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。
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。
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。
.. 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。
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。
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。
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
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
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
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
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。
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。
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
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
The standard deviation is the square root of the variance.
标准差是方差的平方根
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。
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。
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
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。
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
What is the standard deviation?
标准差是多少
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。
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。
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。
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。
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。
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
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
应用推荐