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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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And then I could also do a Gaussian one here, with the mean of and the standard deviation of volatility divided by 2.
然后我在这里再写一个高斯分布的函数，它的浮动值的平均值和,标准偏差值都除了2。
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so all of these things with addition of the deviation of the policy, personnel and material to Iraq, led to the turnanoud.
所有这些事情加上政策，人员，物资向伊拉克的转移，使得局势有了改变。
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So the other possible deviation we have to consider, is a deviation of the form of one of these guys dropping out.
那么另外一个我们必须要考虑的偏差,是她们俩有一个人退出选举
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And when we're talking about the amplitude of the wave, we're talking about the deviation from that average level. So, if we define the average level as zero, you can have either a positive amplitude or a negative amplitude.
当我们讨论一个波的振幅时,我们说的是偏离平均位置的量,如果我们把平均位置,定义为零的话，那幅值不是,正的就是负的，有时候人们在。
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He will not tolerate any deviation in the service of alien gods.
他无法容忍对任何异教神灵的偏向。
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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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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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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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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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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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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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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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So there's three possible types of deviation here that we need to check.
这有三种可能的偏差,需要我们验证
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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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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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The standard deviation is the square root of the variance.
标准差是方差的平方根
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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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We need to check another entrant from the outside, left wing or right wing, we need to check another entrant in the middle, there is only one possible one there, and there's a third kind of deviation we should check, what's the third type of deviation?
我们需要验证另外一个外部的参选人,左派或右派,我们需要验证另外一个中间的参选人,只有一个可能参选的人,还有第三种要验证的偏差类型,第三种偏差类型是什么
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