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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 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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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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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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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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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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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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The way you would go about it, if you're a portfolio manager, is you have to come up with estimates of the inputs to these formulas-- that means the expected returns, the standard deviations, and the covariances.
你所要做的，如果你是一个资产经理，你要做的事情就是,对公式里面的一些参数进行估计-,那些参数包括预期收益，标准差，和协方差。
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But, I've dropped that assumption and now I'm going on to assuming that they're taking account of their dependence on each other, taking account of their different expected returns, and taking account of their different covariances and variances; so that's what we've got.
不过我已经放弃了那个假定,我现在假定,我们需要考虑它们彼此间的相关性，它们有着不同期望收益，不同的协方差和方差;,这是我们所学到的。
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I don't find that my analysis is profound in the final answer, I just took some estimates using my data and, again, we could-- if someone wanted to argue with us they could argue with my estimates of the expected returns of the standard deviations and the covariances, but not with this theory.
我在计算过程中并没有做太深入的分析，我只是用我的数据做了一下大概的估计,我再说一次，我们可以-,如果有人想就这个问题与我们争辩,他们可以争论我对期望收益的估计,或是争论标准差和协方差的估计值，但并不会针对理论本身。
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Covariance is--we'll call it--now we have two random variables, so cov... I'll just talk about it in a sample term.
协方差是...我们有两个随机变量,x和y的协方差是,从样本的角度来说
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So, the higher the covariance is, generally, the higher--you can see from here-- 2 of the portfolio.
所以总的来说，你可以从这里看出，协方差越大-,投资组合的σ2越高，the，higher，the，σ
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If they tend to move together, when x is high and y is high together at the same time, then the covariance will tend to be a positive number.
如果x和y同向变动,当x值和y值同时都很大,协方差的结果将会是一个正值
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It is defined as rho= That's the correlation coefficient.
定义为,rho等于xy的协方差比xy各自的标准差的乘积,这就是相关系数
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