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The basic idea is, you take a guess and you -- whoops -- and you find the tangent of that guess.
首先取个猜想数,然后，嗯,去取猜想数那儿的切线。
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Somebody else might say, well I want to just hold this point, I want to hold the tangency portfolio.
而另外的某些人可能会说，我就想按这个点的比例来持有投资，我想持有切线投资组合。
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Show me a place where that's not true where the tangent line will be really bad.
请给我个这个原则不对的例子,也就是说切线没起到相应作用的例子。
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The tangent's pointing towards the direction you are headed at that instant.
切线的方向就是,速度矢量在那个瞬时的指向
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Then finally, the final step is to find what is the tangency line that goes through the riskless rate.
在最后，最终的步骤是找出一条,穿过无风险收益率的切线。
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Now, he's using a much longer sample than I did, so he's not going to get this tangency portfolio that I did.
他的样本跨度比我的要大多了，所以他得出的切线资产组合会和我的不同。
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In my diagram, I said that the tangency portfolio-- I estimated that the tangency portfolio is 9% oil, 27% stocks, and 64% bonds.
在我的曲线图里我有提到切线资产组合-,我估算出切线资产组合是9%的石油，27%的股票和64%的债券。
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The theory of mutual funds is: nobody is supposed to be holding anything other than-- ... the ideal theory of mutual funds--is holding something other than this tangency portfolio.
共同基金定理是指：,所有人都应该持有-,理想的共同基金定理说,都应该持有这种切线投资组合。
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That would mean that everybody is holding that same portfolio of risky assets and nobody is different, they're only different in how-- what proportions they hold the risky-- the tangency portfolio.
这就意味着每个人,都持有相同风险资产投资组合,每人都是一样的，他们唯一的不同在于-,他们所持有风险资产的比例-,也就是切线资产组合。
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They have lots of maybe good-- maybe it's not because they're irrational, it's that they're political or they're constrained by tradition or laws or regulations, all sorts of things; but, they're not holding the tangency portfolio.
他们有很多好的原因-,也许并不是因为他们不够理性，而是由于他们有自己政治上的考虑,或者是他们本身被传统,法律以及规则等一系列的因素，所限制;,因此他们不会持有切线资产组合。
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I don't know how well you can see it in this figure here, is the slope of a straight line connecting these two points, and as the points come closer and closer, the straight line would become tangent to the curve.
我不清楚你们对于这个图像的理解,这条连接两点的斜线,随着两点距离逐渐缩小,两点连线会变成曲线的切线
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The asset pricing model--and this is critical-- assumes everyone is rational and holds the tangency portfolio.
资本资产定价模型是非常重要的模型-,假设每人是理性的，并持有切线资产组合。
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That would be a portfolio where you borrowed at the riskless rate and you put more than 100% of your money into the tangency portfolio.
在这种组合里,你可以以无风险利率借贷到一些资金,从而可以投入比你本金更多的资金,来购买切线投资组合。
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At any point on the graph you can take the derivative, which will be tangent to the curve at each point, and its numerical value will be what you can call the instantaneous velocity of that point and you can take the derivative over the derivative and call it the acceleration.
在图上的任意一点,你可以进行求导,得到曲线上每一点的切线斜率,所得到的数值,即为该点处的瞬时速度,然后你再求一次导,得出它的加速度
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Yeah. Suppose I choose it right down there I guess 0. Well, the tangent there will not even have an x intercept. So I'm really going to be dead in the water.
好，如果我选猜想数为0，好吧,这个点的切线甚至和x轴都没交点,所以在这儿这一原则,真的不起作用了。
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If you agree with my estimates, then you should do this as an investor, you should hold only some mixture of this tangency portfolio, which is 9% oil, 27% stocks, and 64% bonds.
如果你赞同我的估计值，那么作为一个投资者的话你应该这么做，你应该只持有,符合这个切线投资组合比例的投资，即9%的石油，27%的股票，和64%的债券。
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