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We're going to assume that everybody knows the possible strategies everyone else could choose and everyone knows everyone else's payoffs.
我们假设,每个人都知道其他人可能选择的策略,每个人都知道其他人的收益
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The difference between the average return for colleges and universities and Yale's returns has added $14.4 billion dollars to the University's coffers.
其他高校的平均收益率,与耶鲁的收益率的差距,为耶鲁财政增加了144亿美元
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We had the kind of payoff where we care about our own grade, and Travis has mentioned the kind of payoff where you might care about other people's grades.
一种是只在意自己的收益,另一种像特拉维斯提到的,在意其他人的收益
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When Modigliani and Miller wrote, there was a differential tax rate between dividends and capital gains.
莫迪利阿尼和米勒写到,如果在股利和资本收益间,有一个随其他因素变化的税率
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It goes up and down depending on the outlook for earnings and maybe other factors.
根据收益前景或者其他因素,这个数字可能会上升或下降
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As I solve the maximization problem, how do I maximize my payoff given that other people are choosing S-i?
解最大化问题时,如果其他人选了S-i,我如何最大化自己的收益呢
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So to say it in words, Player i's strategy "s'i" is strictly dominated by her strategy "si," if "si" always does strictly better -- always yields a higher payoff for Player i -- no matter what the other people do.
用文字来描述就是,参与人i的策略s'i严格劣于si,如果si总是更好的选择,即总能给参与人i带来更高的收益,而无论其他参与人怎么选
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That term was actually coined by economists, Prescott and Mehra; it's now in general use. That is, it just seems that stocks so much outperform other investments.
这个术语是由经济学家,普雷斯科特和梅拉提出,现在被广泛引用,这表明股票收益远超其他投资
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The title of the book, Stocks for the Long Run-- stocks always outperform other investments for the long run and he says it's not due to selection bias.
书名是为《股市长线法宝》,长期投资中股票总是比其他资产有更高的收益,他认为他在研究中排除了选择性偏差
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So, we should use that, but people in finance resist using that because it's a lower number and when you're advertising your return you want to make it look as big as possible.
所以我们应该用这个指标,但金融界反感使用几何平均,因为它比其他平均数都来得小,他们为自己的收益率做广告时,当然希望数字越大越好
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I'll let you read Siegel and his discussion of this possibility, ... but I think that-- what I want to get now is not necessarily any agreement on whether you believe that there's such a high excess return for stocks.
我会要求你们读西格尔的书,以及他对这种可能性的讨论，但是我认为-,你们并不需要,同意炒股的收益,远远高于其他的投资方式。
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The price of a share is the price of the ownership of that earnings' stream If I buy a share I'm in with everyone else who owns the company and I have a claim on the earnings' stream, but the earnings' stream is a year-by-year thing.
每股价格是指,收入所有权的价格,如果我和其他股东一样买了一份股票,那么我就对收益有要求权,但收益是逐年计算的
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