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。

耶鲁公开课 - 金融市场课程节选

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。

耶鲁公开课 - 金融市场课程节选

I know this might be changing the game a little bit, but if you ever expected to play the same game with the partner you have more.

我知道这可能会稍微改变点这个博弈,但是如果你认为以后你还会,和你的对手进行相同博弈

耶鲁公开课 - 博弈论课程节选

I probably whip out a do while loop very rarely, but very often when programming games or any program that takes user input and has to check that user input and yell at the user if they're messing with you or aren't providing what's expected.

我可能很少用do，while，循环，但常常是,当编制程序游戏或需要用户输入的程序是,需要检查用户的输入并提醒用户,如果他们干扰了你,或没有提供所期望的输入。

哈佛公开课 - 计算机科学课程节选

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。

耶鲁公开课 - 金融市场课程节选

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。

耶鲁公开课 - 金融市场课程节选

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。

耶鲁公开课 - 金融市场课程节选

So one way to think about it is, is the expected distance from her of the winning candidates, is: with probability of a half it's herself so that's nothing, No distance, and with probability of a half it's two places away.

所以一种考虑的方法是,预期她与获胜者的距离是,由于她有一半获胜的机会所以没有成本,没有距离,且,距她两个位置远的人有另一半获胜的机会

耶鲁公开课 - 博弈论课程节选

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。

耶鲁公开课 - 金融市场课程节选

With the government expected return, we want to make that expected return as a fourth asset-- rf we could call it r4 but I'll call it rf-- it's a special asset.

根据政府的期望收益率，我们将其作为第四种资产-,可以称之为r4，我们写成-,这是个特殊的资产。

耶鲁公开课 - 金融市场课程节选