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.. 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。
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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。
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It was as if, when we went through this search tree, we never remembered what we got at the bottom, and we just re-computed things over and over.
如果当我们遍历完这棵树，我们不可能，记得我们在最下面得到什么结果,我们只是不断地重复计算，所以这让。
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I wanted to show an example with real data that I computed and that's what's up on the screen.
我用真实的数据做了一个案例,请看上方的屏幕。
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I computed the average return on stocks over that time period and I computed the average return on bonds over that time period.
我计算了那个时间段的股票平均收益率,和债券平均收益率。
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So I just computed the radius of that particular thing. Right?
这个点的半径，对不对？,计算角度是一样的道理？
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I've computed a 13 value which is 13.
我已经计算了,一个值答案是。
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i I computed the value if I don't include i.
如果我不包括。
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The real interest rate, computed from nominal rates, is equal to one plus the nominal rate divided by one plus the inflation rate, so it corrects for inflation.
由名义利率算得的实际利率 等于,/,它是一个经通胀调整后指标
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You can see the different points-- I've calculated this using data from 1983 until 2006-- and I computed all of the inputs to those equations that we just saw.
你可以观察不同的点-,我用从1983年到2006年的数据-,代入我们刚教授的等式,进行了计算。
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There're some things that cannot be computed.
总会有一些无法计算的东西。
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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。
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i I've computed the value if I include i.
如果我包括了,我已经计算过总价值。
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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。
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, r1, and r2 for those and I plugged it into that formula, which we just showed.
我计算了σ1，σ2，r1和r2，I，computed，the，σ1，，σ,代入我们刚刚展示的公式。
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So I might as well return the without i value I just computed.
所以我不妨返回除去i外,我刚算过的值。
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