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That's got the lowest possible standard deviation of expected return and that's 25% stocks and 75% bonds with this sample period.
这个组合预期回报的标准差最小,在这一点上，投资组合,由25%的股票和75%的债券构成。
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It shows the standard deviation of the return on the portfolio as a function of the expected return on the portfolio.
它是投资组合的收益标准差,关于预期收益率的函数图像。
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But if I would confine myself just to stocks and bonds, then I would get a much higher standard deviation.
但若组合里只有股票和债券，我的标准差会高得多。
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.. You want to get it-- if you keep adding assets, you can do better and better on your portfolio standard deviation.
你想得到-,如果不断增加资产,组合的标准差就会越来越小。
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You could always find a portfolio that had a higher expected return for the same standard deviation.
你总是可以找到一个投资组合,具有较高的预期回报,而标准差不变。
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Let's suppose that all of them are the same-- they all have the same standard deviation.
我们假设这些资产的收益率标准差-,均相等。
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One standard deviation happens one draw out of three, two standard deviations one out of twenty, three standard deviations is one out of one hundred.
落在一个标准偏差之外的概率是1/3,两个标准差之外的概率是1/20,三个标准差之外是百分之一
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Number of policies doesn't affect the means but it affects that standard deviation, so it becomes very collapsed and this is the basic core idea of insurance.
保单的数量并不影响其均值,但是会影响其标准差,所以这条曲线非常陡峭,而这就是保险的核心原理
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To calculate the expected utility of your wealth, you might also have to look at the expected return, or the geometric expected return, or the standard deviation.
要计算你财富的期望效用,你也许还要研究预期收益曲线,或几何预期收益率,或是标准差
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An eight standard deviation event happens once out of every six trillion trials.
而八个标准差的偏离就意味着,六万亿分之一的概率
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Because the square root of 10,000 is 100, whatever the standard deviation of the portfolio is, you would divide it by 100 and it would become really small.
因为一万的平方根是一百，无论这个投资组合的标准差是多大，当除以100后就都变得很小很小了。
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Over this time period, that portfolio had an expected return of something like a little over 9% and it had a standard deviation of a little over 9%.
在这个时间段，这个投资组合的预期收益率是,9%多一点%,标准差是9%多一点。
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You can't come up with a number to describe the twenty-five standard deviation event; it's just too large a number, I think, for any of us to really comprehend.
你根本无法想出一个数字,来描述这个偏离25倍标准差的事件,对我们普通人来说,这是个难以想象的天文数字
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According to my calculations it was a twenty-five standard deviation event.
根据我的估算,那次波动偏离均值有25倍标准差之巨
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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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You want to, for any given expected return, you want to minimize the standard deviation, so it's the left-most line and that means that everyone will be holding the same portfolio.
你希望，在期望收益固定的情况下，你肯定希望将标准差最小化，而这条线是最左边的线,这就意味着所有人,都愿意持有这样的投资组合。
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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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So that's .16/100; so the standard deviation is .04.
那就是0.16/100,所以标准差等于0.04
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So, for example, at an annual expected return of 12% if I have a portfolio of stocks, bonds, and oil I can get a standard deviation of something like 8% on my portfolio.
例如，在年预期收益12%的情况下%,我有股票，债券和石油的投资组合,在这个组合里,我的投资组合可以取到8%的标准差。
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Then, once we did that we could plug that into the formula that I gave you last time and get the standard deviation of the portfolio and the expected return on the portfolio.
再将估算出的数值代入到,上节课给你们的公式中,就能得到资产投资组合的标准差,和该投资组合的预期收益率
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What is the standard deviation?
标准差是多少
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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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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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So, the optimal thing to do if you live in a world like this n is to get n as large possible and you can reduce the standard deviation of the portfolio very much and there's no cost in terms of expected return.
如果现实中也这样简单的话,那么你就尽量增大,这样就能让投资组合的标准差,就会大大降低,从预期收益率的角度来看,这样做的成本是零。
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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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Or, especially when talking about estimates of the variance, we sometimes say S2 or we say standard deviation2.
又或者,在讨论方差估计的时候,我们常用S2,称为标准差的平方
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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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