So Yale had a 28% return on its portfolio last year, which was number one of all college endowments.

去年耶鲁基金获得了28%的收益,收益率高居全美高校榜首

耶鲁公开课 - 金融市场课程节选

It's the world portfolio, it's everything and we compute the expected return on that portfolio, rm that's rm.

这就产生了世界投资组合,然后我们在此基础上计算出预期收益，所得值就是。

耶鲁公开课 - 金融市场课程节选

The return on the portfolio is x1 r1 + x2 r2 + x3 r3.

这个投资组合的收益是。

耶鲁公开课 - 金融市场课程节选

This is a year of financial crises, so I'm warning you ahead that -don't expect a 28% return on the Yale portfolio for the coming year.

金融危机爆发,所以我先提前给大家打预防针,别期望今年耶鲁基金,能延续28%的收益

耶鲁公开课 - 金融市场课程节选

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。

耶鲁公开课 - 金融市场课程节选

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。

耶鲁公开课 - 金融市场课程节选

So that's the expected return and efficient portfolio frontier problem.

这就是预期收益,和有效边界问题。

耶鲁公开课 - 金融市场课程节选

What is the portfolio expected return?

投资组合的预期收益率是什么？

耶鲁公开课 - 金融市场课程节选

So, for example, at an annual expected return of 12% if I have a portfolio of stocks, bonds, and oil I can get a standard deviation of something like 8% on my portfolio.

例如，在年预期收益12%的情况下%,我有股票，债券和石油的投资组合,在这个组合里,我的投资组合可以取到8%的标准差。

耶鲁公开课 - 金融市场课程节选

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。

耶鲁公开课 - 金融市场课程节选

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

耶鲁公开课 - 金融市场课程节选

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。

耶鲁公开课 - 金融市场课程节选

.. The portfolio expected return-- x3 we have to choose three things now: x1, x2, and x3.

要计算投资组合的预期收益-,我们必须确定三个值x1，x2和。

耶鲁公开课 - 金融市场课程节选

Again, I'm not going to spend much time on this, of the ith asset is the regression coefficient when you regress the return on the ith asset on the return of the market portfolio.

再强调一次，我不打算花太多时间在这个等式上面，但要注意的是当你想将市场组合收益，but，the，β,回归到第i资产收益中去,第i资产β系数是线性回归方程的,回归系数。

耶鲁公开课 - 金融市场课程节选