def getOptPort(naRets,
fTarget,
lPeriod=1,
naLower=None,
naUpper=None,
lNagDebug=0):
"""
@summary Returns the Markowitz optimum portfolio for a specific return.
@param naRets: Daily returns of the various stocks (using returnize1)
@param fTarget: Target return, i.e. 0.04 = 4% per period
@param lPeriod: Period to compress the returns to, e.g. 7 = weekly
@param naLower: List of floats which corresponds to lower portfolio% for each stock
@param naUpper: List of floats which corresponds to upper portfolio% for each stock
@return tuple: (weights of portfolio, min possible return, max possible return)
"""
''' Attempt to import library '''
try:
pass
import nagint as nag
except ImportError:
print 'Could not import NAG library, make sure nagint.so is in your python path'
return ([], 0, 0)
''' Get number of stocks '''
lStocks = naRets.shape[1]
''' If period != 1 we need to restructure the data '''
if (lPeriod != 1):
naRets = getReindexedRets(naRets, lPeriod)
''' Calculate means and covariance '''
naAvgRets = np.average(naRets, axis=0)
naCov = np.cov(naRets, rowvar=False)
''' Special case for None == fTarget, simply return average returns and cov '''
if (fTarget is None):
return naAvgRets, np.std(naRets, axis=0)
''' Calculate upper and lower limits of variables as well as constraints '''
if (naUpper is None):
naUpper = np.ones(lStocks) # max portfolio % is 1
if (naLower is None):
naLower = np.zeros(lStocks) # min is 0, set negative for shorting
''' Two extra constraints for linear conditions, result = desired return, and sum of weights = 1 '''
naUpper = np.append(naUpper, [fTarget, 1.0])
naLower = np.append(naLower, [fTarget, 1.0])
''' Initial estimate of portfolio '''
naInitial = np.array([1.0 / lStocks] * lStocks)
''' Set up constraints matrix, composed of expected returns in row one, unity row in row two '''
naConstraints = np.vstack((naAvgRets, np.ones(lStocks)))
''' Get portfolio weights, last entry in array is actually variance '''
try:
naReturn = nag.optPort(naConstraints, naLower, naUpper, naCov,
naInitial, lNagDebug)
except RuntimeError:
print 'NAG Runtime error with target: %.02lf' % (fTarget)
return (naInitial, sqrt(naCov[0][0])
) #return semi-junk to not mess up the rest of the plot
''' Calculate stdev of entire portfolio to return, what NAG returns is slightly different '''
fPortDev = np.std(np.dot(naRets, naReturn[0, 0:-1]))
''' Show difference between above stdev and sqrt NAG covariance, possibly not taking correlation into account '''
#print fPortDev / sqrt(naReturn[0,-1])
''' Return weights and stdDev of portfolio. note again the last value of naReturn is NAG's reported variance '''
return (naReturn[0, 0:-1], fPortDev)
def getOptPort(rets, f_target, l_period=1, naLower=None, naUpper=None, lNagDebug=0):
"""
@summary Returns the Markowitz optimum portfolio for a specific return.
@param rets: Daily returns of the various stocks (using returnize1)
@param f_target: Target return, i.e. 0.04 = 4% per period
@param l_period: Period to compress the returns to, e.g. 7 = weekly
@param naLower: List of floats which corresponds to lower portfolio% for each stock
@param naUpper: List of floats which corresponds to upper portfolio% for each stock
@return tuple: (weights of portfolio, min possible return, max possible return)
"""
# Attempt to import library """
try:
pass
import nagint as nag
except ImportError:
print 'Could not import NAG library'
print 'make sure nagint.so is in your python path'
return ([], 0, 0)
# Get number of stocks """
lStocks = rets.shape[1]
# If period != 1 we need to restructure the data """
if( l_period != 1 ):
rets = getReindexedRets( rets, l_period)
# Calculate means and covariance """
naAvgRets = np.average( rets, axis=0 )
naCov = np.cov( rets, rowvar=False )
# Special case for None == f_target"""
# simply return average returns and cov """
if( f_target is None ):
return naAvgRets, np.std(rets, axis=0)
# Calculate upper and lower limits of variables as well as constraints """
if( naUpper is None ):
naUpper = np.ones( lStocks ) # max portfolio % is 1
if( naLower is None ):
naLower = np.zeros( lStocks ) # min is 0, set negative for shorting
# Two extra constraints for linear conditions"""
# result = desired return, and sum of weights = 1 """
naUpper = np.append( naUpper, [f_target, 1.0] )
naLower = np.append( naLower, [f_target, 1.0] )
# Initial estimate of portfolio """
naInitial = np.array([1.0/lStocks]*lStocks)
# Set up constraints matrix"""
# composed of expected returns in row one, unity row in row two """
naConstraints = np.vstack( (naAvgRets, np.ones(lStocks)) )
# Get portfolio weights, last entry in array is actually variance """
try:
naReturn = nag.optPort( naConstraints, naLower, naUpper, \
naCov, naInitial, lNagDebug )
except RuntimeError:
print 'NAG Runtime error with target: %.02lf'%(f_target)
return ( naInitial, sqrt( naCov[0][0] ) )
#return semi-junk to not mess up the rest of the plot
# Calculate stdev of entire portfolio to return"""
# what NAG returns is slightly different """
fPortDev = np.std( np.dot(rets, naReturn[0,0:-1]) )
# Show difference between above stdev and sqrt NAG covariance"""
# possibly not taking correlation into account """
#print fPortDev / sqrt(naReturn[0, -1])
# Return weights and stdDev of portfolio."""
# note again the last value of naReturn is NAG's reported variance """
return (naReturn[0, 0:-1], fPortDev)
