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