马克维茨投资组合中组合的收益率，用单个资产的对数收益率还是简单收益率按权重加和？

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马克维茨投资组合中组合的收益率理论上应该是单个资产的简单收益率按权重加和  
用简单收益率还是对数收益率？？
写的论文马上要定稿了 发现我用的对数收益率加和 这样是不是错了？？着急啊 错了改动就大了

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关键词：对数收益率 马克维茨 投资组合 收益率 论文 投资组合 收益率

自顶 求大家帮忙 下周交论文盲评  
学得比较差

ding

mengjincui 发表于 2013-3-6 15:18
ding

没问题。对数收益率更好，更符合模型假设。因为对数收益更加正态,而正态是模型隐含条件，因为只有正态分布可以由均值和方差完全确定。

你也可以用普通收益，但是效果可能差一些，一般简单收益只用在实务中比如你给客户算个收益什么的，做研究一般都指对数收益

Chemist_MZ 发表于 2013-3-6 20:04
没问题。对数收益率更好，更符合模型假设。因为对数收益更加正态,而正态是模型隐含条件，因为只有正态分布 ...

版主 多谢回复！
我之前的想法和你一样 觉得考虑到对数收益率更接近正态分布，线性特性也更好 就用了对数收益率（我用的是日对数收益率，除了做马克维茨投资组合还要做做时间序列的协整和Granger）

但是我昨天仔细想了一下：马克维茨的理论推导过程 发现他做的推导是用简单收益率才成立的 使用对数收益率推导只能是一个近似 而且我使用的数据长度较大 可能偏差比较大

我觉得可能应该这么说：两种收益率各有优劣，一个是严格数学推导（简单收益率），一个更符合假设前提（正态分布，线性）
所以我就迷茫了  版主觉得这个对数收益率的偏差没问题？
我正在修改论文了 但是原版对数收益率的也保留着  马上要送去盲评 最后定那个也不知道 着急啊 导师出国开会也联系不上

mengjincui 发表于 2013-3-7 14:21
版主 多谢回复！
我之前的想法和你一样 觉得考虑到对数收益率更接近正态分布，线性特性也更好 就用了对数 ...

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In my opinion, the volatility and expected return of Markowiz is exogenously given, so that it does not care about which method you use for calculation. I don't know why you say the derivation only holds for arithmetic return, since I have never used this assumption when deriving this model.Actually geometric return is always used and if you use daily return, the GR is better.It is possible that I ignore some stuff. Please let me know if you have further questions.

Chemist_MZ 发表于 2013-3-7 14:49
In my opinion, the volatility and expected return of Markowiz is exogenously given, so that it d ...

马克维茨的组合收益率公式如上，这个公式我认为对对数收益率的E(Ri)应该不成立  或者说只是近似成立
不知道我理解得对不对  多谢版主

Forgive my sleeping since it is too late.

I am happy you notice this problem. But remember, if you use geometric return, you should use the corresponding geometric average otherwise you are ignoring the convexity of the exponential function if you treat them in a linear way.

You can show that if log return is normal then arithmetic return is log normal so does the asset price. However, the summation of log normal is not log normal any more. It seems a little wierd, since you may say that you can derive the portfolio's return as Pt+1/Pt -1=Σwi(Ait+1/Ait -1) where Ait is the price of ith asset in the portfolio at time t. Remember, if you accept the fact that the At+1/At is log normally distributed, Pt+1/Pt can not be log normal , so that there is some inconsistency. This is one draw back of arithmetic return. That' why log return is so popular.

For log return, the summation is still normal. It is convenient. This question is a little trivial if you really want to dig out the detailed part. The main reason we use the log return is mainly describe in my explanation above. Anyway, you don't need to be worried about that, you can use both returns.  Actually log return works both correct in mathematical derivation and better in statistical property. So take it easy.

What I said does not mean you're wrong. What you said is also reasonable. I just give some advice to calm you down.

Hope help~

Chemist_MZ 发表于 2013-3-7 19:55
Forgive my sleeping since it is too late.

I am happy you notice this problem. But remember, if yo ...

非常感谢版主如此热心！！
您说的我觉得非常有道理！我之前也是这样考虑的（正态分布，并且线性，方便加和，多期后总收益不会偏差等等）
我只是觉得使用日对数收益率也有一定的问题，就是在合成组合的日对数收益率的时候：
如果用各种资产的对数收益率（我没有用收益率）按权重加和，得到组合的对数收益率，这种算法似乎也有点偏差——
正确的算法似乎应该是：把各种资产的对数收益率换算回收益率，再按权重加权，得出的总值再取对数（这样的话，马克维茨模型计算方差的公式就不是原来的公式那样了，会很复杂）



思路好像有点乱。。。不好意思
不知版主的看法如何，多谢多谢

mengjincui 发表于 2013-3-8 01:36
非常感谢版主如此热心！！
您说的我觉得非常有道理！我之前也是这样考虑的（正态分布，并且线性，方便加 ...

No problem, this is my duty.

Yes,that is the definition of the geometric average and you can do that.

GR works good for small time interval, both in the normal and linear weighted aspects. Actually my JP Morgan professor told us that usually they use log return for portfolio management. So I recommend you to use that although you have pointed out that it has some linear weight summation issue. In your daily return case, it should works good and it has many good properties.

You don't need to worry about that. If the committee challenge you , I have given you sufficient reasons to argue