Question

我正在创建风险平价过程，我需要使用Power方法，这是一个迭代过程来查找系统的特征值。

目标是找到您准备投资的eaach资产的权重。

为了意识到我需要实现一种功率方法，所以我猜每种资产的重量，我看是否满足当前条件：

sqr((1/(N-1))Sum((Xi*Betai - 1/N)^2) < epsilon

其中sqr是平方根 N资产数量 Xi每个资产的重量 Betai每个资产的测试版 epsilon是我决定的门槛

Beta可以找到

Covariance i with P / variance of P

我是资产i和P投资组合

当我的病情没有得到尊重时，我将我的测试重新分配为我的新体重，直到我的病情得到尊重。

问题是系统不会收敛但会爆炸。我认为我完全尊重Denis B Chaves Jason C. Hsu Feifei Li和Omid Shakernia的文章：

Efficient Algorithms for Computing Risk Parity Portfolio Weights

我尝试在第7页实施算法2

这是我的代码：

Sub RiskParityPowerMethod()

    'prendre des poids equiponderes
    Dim lastColumnReturn As Long
    Dim lastRowReturn As Long
    Dim tempReturnPtf As Double

    lastRowReturn = Cells(Rows.Count, 1).End(xlUp).Row
    lastColumnReturn = Cells(1, Columns.Count).End(xlToLeft).Column

        'calcul du rendement du portefeuille pour les 90 premieres dates
        Sheets("Return").Select
        For k = 3 To 92
            tempReturnPtf = 0
            For j = 3 To lastColumnReturn
                tempReturnPtf = tempReturnPtf + (1 / (lastColumnReturn - 2) * Cells(k, j))
            Next j
            Sheets("Portfolio").Cells(k, 2).Value = tempReturnPtf
            Cells(k, 2).Value = tempReturnPtf
        Next k

    ReDim vecteurPoids(3 To lastColumnReturn)
    ReDim covarIP(3 To lastColumnReturn)
    ReDim matrixVarCovar(92 To lastRowReturn, 3 To lastColumnReturn, 3 To lastColumnReturn)
    ReDim matrixVarCovarFinal(3 To lastColumnReturn, 3 To lastColumnReturn)
    ReDim beta(3 To lastColumnReturn)

    For k = 92 To lastRowReturn
            'initialisation des poids
            For i = 3 To lastColumnReturn
                vecteurPoids(i) = 1 / (lastColumnReturn - 2)
            Next i
            Condition = 1
            seuil = 0.05

        While Condition > seuil
            'calcul du return du portefeuille
            tempReturnPtf = 0
            For i = 3 To lastColumnReturn
                tempReturnPtf = tempReturnPtf + vecteurPoids(i) * Sheets("Return").Cells(k, i).Value
            Next i
            Sheets("Portfolio").Cells(k, 2).Value = tempReturnPtf
            Cells(k, 2).Value = tempReturnPtf

            'calcul de la covariance de l'actif i avec le portefeuille
            For i = 3 To lastColumnReturn
                covarIP(i) = Application.WorksheetFunction.Covar(Range(Cells(k - 90, i), Cells(k, i)), Range(Cells(k - 90, 2), Cells(k, 2)))
            Next i

            'i is the asset i
            For i = 3 To lastColumnReturn
                'j is the asset  j
                For j = 3 To lastColumnReturn
                    'Sheets("Return").Select
                    matrixVarCovar(k, i, j) = Application.WorksheetFunction.Covar(Range(Cells(k - 90, i), Cells(k, i)), Range(Cells(k - 90, j), Cells(k, j)))
                    matrixVarCovarFinal(i, j) = matrixVarCovar(k, i, j)
                Next j
            Next i

            'calcul de la volatilite du portefeuille
            tempVolPtf = 0
            For i = 3 To lastColumnReturn
                For j = 3 To lastColumnReturn
                    tempVolPtf = tempVolPtf + (matrixVarCovar(k, i, j)) * vecteurPoids(i) * vecteurPoids(j)
                Next j
            Next i
            volPtfCarre = tempVolPtf

            'calcul du beta pour chaque actif
            For i = 3 To lastColumnReturn
                beta(i) = covarIP(i) / volPtfCarre
            Next i

            'condition d'iteration
            For i = 3 To lastColumnReturn
                tempCondition = tempCondition + (vecteurPoids(i) * beta(i) - (1 / (lastColumnReturn - 2))) ^ (2)
                'MsgBox tempCondition
            Next i

                tempCondition = (1 / (lastColumnReturn - 2 - 1)) * tempCondition
                'MsgBox tempCondition
                Condition = Sqr(tempCondition)
                MsgBox Condition

                    If Condition > seuil Then

                        'changement des poids
                        tempSumBeta = 0
                        For i = 3 To lastColumnReturn
                                tempSumBeta = tempSumBeta + (1 / beta(i))
                        Next i
                        sumBeta = tempSumBeta

                        For i = 3 To lastColumnReturn
                            vecteurPoids(i) = (1 / beta(i)) / (1 / sumBeta)
                            'MsgBox vecteurPoids(i)
                        Next i

                    End If
        Wend        
    Next k    
End Sub

任何想法为什么系统不会收敛而是爆炸？

Answer 1

最后，如果我初始化变量条件和tempSumBeta，我的系统会收敛到0,57：

    Condition = 0
    seuil = 0.57

While Condition < seuil

     tempSumBeta = 0
     Condition = 0

功率方法 - 非会聚系统

1 个答案: