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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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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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In fact, different people might make different choices about how much risk they're willing to bear to get a higher expected return.
事实上，为了获得高的预期收益率,人们愿意承受的风险,也会不同。
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To calculate the expected utility of your wealth, you might also have to look at the expected return, or the geometric expected return, or the standard deviation.
要计算你财富的期望效用,你也许还要研究预期收益曲线,或几何预期收益率,或是标准差
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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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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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I'm going to drop more than the independence assumption, I'm going to assume that the assets don't have the same expected return and they don't have the same expected variance.
我还想做出一些改动，即这些资产的预期收益率,是各不相同的,方差也是不同的。
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You should see that the blue line is better than the pink line because, for any expected return, the blue line is to the left of the pink line, right?
可以看到蓝线比粉线好,原因是对于任意的预期收益率，蓝线都在粉线的左边，对吧？
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You'd have a higher expected return with no more variance.
你的预期收益率提高了，但风险没有增加。
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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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You take all the risky assets ... and you analyze them first to get their-- you have to do a statistical analysis to get their expected returns, their variances, and their covariances.
你需要对所有的风险资产进行分析,首先要得到它们的-,你必须要做一个统计分析,算出它们的预期收益率，方差，和它们的协方差。
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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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r1 Asset 1 has expected return r1.
第一项资产的预期收益率是。
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I computed the returns on the stocks, bonds, and oil for every year from 1983 and I computed the average returns, which I take as the expected returns, I took the standard deviations, and I took the covariance.
我计算了从1983年以来每年的股票,债券和石油的收益，从而得出平均收益率，这些平均收益率作为预期收益率，然后算得标准差及协方差。
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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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