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Underlying this analysis, we have estimates of the expected returns on assets, notably, the expected returns on stocks and bonds.
凭借这个分析，我们可以估算出资产预期投资收益，特别是股票和债券的预期收益。
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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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Finally, let's do it in green, let's look at the payoffs, the expected payoffs if I shoot to the right.
最后,用绿线来表示吧,我们来看看我从右路射门的预期收益
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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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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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And let's start by considering my payoffs on this picture, just to help myself a bit, let me put some points in here.
我们从在图上表示预期收益开始,稍微等我一下,我先标注出来几个点
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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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And in principle, I could redo this calculation for every single possible probability you could think of.
并且理论上,对于每一个可能的概率对,我们都可以进行预期收益计算
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So in this case, my expected payoff is a ? of 1 plus a ? of 4, for a total of again 2.5.
在这种情况下,我预期收益是?乘1加?乘4,总和还是2.5
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So what's my expected payoff from choosing Up where I believe the other person's going to choose Left and Right, equally likely? It's what?
那么在我对手选择左或右,可能性相同的情况下,我的预期收益会是什么样的呢
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On the vertical axis I'll put two vertical axes in, just for the sake of things on the vertical axis I'll put my expected payoffs.
坐标系的纵轴,由于种种原因,我花了两个纵轴,纵轴表示我的预期收益
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It's the expected payoff to Player 1 if shooting to the left as it depends on the probability that the goal keeper dives to the right.
它表示参与人1,从左路射门的预期收益,与门将扑向右路的概率有关
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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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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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Let's start by plotting my expected payoff from choosing the strategy Up.
我先把选上的预期收益,标注出来
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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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What about my expected payoff from choosing Middle against , so in this case where I think it's equally likely that my opponents going to choose Left or Right?
那我在情况下,选中的预期收益是什么呢,在此情况下我依然认为,对手选左选右的可能性相同
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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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How about my expected payoff from choosing Down versus ?
那在情况下我选下的预期收益呢
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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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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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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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So what we're going to look at is the expected payoff of Up versus, let me call it a : a being equally likely that my opponent chooses Left and Right.
所以接下来我们看看在我认为对手,选择左右的可能性相同下的预期收益,我们把它称为
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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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