Probability of Exceeding Return Chart

chartxceedbenchmark.py

import numpy as np

def vcdist(alpha):
    # generates one pick from the VC distribution
    # prob density distribution = 1/3 0x, 1/3 1x, 1/3 power law with alpha=alpha
    # returns one draw from the distribution as a float
    pn=np.random.randint(0,3)
    if pn==2:
        td = powerlaw.Power_Law(xmin=1.0, parameters=[alpha])
        return td.generate_random(1)[0]
    return pn

def vcportfolios(alpha,n):
    # creates 10,000 random portfolios, each of size n and finds average mean
    # of those portfolios and the percent of those portfolios above 1x,2x,3x,4x
    # returns tuple: (mean, %>1x, %>2x, %>3x, %>4x)
    runs=10000.
    portfolioavgs=[average([vcdist(alpha) for i in range(n)]) for j in range(int(runs))]
    return (average(portfolioavgs),
            (len([i for i in portfolioavgs if i>1.])/runs),
            (len([i for i in portfolioavgs if i>2.])/runs),
            (len([i for i in portfolioavgs if i>3.])/runs),
            (len([i for i in portfolioavgs if i>4.])/runs))

def plt_vcports(alpha):
    # runs vcportfolios at portfolio sizes from 1 to 100
    # charts result
    # no return value
    xm,xm1,xm2,xm3,xm4=[],[],[],[],[]
    X=range(1,101,1)
    for i in X:
        m,m1,m2,m3,m4 = vcportfolios(alpha,i)
        xm.append(m)      #mean, not charted here
        xm1.append(m1)    #more than 1x
        xm2.append(m2)    #more than 2x
        xm3.append(m3)    #more than 3x
        xm4.append(m4)    #more than 4x
 
    # chart results
    ax = plt.figure(figsize=(10, 10)).add_subplot(211)
    ax.plot(X,xm1,X,xm2,X,xm3,X,xm4) 
    ax.set(xlim=[0, 100], ylim=[0,1],
           title='Probability of Exceeding Benchmark Return by Portfolio Size',
           xlabel='Portfolio Size', yticks=np.arange(0,1.1,.1))
    ax.yaxis.set_major_formatter(FuncFormatter(lambda y, _: '{:.0%}'.format(y)))
    ax.grid(True)
    ax.legend( ('% more than 1x','% more than 2x','% more than 3x','% more than 4x'),loc='upper left')