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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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One more thing, I said they're not independent, so we have to talk about the covariance between the returns.
还有，我说过它们不是相互独立的，因此我们还需要讨论两个收益率的协方差。
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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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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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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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.. 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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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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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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If you get a lot of negative products, that makes the covariance negative.
很多个负值的结果相加,就会使协方差是一个负值
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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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.. 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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A negative covariance means that they tend to move opposite each other.
负值的协方差就表示,二者反向变动
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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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Covariance is a measure of how much two variables move together.
协方差衡量的是两个变量一起变动的情况
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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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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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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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A positive covariance means that the two move together.
一个正值的协方差表示两个变量同向变动
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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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You take all the risky assets ... and you analyze them first to get their-- you have to do a statistical analysis to get their expected returns, their variances, and their covariances.
你需要对所有的风险资产进行分析,首先要得到它们的-,你必须要做一个统计分析,算出它们的预期收益率，方差，和它们的协方差。
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Another concept that's very basic here is covariance.
另一个基本的概念是协方差
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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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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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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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