• One standard deviation happens one draw out of three, two standard deviations one out of twenty, three standard deviations is one out of one hundred.

    落在一个标准偏差之外的概率是1/3,两个标准差之外的概率是1/20,三个标准差之外是百分之一

    耶鲁公开课 - 金融市场课程节选

  • Depending on where the assets expected returns are and the assets' standard deviations, we can see that we might be able to do better than--have a lower variance than either asset.

    根据资产的预期收益,以及收益的标准差,可以看到我们有更好的选择,这里的方差值比以上两种方案都要低。

    耶鲁公开课 - 金融市场课程节选

  • 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。

    耶鲁公开课 - 金融市场课程节选

  • The way you would go about it, if you're a portfolio manager, is you have to come up with estimates of the inputs to these formulas-- that means the expected returns, the standard deviations, and the covariances.

    你所要做的,如果你是一个资产经理,你要做的事情就是,对公式里面的一些参数进行估计-,那些参数包括预期收益,标准差,和协方差。

    耶鲁公开课 - 金融市场课程节选

  • I don't find that my analysis is profound in the final answer, I just took some estimates using my data and, again, we could-- if someone wanted to argue with us they could argue with my estimates of the expected returns of the standard deviations and the covariances, but not with this theory.

    我在计算过程中并没有做太深入的分析,我只是用我的数据做了一下大概的估计,我再说一次,我们可以-,如果有人想就这个问题与我们争辩,他们可以争论我对期望收益的估计,或是争论标准差和协方差的估计值,但并不会针对理论本身。

    耶鲁公开课 - 金融市场课程节选

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