[Returnanalytics-commits] r2484 - pkg/PerformanceAnalytics/sandbox/pulkit/week1/code
noreply at r-forge.r-project.org
noreply at r-forge.r-project.org
Mon Jul 1 15:56:05 CEST 2013
Author: pulkit
Date: 2013-07-01 15:56:05 +0200 (Mon, 01 Jul 2013)
New Revision: 2484
Added:
pkg/PerformanceAnalytics/sandbox/pulkit/week1/code/PSROpt.py
pkg/PerformanceAnalytics/sandbox/pulkit/week1/code/data.csv
Modified:
pkg/PerformanceAnalytics/sandbox/pulkit/week1/code/PSRopt.R
Log:
Verified PSR Optimization - added Python code with data
Added: pkg/PerformanceAnalytics/sandbox/pulkit/week1/code/PSROpt.py
===================================================================
--- pkg/PerformanceAnalytics/sandbox/pulkit/week1/code/PSROpt.py (rev 0)
+++ pkg/PerformanceAnalytics/sandbox/pulkit/week1/code/PSROpt.py 2013-07-01 13:56:05 UTC (rev 2484)
@@ -0,0 +1,155 @@
+#!/usr/bin/env python
+# PSR class for Portfolio Optimization
+# On 20121128 by MLdP <lopezdeprado at lbl.gov>
+
+import numpy as np
+#-------------------------------------------
+#-------------------------------------------
+class PSR_Opt:
+ def __init__(self,series,seed,delta,maxIter,bounds=None):
+ # Construct the object
+ self.series,self.w,self.delta=series,seed,delta
+ self.z,self.d1Z=None,[None for i in range(series.shape[1])]
+ self.maxIter,self.iter,self.obs=maxIter,0,series.shape[0]
+ if len(bounds)==None or seed.shape[0]!=len(bounds):
+ self.bounds=[(0,1) for i in seed]
+ else:
+ self.bounds=bounds
+#-------------------------------------------
+ def optimize(self):
+ # Optimize weights
+ mean=[self.get_Moments(self.series[:,i],1) for i in range(self.series.shape[1])]
+ w=np.array(self.w)
+ # Compute derivatives
+ while True:
+ if self.iter==self.maxIter:break
+ # Compute gradient
+ d1Z,z=self.get_d1Zs(mean,w)
+ # Evaluate result
+ if z>self.z and self.checkBounds(w)==True:
+ # Store new local optimum
+ self.z,self.d1Z=z,d1Z
+ self.w=np.array(w)
+ # Find direction and normalize
+ self.iter+=1
+ w=self.stepSize(w,d1Z)
+ if w==None:return
+ return
+#-------------------------------------------
+ def checkBounds(self,w):
+ # Check that boundary conditions are satisfied
+ flag=True
+ for i in range(w.shape[0]):
+ if w[i,0]<self.bounds[i][0]:flag=False
+ if w[i,0]>self.bounds[i][1]:flag=False
+ return flag
+#-------------------------------------------
+ def stepSize(self,w,d1Z):
+ # Determine step size for next iteration
+ x={}
+ for i in range(len(d1Z)):
+ if d1Z[i]!=0:x[abs(d1Z[i])]=i
+ if len(x)==0:return
+ index=x[max(x)]
+ w[index,0]+=self.delta/d1Z[index]
+ w/=sum(w)
+ return w
+#-------------------------------------------
+ def get_d1Zs(self,mean,w):
+ # First order derivatives of Z
+ d1Z=[0 for i in range(self.series.shape[1])]
+ m=[0 for i in range(4)]
+ series=np.dot(self.series,w)[:,0]
+ m[0]=self.get_Moments(series,1)
+ for i in range(1,4):m[i]=self.get_Moments(series,i+1,m[0])
+ stats=self.get_Stats(m)
+ meanSR,sigmaSR=self.get_SR(stats,self.obs)
+ for i in range(self.series.shape[1]):
+ d1Z[i]=self.get_d1Z(stats,m,meanSR,sigmaSR,mean,w,i)
+ return d1Z,meanSR/sigmaSR
+#-------------------------------------------
+ def get_d1Z(self,stats,m,meanSR,sigmaSR,mean,w,index):
+ # First order derivatives of Z with respect to index
+ d1Mu=self.get_d1Mu(mean,index)
+ d1Sigma=self.get_d1Sigma(stats[1],mean,w,index)
+ d1Skew=self.get_d1Skew(d1Sigma,stats[1],mean,w,index,m[2])
+ d1Kurt=self.get_d1Kurt(d1Sigma,stats[1],mean,w,index,m[3])
+ d1meanSR=(d1Mu*stats[1]-d1Sigma*stats[0])/stats[1]**2
+ d1sigmaSR=(d1Kurt*meanSR**2+2*meanSR*d1meanSR*(stats[3]-1))/4
