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？

As far as i know, arithmetic return is more broadly used by practitioner especially when you do not reinvest on daily basis. Also when you need to do linear combination of returns. Yet log return is more favored by academical world because its nice mathematical property(especially when you do time series models and do simulation.). In terms of your problem. I'm assuming you're trying to estimate expected return and volatility by daily data. Both of them works fine. But you need to be careful. Say you need use yearly return and volatility to calculate shape ratio,  arithmetic return makes more sense.
  

agree.

One thing need to be pointed out is that GR and AR are just two ways to calcuate return. It does not mean that if the time is discrete you need to use AR, while if it is continuous you have to use GR.  You can use both but GR is more consistent with continous time finance which does not indicates GR is very bad for discrete time case. In discrete time basis, both works. (just a big diffence between AR and GR). It does not make sense that if you use log return for daily basis but their summation can not be used in the yearly basis. Actually for monthly and yearly basis, log return works better than daily basis since it is more normally distributed with is garanteed by central limit theorem.

So the most practical way to handle with this question is that you derive the model in the log return framework, since it has good mathematical and statistical property so the result is more stable and then finally convert it into the arithmetical one if you want.

Actually on the street, people has a approximation for GR and AR, GR=AR-1/2*variance. This result can be easily get if you are familiar with Geometric Brownian motion.

Different people has different perspective. AR has it's advantage when calculate the linear weighted return. I prefer log return since it has more advantages.

tanheng8 发表于 2013-3-8 03:53
As far as i know, arithmetic return is more broadly used by practitioner especially when you do not  ...

我之前的做法是：
步骤1.求取各ith资产的日对数收益率的均值LRi、标准差Qi以及他们之间的相关系数矩阵
步骤2.使用马克维茨的模型标准公式：组合日对数收益率LRp=sum wi*LRi,wi为权重，以及组合的标准差Qp
步骤3.计算日sharpe ratio
步骤4.比较夏普比例大小确定风险资产的最优组合

我觉得好像不太对，就来发帖子询问。

Chemist_MZ 发表于 2013-3-8 10:16
agree.

One thing need to be pointed out is that GR and AR are just two ways to calcuate return. I ...

版主 多谢
我的做法如上，做的时候就是用日对数收益率 套经典的马克维茨 是不是有问题

请问楼主：马克维茨投资组合的收益率是单个资产的对数收益率加权平均还是简单收益率加权平均呢？