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But, I don't know what you were thinking, we got a 28% portfolio return last year.
不知道你们觉得如何,我们去年获得了28%的收益
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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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A managed portfolio, you find somebody you think is really smart and you pay them a fair amount of money and in return they assert that they will pick winners for you, and in fact, you will outperform the stock market.
而代管投资组合就是说，你找一个你觉得很聪明的人,给他们一些钱,然后他们会说一定会帮你选出,赚钱的股票，实际上你会比股市整体表现要好。
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So Yale had a 28% return on its portfolio last year, which was number one of all college endowments.
去年耶鲁基金获得了28%的收益,收益率高居全美高校榜首
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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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The return on the portfolio is x1 r1 + x2 r2 + x3 r3.
这个投资组合的收益是。
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This is a year of financial crises, so I'm warning you ahead that -don't expect a 28% return on the Yale portfolio for the coming year.
金融危机爆发,所以我先提前给大家打预防针,别期望今年耶鲁基金,能延续28%的收益
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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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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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So,70% of the portfolio is in absolute return, real assets,private equity, alternatives--broadly defined.
因此资产的70%分布于绝对收益组合,不动产,私募权益等广泛的投资品种中
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Last year the return on the Yale portfolio was 28% in one year.
去年耶鲁大学投资组合的收益率,是28%
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The return, of course, in any given time period is the percentage increase in the portfolio; or, it could be a negative number, it could be a decrease.
当然了，收益率是一定时间内,投资组合的增长率;,也可能是一个负数，表示负增长。
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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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What is the portfolio expected return?
投资组合的预期收益率是什么？
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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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Over the past twenty years, we've generated 15.6% per annum return, but that headline number obviously has a lot to do with the equity orientationof the portfolio but doesn't describe the importance of the diversification.
过去20年间,我们的年收益率达到15.6%,虽然媒体头条报道这一收益率,总强调与投资组合的股权导向有很大关系,但没有描述出投资多元化的重要性
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Now, underlying our theory is the idea that we measure the outcome of your investment in your portfolio by the mean of the return on the portfolio and the variance of the return on the portfolio.
而理论的基础是,我们通过计算,组合收益率的均值，和组合收益率的方差,来衡量一个投资组合的优劣。
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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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In that year, we were early on in terms of diversifying the portfolio -we'd only been working on that program for two years -and even so,the negative return was less than 1%, so it was a modest negative return.
在那一年,我们还处于投资组合多元化的初期,刚刚开始2年,即便如此,股灾时我们的亏损小于1%,这只是一个轻微的亏损
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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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Again, I'm not going to spend much time on this, of the ith asset is the regression coefficient when you regress the return on the ith asset on the return of the market portfolio.
再强调一次，我不打算花太多时间在这个等式上面，但要注意的是当你想将市场组合收益，but，the，β,回归到第i资产收益中去,第i资产β系数是线性回归方程的,回归系数。
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