.. I computed the efficient portfolio frontier for various-- it's the efficient portfolio frontier using the formula I just gave you.

我计算了来自不同组合有效边界-,这一条有效投资组合边界,就是用刚刚给出的公式算出来的。

耶鲁公开课 - 金融市场课程节选

What I did in this diagram is I computed the efficient portfolio frontier-- now it's the blue line with three assets.

在这张图表中,我计算了有效边界-,蓝色线表示三种资产的组合。

耶鲁公开课 - 金融市场课程节选

What I have up there on the diagram are calculations I made for the efficient portfolio frontier with three assets.

上面的图形是我已经算好的,三种资产的有效投资组合边界。

耶鲁公开课 - 金融市场课程节选

The pink line here is the efficient portfolio frontier when we have only stocks and bonds to invest.

这条粉色曲线就是有效边界,这个投资组合只包括了股票和债券。

耶鲁公开课 - 金融市场课程节选

Once you've got them together, then you can compute the efficient portfolio frontier without the riskless asset.

当你明确了这些参数后，就可以算出没有无风险资产情况下的,有效边界了。

耶鲁公开课 - 金融市场课程节选

In fact, I have it--suppose we have three assets and we want to compute the efficient portfolio frontier, the mean and variance of the portfolio.

事实上，假如我们拥有三种资产,我们想计算有效边界，及投资组合的均值和方差。

耶鲁公开课 - 金融市场课程节选

He estimates, for his purposes, and he shows you calculations of the efficient portfolio frontier.

他用自己的角度估算了参数,他还给出了计算有效边界的方法。

耶鲁公开课 - 金融市场课程节选

That's what we have to know to compute the efficient portfolio frontier with three assets.

这些都是计算三种资产的有效边界,所需要用到的。

耶鲁公开课 - 金融市场课程节选

That means that you want to pick, ultimately, a point on this-- this line is tangent to the efficient portfolio frontier with all the other assets in it.

那意味着你会最终会在这上面选一个点-,这条直线是与有效边界相切的,后者包含了所有的资产组合。

耶鲁公开课 - 金融市场课程节选

Jeremy Siegel, in his book, which is assigned for this course, is really emphasizing this capital asset pricing model, emphasizing the kind of efficient portfolio frontier calculations that I've done.

杰里米·西格尔的著作，是本课的指定书目，书中着重讲述了资本资产定价模型，以及有效边界等的计算方法,这部分我已经讲完了。

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。

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If we want to add that asset to the portfolio, what it does is it produces an efficient portfolio frontier that is now a straight line; I show that on the diagram.

如果我们将其加入到投资组合中去，则会生成一条资产组合的有效边界,即一条直线;,我在图里把它画出来了。

耶鲁公开课 - 金融市场课程节选

Where are they on the efficient portfolio frontier?

那运用有效边界分析会如何呢？

耶鲁公开课 - 金融市场课程节选

You would call it an efficient portfolio frontier.

这就是有效边界。

耶鲁公开课 - 金融市场课程节选

Then he computes the efficient portfolio frontier.

然后他又计算出有效资产组合边界。

耶鲁公开课 - 金融市场课程节选

Tangent means that it has the same slope, it just touches the efficient portfolio frontier for risky assets at one point, and the slope of the efficient portfolio frontier, including the riskless asset, is a straight line that goes through the tangency point, here.

相切意味着斜率相同，它与包含风险资产的有效边界,交与一点，而包含无风险资产的，有效边界，则是一条过切点的直线，切点在这里。

耶鲁公开课 - 金融市场课程节选