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It shows the standard deviation of the return on the portfolio as a function of the expected return on the portfolio.
它是投资组合的收益标准差,关于预期收益率的函数图像。
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I want now to carry that forward into something a little bit more focused on the portfolio problem.
现在从这个基础上拓展一下,更侧重于投资组合方面的问题。
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The return on the portfolio is x1 r1 + x2 r2 + x3 r3.
这个投资组合的收益是。
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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。
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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
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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。
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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。
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If you read his Pioneering Portfolio Management on the syllabus, he really has a preference for equities.
如果你阅读他的著作《开拓投资组合的管理》的摘要,他确实对股票有偏好。
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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
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This point right here is, on the pink line, is a portfolio 100% bonds.
粉线上的这一点，是一个100%债券的投资组合。
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Last year the return on the Yale portfolio was 28% in one year.
去年耶鲁大学投资组合的收益率,是28%
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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。
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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。
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Where are they on the efficient portfolio frontier?
那运用有效边界分析会如何呢？
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In that year, we were early on in terms of diversifying the portfolio -we'd only been working on that program for two years -and even so,the negative return was less than 1%, so it was a modest negative return.
在那一年,我们还处于投资组合多元化的初期,刚刚开始2年,即便如此,股灾时我们的亏损小于1%,这只是一个轻微的亏损
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x1 The portfolio mean and variance will depend on x1 x1=1 in the way that if you put--if you made x1 = 1, it would be asset 1 x1=0 and if you made x1 = 0, then it would be the same as asset 2 returns.
投资组合的均值和方差取决于1,如果你令，投资组合的均值方差就与第一项资产相等1,如果你令，那么它们就会与第二项资产的参数相等。
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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。
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