Why Agent Based Model

Suppose we have an investment fund currently valued at $1,000,000, 100% invested in the S&P 500 ETF.

We plan to take out the money in 30 years. How much do we expect to have in the account at that time?

Deterministic approach

The deterministc approach is the simplest (also unrealistic). We assume an annual rate of return of 8% for the next 30 years.

codedeterministic_value.py

pv = 1000000
i = 0.08
time_horizon = 30
balance_t = 0
print("{:10s} {:15s} ".format("Year", "Ending Balance"))
print("-"*25)
for yr in range(1, time_horizon + 1):
    balance_t = pv * (1 + i)
    print("{:<10d} {:15,.0f}".format(yr, balance_t))
    pv = balance_t

Non-deterministic approach

Can we rely on the fixed paramters? It seems unrealistic to assume 8% fixed annual return. We need to incorporate changes.

codenon_deterministic_value.py

import numpy.random as npr
stdev = 0.15
pv = 1000000
i = 0.08
time_horizon = 30
# balance_t
print("{:10s} {:15s} ".format("Year", "Ending Balance"))
print("-"*25)
for yr in range(1, time_horizon + 1):
    yr_return = npr.normal(i, stdev)
    balance_t = pv * (1 + yr_return)
    print("{:<10d} {:15,.0f}".format(yr, balance_t))
    pv = balance_t

We can run the above simulation many times (e.g. 100000 times) to get an idea of the possibilities.

Agent Based Model

$1,000,000 starter fund
8% average annual return
15% volatility
30 year time horizon

We run the simulation 100,000 times.

We create a 2-dimensional array np.zeros((iterations, time_horizon)) to store the results.

codemonte_carlo_simulation.py

import numpy as np
import numpy.random as npr
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
stdev = 0.15
pv = 1000000
i = 0.08
time_horizon = 30
iterations = 100000
returns_array = np.zeros((iterations, time_horizon))
for iteration in range(iterations):
    for yr in range(0, time_horizon ):
        returns_array[iteration][yr] = npr.normal(i, stdev)


print("{:10s} {:15s} ".format("Year", "Ending Balance"))
print("-"*25)
for yr in range(1, time_horizon + 1):
    yr_return = npr.normal(i, stdev)
    balance_t = pv * (1 + yr_return)
    print("{:<10d} {:15,.0f}".format(yr, balance_t))
    pv = balance_t