[Returnanalytics-commits] r2238 - pkg/PerformanceAnalytics/sandbox/Meucci/R

[noreply at r-forge.r-project.org]

Author: mkshah
Date: 2012-08-17 00:32:13 +0200 (Fri, 17 Aug 2012)
New Revision: 2238

Modified:
   pkg/PerformanceAnalytics/sandbox/Meucci/R/MeanDiversificationFrontier.R
Log:
Completing functions for MeanDiversificationFrontier.R

Modified: pkg/PerformanceAnalytics/sandbox/Meucci/R/MeanDiversificationFrontier.R
===================================================================
--- pkg/PerformanceAnalytics/sandbox/Meucci/R/MeanDiversificationFrontier.R	2012-08-16 22:06:07 UTC (rev 2237)
+++ pkg/PerformanceAnalytics/sandbox/Meucci/R/MeanDiversificationFrontier.R	2012-08-16 22:32:13 UTC (rev 2238)
@@ -33,4 +33,73 @@
       L[ n ] = L_[ N - n + 1 , N - n + 1 ]
     }
   }
+  return( list( E = E, L = L, G = G ) )
+}
+
+MaxEntropy = function( G , w_b , w_0 , Constr )
+{
+  # Nested function that computes fitness
+  nestedfun = function( x )
+  {
+    v_ = G %*% ( x - w_b )
+    p = v_ * v_
+    R_2 = max( 10^(-10), p / colSums( p ) )
+    Minus_Ent = t( R_2 ) * log( R_2 )
+    return( Minus_Ent )
+  }
+  x = fmincon( @nestedfun , w_0 , Constr.A , Constr.b , Constr.Aeq , Constr.beq )
+  return( x )
+}
+
+MeanTCEntropyFrontier = function( S , Mu , w_b , w_0 , Constr )
+{
+  # compute conditional principal portfolios
+  GenPCBasisResult = GenPCBasis( S, emptyMatrix )
+
+  # compute frontier extrema
+  w_MaxExp = linprog( -Mu , Constr.A , Constr.b , Constr.Aeq , Constr.beq )
+  MaxExp = t( Mu ) %*% ( w_MaxExp - w_b )
+
+  w_MaxNe = MaxEntropy( G , w_b , w_0 , Constr )
+  ExpMaxNe = t( Mu ) %*% ( w_MaxNe - w_b )
+
+  # slice efficient frontier in NumPortf equally thick horizontal sections
+  NumPortf = 10
+  Grid_L = .0
+  Grid_H = .9
+  Grid = c( seq( from = Grid_L, to = Grid_H, length.out = NumPortf ) )
+  TargetExp = ExpMaxNe + Grid %*% ( MaxExp - ExpMaxNe )
+
+  # compute diversification distribution
+  Weights = emptyMatrix
+  R_2_s = emptyMatrix
+  Ne_s = emptyMatrix
+  m_s = emptyMatrix
+  s_s = emptyMatrix
+
+  for ( k in 1:NumPortf )
+  {
+    ConstR = Constr
+    ConstR.Aeq = cbind( Constr.Aeq, t( Mu ) )
+    ConstR.beq = cbind( Constr.beq, TargetExp[ k ] + t( Mu ) %*% w_b )
+
+    w = MaxEntropy( G , w_b , w_0 , ConstR )
+
+    m = t( Mu ) %*% ( w - w_b )
+    
+    s = sqrt( t( w - w_b ) %*% S %*% ( w - w_b ) )
+    
+    v_ = G %*% ( w - w_b )
+    TE_contr = v_ * v_ / s
+
+    R_2 = max( 10^(-10) , TE_contr / colSums( TE_contr ) )
+    Ne = exp( -R_2 * log( R_2 ) )
+    
+    Weights = cbind( Weights, w )
+    m_s = cbind( m_s, m )
+    s_s = cbind( s_s, s )
+    R_2_s = cbind( R_2_s, R_2 )
+    Ne_s = cbind( Ne_s, Ne )
+  }  
+  return( list( Weights = Weights, Ne_s = Ne_s, R_2_s = R_2_s, m_s = m_s, s_s = s_s ) )
 }
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