+ d1sigmaSR-=d1Skew*meanSR+d1meanSR*stats[2]
+ d1sigmaSR/=2*sigmaSR*(self.obs-1)
+ d1Z=(d1meanSR*sigmaSR-d1sigmaSR*meanSR)/sigmaSR**2
+ return d1Z
+#-------------------------------------------
+ def get_d1Mu(self,mean,index):
+ # First order derivative of Mu
+ return mean[index]
+#-------------------------------------------
+ def get_d1Sigma(self,sigma,mean,w,index):
+ # First order derivative of Sigma
+ return self.get_dnMoments(mean,w,2,1,index)/(2*sigma)
+#-------------------------------------------
+ def get_d1Skew(self,d1Sigma,sigma,mean,w,index,m3):
+ # First order derivative of Skewness
+ d1Skew=self.get_dnMoments(mean,w,3,1,index)*sigma**3
+ d1Skew-=3*sigma**2*d1Sigma*m3
+ d1Skew/=sigma**6
+ return d1Skew
+#-------------------------------------------
+ def get_d1Kurt(self,d1Sigma,sigma,mean,w,index,m4):
+ # First order derivative of Kurtosis
+ d1Kurt=self.get_dnMoments(mean,w,4,1,index)*sigma**4
+ d1Kurt-=4*sigma**3*d1Sigma*m4
+ d1Kurt/=sigma**8
+ return d1Kurt
+#-------------------------------------------
+ def get_dnMoments(self,mean,w,mOrder,dOrder,index):
+ # Get dOrder derivative on mOrder mean-centered moment with respect to w index
+ x0,sum=1.,0
+ for i in range(dOrder):x0*=(mOrder-i)
+ for i in self.series:
+ x1,x2=0,(i[index]-mean[index])**dOrder
+ for j in range(len(i)):x1+=w[j,0]*(i[j]-mean[j])
+ sum+=x2*x1**(mOrder-dOrder)
+ return x0*sum/self.obs
+#-------------------------------------------
+ def get_SR(self,stats,n):
+ # Set Z*
+ meanSR=stats[0]/stats[1]
+ sigmaSR=((1-meanSR*stats[2]+meanSR**2*(stats[3]-1)/4.)/(n-1))**.5
+ return meanSR,sigmaSR
+#-------------------------------------------
+ def get_Stats(self,m):
+ # Compute stats
+ return [m[0],m[1]**.5,m[2]/m[1]**(3/2.),m[3]/m[1]**2]
+#-------------------------------------------
+ def get_Moments(self,series,order,mean=0):
+ # Compute a moment
+ sum=0
+ for i in series:sum+=(i-mean)**order
+ return sum/float(self.obs)
+#-------------------------------------------
+#-------------------------------------------
+def main():
+ #1) Inputs (path to csv file with returns series)
+ path='data.csv'
+ maxIter=1000 # Maximum number of iterations
+ delta=.005 # Delta Z (attempted gain per interation)
+
+ #2) Load data, set seed
+ series=np.genfromtxt(path,delimiter=',') # load as numpy array
+ seed=np.ones((series.shape[1],1)) # initialize seed
+ bounds=[(0,1) for i in seed] # min and max boundary per weight
+
+ #3) Create class and solve
+ psrOpt=PSR_Opt(series,seed,delta,maxIter,bounds)
+ psrOpt.optimize()
+
+ #4) Optimize and report optimal portfolio
+ print 'Maximized Z-value: '+str(psrOpt.z)
+ print '# of iterations: '+str(psrOpt.iter)
+ print 'PSR optimal portfolio:'
+ print str(psrOpt.w)
+#-------------------------------------------
+# Boilerplate
+if __name__=='__main__': main()
Modified: pkg/PerformanceAnalytics/sandbox/pulkit/week1/code/PSRopt.R
===================================================================
--- pkg/PerformanceAnalytics/sandbox/pulkit/week1/code/PSRopt.R 2013-07-01 12:52:03 UTC (rev 2483)
+++ pkg/PerformanceAnalytics/sandbox/pulkit/week1/code/PSRopt.R 2013-07-01 13:56:05 UTC (rev 2484)
@@ -30,45 +30,45 @@
if(is.null(bounds)){
- message("Bounds not given assumeing bounds to be (0,1) for each weight")
+ message("Bounds not given assuming bounds to be (0,1) for each weight")
bounds = matrix(rep(c(0,1),columns),nrow = columns,byrow = TRUE)
}
-
+ z = 0
+ iter = 0
+ w = rep(1,columns)
+ d1z = 0
#Optimization Function
optimize<-function(){
- weights = rep(1,columns)/columns
- d1z = 0
- z = 0
- iter = 0
