How often do Afterpay transactions attract late fees? (Part 5)

Let’s take a high-level view of how often Afterpay customers pay late, based on Afterpay’s FY2019 Annual report.
Bayesian
PyMC3
Finance
Monte Carlo Simulation
Afterpay
Published

August 29, 2020

Introduction

Now that we have more data from Afterpayon the actual rate of purchases that attract late fees (±10%), I wanted to go back and compute the average late fees. This post is effectively an adaption of the work I did in this post.

Important

Obviously, I need a disclaimer. If you use anything I say as the basis for any decision, financial or otherwise, you are an idiot.

Average Late Fees

%matplotlib inline
import pymc3 as pm
import matplotlib.pyplot as plt
import numpy as np
import math
import seaborn as sns
import scipy.stats as st

plt.rcParams["figure.figsize"] = (10,10)
from warnings import filterwarnings
filterwarnings('ignore')
with pm.Model() as average_late_fee_model:
    underlying_sales_aud = pm.Uniform('underlying_sales_aud', lower=5.24715*10**9, upper=5.247249*10**9)
    
    late_fees_rev_aud = pm.Uniform('late_fees_rev', lower=46.05 * 10**6, upper=46.149 * 10**6)
    
    average_transaction_value_aud = pm.Uniform('average_transaction_value', lower=144.50, upper=154.49)
    
    late_payment_rate = pm.Uniform('late_payment_rate',lower=9.5,upper=10.5)/100.0
    
    number_of_transactions = pm.Deterministic('number_of_transactions', underlying_sales_aud / average_transaction_value_aud)
    
    late_transactions = pm.Deterministic('late_transactions', late_payment_rate * number_of_transactions)
                                         
    average_late_fee_aud = pm.Deterministic('average_late_fee_aud', late_fees_rev_aud / late_transactions)
    
pm.model_to_graphviz(model)

with average_late_fee_model:
    samples = pm.sample_prior_predictive(samples = 100_000)

Results

late_fee_samples = samples['average_late_fee_aud']
plt.title('Histogram of late fees')
plt.ylabel('Relative Frequency')
plt.xlabel('Late fee (AUD)')
sns.distplot(late_fee_samples,kde=False, norm_hist=True)
plt.show()

pm.summary(samples["average_late_fee_aud"])
arviz.stats.stats_utils - WARNING - Shape validation failed: input_shape: (1, 100000), minimum_shape: (chains=2, draws=4)
mean sd hpd_3% hpd_97% mcse_mean mcse_sd ess_mean ess_sd ess_bulk ess_tail r_hat
x 13.146 0.458 12.313 13.982 0.001 0.001 99393.0 99393.0 99248.0 99302.0 NaN

Conclusion

The late fees that Afterpay customers pay are low, somewhere between 12 AUD and 14 AUD on average. This fits what we observed in previous posts, where customers were typically late on only one of the four payments.