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They like to--when they're computing the investment yield, they want to be completely honest and not use any rules of thumb.
当他们计算投资收益率的时候,他们需要完全精确,而非用经验公式
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If you're comparing two portfolios with the same expected return, then you want the one with the lower variance.
比较两个有相同预期收益率的投资组合时，你会选择方差小的那一个。
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The investment rate is telling you how much money you're really making on an annualized basis, so it's very simple.
投资收益率反映了基于一年来看,你实际赚了多少钱,非常简单
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It shows the standard deviation of the return on the portfolio as a function of the expected return on the portfolio.
它是投资组合的收益标准差,关于预期收益率的函数图像。
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.. The equity premium is the-- 2.8% this short-term 2.8% is the riskless return, historically, for a period of almost 200 years.
股权溢价就是-,这个短期无风险投资收益率是，是根据近200年的数据得出的。
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Also, they don't have to actually--in the old days, they didn't actually have to compute the investment rate.
其实在过去人们不必,真正计算投资收益率
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Stocks have paid 4% more a year over this incredibly long time period than short-term bonds.
股票在相当长的一段时间里,每年都比短期债券投资收益率,高出4个百分点。
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When you ask for the investment rate, you want to know the truth-- how much am I really getting so they don't monkey around here.
当你问投资收益率时,你要知道,我到底能赚多少,所以他们不再偷懒
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The return he got from 1996 to 2006 was 17% a year on investments.
从1996到2006,他的个人投资收益率为一年17%
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2% You could say, I think my portfolio has an expected return of 12%-- that would be better than if it had an expected return of 10%.
如果一个投资组合的预期收益率有-,那就比一个只有10%的投资组合要好。
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So, that's how you go from the discount rate to the investment rate.
这就是从折扣率到投资收益率的换算过程
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This is the return on stocks for a period of almost 200 years.
这个是200年内股票的投资收益率。
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Last year the return on the Yale portfolio was 28% in one year.
去年耶鲁大学投资组合的收益率,是28%
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The return, of course, in any given time period is the percentage increase in the portfolio; or, it could be a negative number, it could be a decrease.
当然了，收益率是一定时间内,投资组合的增长率;,也可能是一个负数，表示负增长。
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Over this time period, that portfolio had an expected return of something like a little over 9% and it had a standard deviation of a little over 9%.
在这个时间段，这个投资组合的预期收益率是,9%多一点%,标准差是9%多一点。
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That's how we go from the discount rate to the investment rate.
这就是从折扣率到投资收益率的换算过程
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They also have something up here called the investment rate. Yes?
这上面还有一个,叫做投资收益率,有问题吗
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But ultimately, everyone agrees I-- that's the premise here, that for the-- if you're comparing two portfolios with the same variance, then you want the one with the higher expected return.
但归根结底大家都会同意这一点-,这是一个前提-,当你比较两个有相同方差的投资组合时，你会选择预期收益率高的那一个。
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Firms that do that are, in practice, however, the minority and most mutual funds have some gimmick or some special-- they claim to be beating the market not forming the optimal portfolio.
然而实际上,这么做的公司很少,大部分共同基金都会耍些花招,或有一些特别的...,他们强调他们的收益率将强于市场平均水平,而非建立最佳投资组合
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Then, once we did that we could plug that into the formula that I gave you last time and get the standard deviation of the portfolio and the expected return on the portfolio.
再将估算出的数值代入到,上节课给你们的公式中,就能得到资产投资组合的标准差,和该投资组合的预期收益率
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What is the portfolio expected return?
投资组合的预期收益率是什么？
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Over the past twenty years, we've generated 15.6% per annum return, but that headline number obviously has a lot to do with the equity orientationof the portfolio but doesn't describe the importance of the diversification.
过去20年间,我们的年收益率达到15.6%,虽然媒体头条报道这一收益率,总强调与投资组合的股权导向有很大关系,但没有描述出投资多元化的重要性
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The equity orientation drove the returns but the diversification allowed us to deliver those returns in a stable fashion, which is incredibly important for an institution like Yale that requires a steady supply of funds to finance its operations.
股票导向型投资会推动收益率上升,但多元化能让收益更平稳,这对于耶鲁这样的机构极为重要,因为它需要稳定的资金供给,为学校运营提供财务支持
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Now, underlying our theory is the idea that we measure the outcome of your investment in your portfolio by the mean of the return on the portfolio and the variance of the return on the portfolio.
而理论的基础是,我们通过计算,组合收益率的均值，和组合收益率的方差,来衡量一个投资组合的优劣。
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So, the optimal thing to do if you live in a world like this n is to get n as large possible and you can reduce the standard deviation of the portfolio very much and there's no cost in terms of expected return.
如果现实中也这样简单的话,那么你就尽量增大,这样就能让投资组合的标准差,就会大大降低,从预期收益率的角度来看,这样做的成本是零。
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Suppose someone has been investing money for n years and xi is the return on the investment in a given year.
假设有人投资了n年,Xi是第i年的收益率
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