Monte Carlo simulation of the payoffs to angel investing

angel_sim.py

#!/usr/bin/python
#
# Monte Carlo simulation of the payoffs to angel investing.
#
# Assume a pool of N different investors, each investing in D deals,
# with a fixed time horizon and a fixed distribution of payoffs.
# Randomly simulate each investor's total payoff, then compute the
# mean and std dev of all IRRs in the overall pool.
#
# This gives an individual angel an idea of what kind of payoff &
# variance to expect from investing in a certain # of deals.
#
# Written by Jeff Miller @jmillerinc.
#
# See: http://jmillerinc.com/2010/04/27/angel-investing-simulation
#
# Payoff distribution from http://www.gabrielweinberg.com/blog/2010/03/
# angel-investing-portfolio-scenario-planner-spreadsheet.html

import math
import optparse
import random


DEFAULT_NUM_INVESTORS = 10000
DEFAULT_NUM_DEALS = 20
NUM_YEARS = 5
PROBS   = [.50, .20, .15, .13, .02]
PAYOFFS = [  0,   1,   3,  10,  20]


def random_draw(cum_probs):
    """Randomly draw from a discrete distribution with the given
    cumulative probabilities. Return the index of the probability
    bucket that was drawn."""
    z = random.random()
    for i, p in enumerate(cum_probs):
        if z <= p:
            return i
    raise Exception('Execution should never reach this point: ' +
                    'cumulative probabilities are invalid.')


def cumulative_probabilities(probs):
    """Given a discrete distribution as a list of probabilities,
    return the list of cumulative probabilities."""
    result = [sum(probs[0:i+1]) for i in range(len(probs))]
    assert abs(result[-1] - 1.0) < 1e-6
    return result


if __name__ == '__main__':
    option_parser = optparse.OptionParser()
    option_parser.add_option('-n', type='int', dest='num_investors', default=DEFAULT_NUM_INVESTORS,
                             metavar='N', help='Simulate N investors (default %d)' % DEFAULT_NUM_INVESTORS)
    option_parser.add_option('-d', type='int', dest='num_deals', default=DEFAULT_NUM_DEALS,
                             metavar='D', help='Simulate D deals per investor (default %d)' % DEFAULT_NUM_DEALS)
    options, args = option_parser.parse_args()

    num_investors = options.num_investors
    num_deals = options.num_deals

    # Simulate N investors doing D deals each.
    n = 0
    summ = 0.0
    summ2 = 0.0
    cum_probs = cumulative_probabilities(PROBS)
    deal_size = 1.0/float(num_deals)
    for i in range(num_investors):
        total_payoff = sum(deal_size * PAYOFFS[random_draw(cum_probs)] for j in range(num_deals))
        irr = pow(total_payoff, 1.0/NUM_YEARS) - 1
        summ += irr
        summ2 += irr*irr
        n += 1

    mean_irr = summ/n
    std_irr = math.sqrt((summ2 - summ*summ/n)/(n-1))
    print 'N = %5d  D = %3d  mean_irr = %8.4f  std_irr = %8.4f' % (num_investors, num_deals, mean_irr, std_irr)