+ weights = w
mean = NULL
for(column in 1:columns){
- mean = c(mean,mean(x[,column]))
+ mean = c(mean,get_Moments(x[,column],1))
}
while(TRUE){
if(iter == MaxIter) break
dZ = get_d1Zs(mean,weights)
- if(dZ$z<z | checkBounds(weights)==FALSE){
- break
+ print(dZ$z)
+ if(dZ$z>z && checkBounds(weights)==TRUE){
+ z = dZ$z
+ d1z = dZ$d1Z
+ w = weights
}
- z = dZ$z
-
- d1z = dZ$d1Z
iter = iter + 1
- weights_new = stepSize(weights,d1z)
- if(is.null(weights_new)) break
- weights = weights_new
+ weights = stepSize(weights,dZ$d1Z)
+ if(is.null(weights)) break
}
- return(weights)
+ return(w)
}
# To Check the bounds of the weights
checkBounds<-function(weights){
flag = TRUE
for(i in 1:columns){
+
if(weights[i] < bounds[i,1]) flag = FALSE
- if(weights[i] > bounds[i,1]) flag = FALSE
+ if(weights[i] > bounds[i,2]) flag = FALSE
}
- return(TRUE)
+ return(flag)
}
#Calculate the step size to change the weights
@@ -76,7 +76,8 @@
if(length(which(d1Z!=0)) == 0){
return(NULL)
}
- weights[which(abs(d1Z)==max(abs(d1Z)))] = weights[which(abs(d1Z)==max(abs(d1Z)))]+(delta/d1Z[which(abs(d1Z)==max(abs(d1Z)))])
+ index = which(abs(d1Z) ==max(abs(d1Z)))
+ weights[index] = weights[index]+delta/d1Z[index]
weights = weights/sum(weights)
return(weights)
@@ -85,13 +86,19 @@
get_d1Zs<-function(mean,weights){
d1Z = NULL
m = NULL
- x_portfolio = Return.portfolio(x,weights)
- mu = mean(x_portfolio)
- sd = StdDev(x_portfolio)
- sk = skewness(x_portfolio)
- kr = kurtosis(x_portfolio)
- stats = c(mu,sd,sk,kr)
- m = c(stats[1],stats[2]^2,stats[3]*(stats[2]^3),stats[4]*(stats[2]^4))
+ x_portfolio = x%*%weights
+
+ m[1] = get_Moments(x_portfolio,1)
+ for(i in 2:4){
+ m = c(m,get_Moments(x_portfolio,i,m[1]))
+ }
+ stats = get_Stats(m)
+ #mu = mean(x_portfolio)
+ #sd = StdDev(x_portfolio)
+ #sk = skewness(x_portfolio)
+ #kr = kurtosis(x_portfolio)
+ #stats = c(mu,sd,sk,kr)
+ #m = c(stats[1],stats[2]^2,stats[3]*(stats[2]^3),stats[4]*(stats[2]^4))
SR = get_SR(stats,n)
meanSR = SR$meanSR
sigmaSR = SR$sigmaSR
@@ -107,13 +114,13 @@
get_d1Z<-function(stats,m,meanSR,sigmaSR,mean,weights,index){
d1Mu = get_d1Mu(mean,index)
d1Sigma = get_d1Sigma(stats[2],mean,weights,index)
- d1Skew = get_d1Skew(d1Sigma,stats[2],mean,weights,index,m[2])
- d1Kurt = get_d1Kurt(d1Sigma,stats[2],mean,weights,index,m[3])
+ d1Skew = get_d1Skew(d1Sigma,stats[2],mean,weights,index,m[3])
+ d1Kurt = get_d1Kurt(d1Sigma,stats[2],mean,weights,index,m[4])
d1meanSR = (d1Mu*stats[2]-d1Sigma*stats[1])/stats[2]^2
d1sigmaSR = (d1Kurt * meanSR^2+2*meanSR*d1meanSR*(stats[4]-1))/4
- d1sigmaSR = d1sigmaSR - d1Skew*meanSR+d1meanSR*stats[3]
+ d1sigmaSR = d1sigmaSR-(d1Skew*meanSR+d1meanSR*stats[3])
d1sigmaSR = d1sigmaSR/(2*sigmaSR*(n-1))
- d1Z = (d1meanSR*sigmaSR-d1sigmaSR*(meanSR-refSR))/sigmaSR^2
+ d1Z = (d1meanSR*sigmaSR-d1sigmaSR*meanSR)/sigmaSR^2
return(d1Z)
}
@@ -164,6 +171,16 @@
SR<-list("meanSR"=meanSR,"sigmaSR"=sigmaSR)
return(SR)
}
+ get_Stats<-function(m){
+ return(c(m[1],m[2]^0.5,m[3]/(m[2]^1.5),m[4]/(m[2]^2)))
+ }
+ get_Moments<-function(series,order,mean = 0){
+ sum = 0
+ for(i in series){
+ sum = sum + (i-mean)^order
+ }
+ return(sum/n)
+ }
weights = optimize()
result = matrix(weights,nrow = columns)
Added: pkg/PerformanceAnalytics/sandbox/pulkit/week1/code/data.csv
===================================================================
--- pkg/PerformanceAnalytics/sandbox/pulkit/week1/code/data.csv (rev 0)
+++ pkg/PerformanceAnalytics/sandbox/pulkit/week1/code/data.csv 2013-07-01 13:56:05 UTC (rev 2484)
@@ -0,0 +1,152 @@
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