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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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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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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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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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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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.. 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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The variance of the Gaussian -- STUDENT: is less.
高斯分布的变化-,学生：更小。
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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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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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Expected value is good and variance is bad because that's risk; that's uncertainty.
期望值越高越好,方差就相反,因为方差代表着风险,也就是不确定性
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I feel like I have to introduce concepts like variance and co-variance and correlation in order to talk about finance; so that's what we'll do in Lecture Two.
我会讲到像方差,协方差,相关系数,这样的概念,为金融学的内容作一些铺垫,我们会在第二课讲到
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But, in between, if some other number, it'll be some blend of the--mean and variance of--the portfolio will be some blend of the mean and variance of the two assets.
但如果是在0和1之间的其他数值，这个投资组合的均值和方差将会是,两项资产各自的均值和方差的综合结果。
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You'd have a higher expected return with no more variance.
你的预期收益率提高了，但风险没有增加。
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But ultimately, everyone agrees I-- that's the premise here, that for the-- if you're comparing two portfolios with the same variance, then you want the one with the higher expected return.
但归根结底大家都会同意这一点-,这是一个前提-,当你比较两个有相同方差的投资组合时，你会选择预期收益率高的那一个。
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The more x moves, the bigger the variance is.
参数的变动越多,方差就越大
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They divide by n-1 to make it an unbiased estimator of the population variance, but I'm just going to show it in a simple way here.
当除以n-1表示的是对总体的,无偏估计,我在这里只是说的简单一点
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