Monte Carlo Simulation of the Basic Model

basicmcs.py

import numpy as np

def pickaportfolio(n):
   # possible outcomes, from Fred's post
   # portfolios of size n
   # returns the mean of a single random portfolio
   possible_outcomes = [0,0,0,0,1,1,1,3,3,10]
   # pick n random elements from the list and take the mean of the outcome
   return np.mean(np.random.choice(possible_outcomes,n))

def lotsofportfolios(m,n):
   # m portfolios of n picks each
   # returns a list of m means of portfolio size n
   return [pickaportfolio(n) for _ in range(m)]

def chartports(n):
   # Plot 10,000 runs with portfolio size n
   # no return value, chart is side-effect
   portfolios = lotsofportfolios(10000,n)
   plt.title('Distribution of returns, portfolio size %d' % n)
   tallest=max(plt.hist(portfolios,bins=[0,1,2,3,4,5,6,7,8], rwidth=0.7,align='mid')[0])
   plt.grid(True)
   plt.xlabel('Portfolio Return Multiple')
   plt.yticks(np.arange(0,tallest-tallest%-len(portfolios)/10.,len(portfolios)/10.),
      ('0%','10%','20%','30%','40%','50%','60%','70%','80%','90%','100%') )
   plt.show()
   print "Mean = %.3f" % np.mean(portfolios)