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

表格

​https://share.weiyun.com/xUw40P4l​

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