Underlying this analysis, we have estimates of the expected returns on assets, notably, the expected returns on stocks and bonds.

凭借这个分析，我们可以估算出资产预期投资收益，特别是股票和债券的预期收益。

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

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。

耶鲁公开课 - 金融市场课程节选

They might say my sample period was off, ... but that's what the theory-- ... using my data for the sample period that I computed-- the expected returns and co-variances says one should do.

他们可能说我的采样周期是有问题的，不过我的结果都是靠理论-,我采用自己收集的数据计算出-,预期收益和协方差可以用来指导我们的投资行为。

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

But, I've dropped that assumption and now I'm going on to assuming that they're taking account of their dependence on each other, taking account of their different expected returns, and taking account of their different covariances and variances; so that's what we've got.

不过我已经放弃了那个假定,我现在假定,我们需要考虑它们彼此间的相关性，它们有着不同期望收益，不同的协方差和方差;,这是我们所学到的。

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

We want a high expected value of returns, but we don't like variance.

我们希望收益的期望值较高,并且稳定

耶鲁公开课 - 金融市场课程节选