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Simple script for estimating bankruptcy probabilities during retirement
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| #!/usr/bin/env python3 | |
| # -*- coding: utf-8 -*- | |
| """ | |
| Created on Sun Feb 5 11:01:52 2017 | |
| @author: andyjones | |
| """ | |
| import scipy as sp | |
| import matplotlib.pyplot as plt | |
| import matplotlib as mpl | |
| import seaborn as sns | |
| import pandas as pd | |
| from itertools import product | |
| def simulate_savings(drawdown, ret, years, vol=0.15, trials=5000): | |
| savings = [sp.ones(trials)] | |
| for i in range(years): | |
| returns = sp.random.normal(ret, vol, (trials,)) | |
| after_expenses = sp.clip(savings[-1] - drawdown, 0, None) | |
| after_returns = sp.clip(after_expenses + returns*after_expenses, 0, None) | |
| savings.append(after_returns) | |
| savings = sp.vstack(savings) | |
| return savings | |
| def failure_probability(drawdown, ret, years, **kwargs): | |
| savings = simulate_savings(drawdown, ret, years=years, **kwargs) | |
| return (savings == 0).mean(1)[-1] | |
| def failure_probabilities(rets): | |
| results = {} | |
| for ret in rets: | |
| print(ret) | |
| rates = sp.linspace(0, 0.1, 51) | |
| years = sp.linspace(5, 50, 46, dtype=int) | |
| results[ret] = {} | |
| for drawdown, year in product(rates, years): | |
| results[ret][(year, drawdown)] = failure_probability(drawdown, ret, years=year) | |
| results[ret] = pd.Series(results[ret]).unstack() | |
| results = pd.Panel(results) | |
| results.major_axis.name = 'years of retirement' | |
| results.minor_axis.name = 'annual expenditure' | |
| return results | |
| def plot_failure_rates(): | |
| results = failure_probabilities(sp.linspace(0, .1, 11)) | |
| sns.set_style('white') | |
| fig, axes = plt.subplots(3, 3, figsize=(22, 18)) | |
| for ax, ret in zip(axes.flatten(), results.items[1:]): | |
| im = ax.imshow(100*results[ret], | |
| cmap=plt.cm.viridis, | |
| interpolation='nearest', | |
| extent=(100*results[ret].columns[0], | |
| 100*results[ret].columns[-1], | |
| results[ret].index[0], | |
| results[ret].index[-1]), | |
| aspect='auto', | |
| origin='lower', | |
| vmin=0, vmax=100) | |
| ax.grid(True, alpha=0.2) | |
| ax.set_title('{:.0f}% annual return'.format(100*ret)) | |
| ax.set_xlabel(results[ret].columns.name) | |
| ax.set_ylabel(results[ret].index.name) | |
| plt.colorbar(im, ax=ax, format='%.0f%%') | |
| ax.xaxis.set_major_formatter(mpl.ticker.FormatStrFormatter('%.0f%%')) | |
| fig.suptitle('Probability of bankruptcy at different rates of expenditure and return\n(Independent normal returns, 15% annual volatility)', fontsize=20) | |
| fig.savefig('failure_prob.png', bbox_inches='tight') | |
| if __name__ == '__main__': | |
| plot_failure_rates() |
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