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There's no correlation between them ... and that means that the variance-- and I want to talk about equally-weighted portfolio.
它们之间没有相关性,也就是说。。。方差-,我想讲一下,权重相等的投资组合。
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There's also another variance measure, which we use in the sample-- There's also another variance measure, which is for the sample.
还有另一个离散指标,我们用以考察样本,这是另一个离散指标,用于考察样本
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So in return to, we have a slight variance here, -- where I'm defining apparently -- declaring a function called cube.
作为应答，这里我们有一点变化，这里我显然定义了-,声明了一个叫做cube的函数。
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STUDENT: The variance of the Gaussian seems to be less than the variance of the uniform.
学生：高斯分布的变化比,均匀分布的变化小。
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If you're comparing two portfolios with the same expected return, then you want the one with the lower variance.
比较两个有相同预期收益率的投资组合时，你会选择方差小的那一个。
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This portfolio, the minimum variance portfolio, is 9% oil, 27% stocks, and 64% bonds and most of the--many choices you can make.
这个最小方差的资产配置是9%的石油，27%的股票和64%的债券,而大部分。。。你可以有许多选择。
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But, on the other hand, you don't want high variance because that's risk; so, both of those matter.
但另一方面，你不想要高水平的方差,因为它代表风险;,因此这两个参数都很重要。
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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。
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Let's look at this 8th variance of this, otherwise, simple example.
这是这个例子的第8个变量版本，很简单。
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I'm not going to tell you what you want to do except to say, you would never pick a point below the minimum variance portfolio, right?
我不是教你怎样去组合，当然了，你不会选择一个,曲线上最小方差点以下的资产组合，对吧？
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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
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.. I started out with the equally-weighted-- I was talking about stocks-- about n stocks that all have the same variance and are all independent of each other.
开始的时候我讲了等权重的-,我开始时讲了股票-,几支拥有相同方差的股票,彼此间相互独立。
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There's a very important principle that finally comes out here, it is that you always want to reduce the variance of your portfolio as much as you can.
现在这里有一个非常重要的原则，即你总是想要降低你投资组合的方差,降得越低越好。
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The variance of the Gaussian -- STUDENT: is less.
高斯分布的变化-,学生：更小。
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I'm going to drop more than the independence assumption, I'm going to assume that the assets don't have the same expected return and they don't have the same expected variance.
我还想做出一些改动，即这些资产的预期收益率,是各不相同的,方差也是不同的。
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The standard deviation is the square root of the variance.
标准差是方差的平方根
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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。
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Well if you're an investor, you don't like variance.
假如你是一个投资者，你不喜欢风险。
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Central tendency is a measure of the center of a probability distribution of the-- Central tendency is a measure-- Variance is a measure of how much things change from one observation to another.
集中趋势用以描述,一组概率分布的中心,集中趋势...,而方差衡量的是,各个观察值之间的变化
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The minimum variance portfolio is down here.
风险最小的投资组合在这一点取到。
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What we want to do now is compute the mean and variance of the portfolio-- or the mean and standard deviation, since standard deviation is the square root of the variance-- for different combinations of the portfolios.
我们现在要做的是,计算这个投资组合的均值和方差-,或者均值和标准差，因为标准差的平方就等于方差-,这对任何投资组合都是一样的。
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The equally-weighted case that I gave a minute ago was one where the two assets had--were at the same-- had the same expected return and the same variance; but this is quite a bit more general.
我刚刚举的相同权重的例子,表示两种资产-,有相同的预期收益和相同的方差;,但这种情况更加普遍一些。
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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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That is the sample variance.
这就是样本方差
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So, that's the variance.
这就是方差
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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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And in this context, the length of that array is stored in Arg C. Well, let's take a look at a slight variance of this that reveals further what we can do and reveals what a string really is.
关于这点，那个数组的长度被存储在ArgC中,好的，让我们看看这个轻微的变化,那个揭示了我们可以做的,和字符串实际上是什么。
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What we did--the core theoretical framework that we had-- was the mean variance theory, which led us to the capital asset pricing model.
我们讲到了投资组合多元化的核心理论框架,即均值-方差模型,之后又讲到了资本资产定价模型
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.. If you can find assets that all have-- that are all independent of each other, you can reduce the variance of the portfolio very far.
如果你能找到这样的一些资产-,一些相互独立的资产，就能很大程度上缩小这个投资组合的方差。
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Oil, bonds, and stocks are all independent-- somewhat independent--they're not perfectly independent, but they're somewhat independent and, to the extent that they are, it lowers the variance.
石油，债券和股票都是互相独立-,一定程度上独立，不是绝对的独立，但一定程度上独立，可以使方差值变小，降低风险。
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