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# 同根策略与同架策略
## 同根策略与同架策略
[若尘的cholesky分解策略](https://www.bfm-unity.com/v/joinquant/jin-rong-li-lun-zong-jie/zi-chan-pei-zhi/ruo-chen-de-ce-lve)
### 表格
### 公式
### 考虑杠杆和做空的公式推广
### 同根策略
同根策略a + b + c = 1a\*(1-x) = b\*(1-y) = c\*(1-z)a\*(1-x)/(1-y) = ba\*(1-x)/(1-z) = ca\*(1-x)/(1-x)+a\*(1-x)/(1-y)+a\*(1-x)/(1-z) = 1b\*(1-y)/(1-x)+b\*(1-y)/(1-y)+b\*(1-y)/(1-z) = 1c\*(1-z)/(1-x)+c\*(1-z)/(1-y)+c\*(1-z)/(1-z) = 1a = 1/(1-x)/(1/(1-x)+1/(1-y)+1/(1-z))b = 1/(1-y)/(1/(1-x)+1/(1-y)+1/(1-z))c = 1/(1-z)/(1/(1-x)+1/(1-y)+1/(1-z))ax = x/(1-x)/(1/(1-x)+1/(1-y)+1/(1-z))by = y/(1-y)/(1/(1-x)+1/(1-y)+1/(1-z))cz = z/(1-z)/(1/(1-x)+1/(1-y)+1/(1-z))ax+by+cz=(x/(1-x)+y/(1-y)+z/(1-z))/(1/(1-x)+1/(1-y)+1/(1-z))我把这个叫做同根策略灰色的是现金，颜色的是资产。每种资产携带的现金相同。所以叫同根策略x,y,z是单独考虑的资产占比a,b,c是分配权重，ax,by,cz是分配后的资产仓位占比
### 同架策略
同架策略a + b + c = 1a/x\*(1-x) = b/y\*(1-y) = c/z\*(1-z)a\*((1-x)/x)/((1-y)/y) = ba\*((1-x)/x)/((1-z)/z) = ca\*((1-x)/x)/((1-x)/x)+a\*((1-x)/x)/((1-y)/y)+a\*((1-x)/x)/((1-z)/z) = 1b\*((1-y)/y)/((1-x)/x)+b\*((1-y)/y)/((1-y)/y)+b\*((1-y)/y)/((1-z)/z) = 1c\*((1-z)/z)/((1-x)/x)+c\*((1-z)/z)/((1-y)/y)+c\*((1-z)/z)/((1-z)/z) = 1a = 1/((1-x)/x)/(1/((1-x)/x)+1/((1-y)/y)+1/((1-z)/z)) = x/(1-x)/(x/(1-x)+y/(1-y)+z/(1-z))b = 1/((1-y)/y)/(1/((1-x)/x)+1/((1-y)/y)+1/((1-z)/z)) = y/(1-y)/(x/(1-x)+y/(1-y)+z/(1-z))c = 1/((1-z)/z)/(1/((1-x)/x)+1/((1-y)/y)+1/((1-z)/z)) = z/(1-z)/(x/(1-x)+y/(1-y)+z/(1-z))ax = x^2/(1-x)/(x/(1-x)+y/(1-y)+z/(1-z))by = y^2/(1-y)/(x/(1-x)+y/(1-y)+z/(1-z))cz = z^2/(1-z)/(x/(1-x)+y/(1-y)+z/(1-z))ax+by+cz = (x^2/(1-x)+y^2/(1-y)+z^2/(1-z))/(x/(1-x)+y/(1-y)+z/(1-z))我把这个叫做同架策略灰色的是现金，颜色的是资产。每种资产携带现金间比例，与资产间比例，相等。所以叫同架策略。x,y,z是单独考虑的资产占比，a,b,c是分配权重，ax,by,cz是分配后的资产仓位占比。
### 策略比较
同根同架策略比较
### 实际应用（同架策略）
实际应用
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