 percent decline in marginal utility for each $21 in additional lifetime wealth, You care less than 2 percent as much about an additional dollar when you are $900 wealthier than you are now. This rate of deterioration for the value of money is absurdly high, and hence leads to absurd risk aversion. nullTable 1 provides a set of further examples based on the theorem in Rabin (2000). In each case, if a rational expected utility maximizer turns down the bet for modest stakes in the left-hand column, then logical consistency will require turning down the corresponding bet in the right-hand column. nullConclusionConclusionRabin的定理用类似的代数运算说明，如果用终身财富的效用来解释面对中等程度风险时的态度，就意味着对于在现实中每个人都认为是极富吸引力的风险机会，预期效用理论的预测是极度回避。 论文认为，预期效用理论是对大多风险态度的解释是不正确的，其中一些经济学家认为用这个理论是误导。What Does Explain Risk Aversion? What Does Explain Risk Aversion? The expected utility theory doesn't explain the modest-scale risk aversion we observe. We think that the right explanation incorporates two concepts that have been mentioned before in the "Anomalies" series: loss aversion and mental accounting. Loss aversion(损失厌恶）Loss aversion(损失厌恶）Loss aversion is the tendency to feel the pain of a loss more acutely than the pleasure of an equal-sized gain. It models decisionmakers who react to changes in wealth, rather than levels, and are roughly twice as sensitive to perceived losses than to gains.nullWhen prospects are considered as gains and losses relative to the status quo (or some other reference point), and losses are weighted roughly twice as much as gains, then coin-flip bets offering less than two-to-one odds are routinely rejected. Mental accounting(心理账户）Mental accounting(心理账户）Mental accounting, which refers to if small-scale better-than-fair gambles were evaluated in broader perspective, people would be more likely to accept them. They would realize that by taking a series of such bets, the gains would tend to outweigh the losses in the long run. nullBenartzi and Thaler (1995) use it to characterize their explanation of the equity premium puzzle. If investors focus on the long-term returns of stocks they would recognize how little risk there is, relative to bonds, and would be happy to hold stocks at a smaller equity premium. Instead, they consider short-term volatility, with frequent mental accounting losses, and demand a substantial equity premium as compensation. The endThe endThanks!