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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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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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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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That's what this whole theory is about, how to get a lot of expected return without getting a lot of risk.
整个金融理论的中心,就是如何获得高收益,同时降低风险
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In fact, different people might make different choices about how much risk they're willing to bear to get a higher expected return.
事实上，为了获得高的预期收益率,人们愿意承受的风险,也会不同。
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It's the world portfolio, it's everything and we compute the expected return on that portfolio, rm that's rm.
这就产生了世界投资组合,然后我们在此基础上计算出预期收益，所得值就是。
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They show the expected return on stocks versus bonds or short-term debt for a whole range of countries.
他们对这些国家的股票预期收益与,国债或者短期债券作出比较。
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It would be anywhere from here to here, depending on how much you're afraid of risk and how much you want expected return.
可以选择从这里到这里的任意一点，取决于你对风险的承受能力,和你的期望回报。
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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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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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2% You could say, I think my portfolio has an expected return of 12%-- that would be better than if it had an expected return of 10%.
如果一个投资组合的预期收益率有-,那就比一个只有10%的投资组合要好。
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What Siegel emphasized--the book is really about this-- he talks about what is the expected return of stocks and what is the expected return of bonds and so on.
西格尔强调的是。。。这书真正讲的是-,他讨论了什么是股票预期投资收益,以及什么是预期投资债券等等内容。
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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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This is the equation that relates the expected return on an asset.
这个等式是关于某一资产的预期收益。
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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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You should see that the blue line is better than the pink line because, for any expected return, the blue line is to the left of the pink line, right?
可以看到蓝线比粉线好,原因是对于任意的预期收益率，蓝线都在粉线的左边，对吧？
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So that's the expected return and efficient portfolio frontier problem.
这就是预期收益,和有效边界问题。
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You'd have a higher expected return with no more variance.
你的预期收益率提高了，但风险没有增加。
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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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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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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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The other thing that I mentioned last time was that there seems to be a really big difference between the expected return on the stock market and the expected return on short-term debt.
上节课提到的另一条内容是,股票市场的预期收益,与短期债券的预期收益,存在着巨大差异
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What is the portfolio expected return?
投资组合的预期收益率是什么？
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r1 Asset 1 has expected return r1.
第一项资产的预期收益率是。
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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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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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.. The portfolio expected return-- x3 we have to choose three things now: x1, x2, and x3.
要计算投资组合的预期收益-,我们必须确定三个值x1，x2和。
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