[求助]如何从CML推导出SML

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如题，我看的是黄达《金融学》，反复几遍没能明白其中的推导过程在哪儿，似是分开论述的。在人大经济论坛上也查了相关帖子，但说的是二者区别。

还请达人帮在下解惑。

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关键词：CML SML 人大经济论坛 推导过程 二者区别 推导 SML CML

似乎应当是ＳＭＬ推出ＣＭＬ吧．

似乎是加上了无风险资产之后所有改变，具体的可以看关于投资学或者金融市场学的书．

另外注意两个横轴是不同的．一个是协方差／方差，另一个是ＢＥＴＡ值．

CML is the Capital market line which show us the relationship between E(Ri) and the security-portfolio(combines the risk free asset and market porfolio) variation.

NOT FOR SINGLE SECURITY

E(Ri)=Rf+[(Rm-Rf)/Vm]*Var(portfolio)

where Rf is risk free rate, Rm is market portfolio return

(Rm-Rf) is the market risk premium. devided by market risk(var) shows the risk premium per var, which gives us the slope of the CML

multipling the Var(portfolio) gives the risk premium required for the security portforlio

This line is actually tangent the efficient frontier, It shows all the combinations of risk free asset and market(optimal) portfolio.

However, SML shows the relationships between the reterns of all securities(not just market portfolio) and their risks. As we all know the market only compensate the systemetic risks which are the risks relating to the market. The nonsystemetic risks can be diversified. Therefore, for a single security the only relevant risk factor is Cov(im)

COULD BE USED FOR ALL SECURITIES AND PORTFOLIO

E(Ri)=Rf+[(Rm-Rf)/Vm]*Cov(im)

reorganize the formula

E(Ri)=Rf+Cov(im)/Vm *(Rm-Rf)

where we let Cov(im)/V(m)= beta

so we get E(Ri)=Rf+ B* (Rm-Rf) This gives the line which is called security market line (SML)

from this SML, we can get the relationship between the E(Ri) and the B(indicates the systemetic risk of the security)

(Here,as we know Cov(mm)=Var(m) so when the return B=1,Ri=Rm)

[此贴子已经被作者于2006-6-21 9:24:49编辑过]

hope my explanation can help~~

I hope so but unfortunately...anyway..don't be upset, you know..this happens.

Well, please let me have a try...like sending sow to Minerva.

As mentioned upstairs, CML plots the relationship between E(R) of a portfolio and

its risk, which is represented by the standerd deviaion whereas SML concerns beta in lieu.

Actually, SML is refered to as the consequence of optimized CML function.

We can find that, in the figure of CML, the securities(as well as portfolios)with common corresponding beta lay on an identical horizontal line, implying thereby same beta requires same expected return.

And bang! We get SML curve from this insight of CML.

The detail algebraic derivation i will try to present here if i fortunately get time and... could remember...

[此贴子已经被作者于2006-6-20 18:45:26编辑过]

Many thanks for all your help!

前几天来看贴，一直无人回复，还以为会就此沉下去。

正打算下午把罗斯《公司理财》中资产定价部分看看，对比一下。

另，破蛹成蝶，期待你的推导哦！

我建议还是看博迪的投资学，讲的很详细

建议楼主看看解决这个问题的作者本人是怎么推导的 那就是夏普的经典著作《投资组合理论与资本市场》 这本书里头讲的 很清楚 而且还易懂 听我的没错