Katkat
Back

Maximize credit card portfolio profit

OneMain FinancialData Scientist · Technical Screen
MediumData ScientistTechnical ScreenAnalytics & Experimentation

Last updated

This problem tests your ability to model expected profitability by balancing credit risk (probability of default) against revenue generation and defining optimal decision thresholds.

Problem Statement

You are tasked with optimizing the approval strategy for a new credit card product. Your goal is to maximize the total expected profit for a cohort of 10,000 applicants.

Data Available

For each applicant, you have:

  • score: A proprietary credit risk score ranging from 300 to 850.
  • EAD (Exposure at Default): The expected balance on the account if they default.
  • LGD (Loss Given Default): The percentage of EAD that cannot be recovered (assume 80% constant).
  • revenue: The estimated annual fee and net interest income expected from the applicant if approved.
  • PD(score): The Probability of Default, modeled as PD(score) = 1 / (1 + exp(0.02 * (score - 600))).

Task

  1. Define the Profit Function P for a single applicant: P = Revenue - (PD * EAD * LGD)
  2. Determine the optimal score_threshold to maximize total portfolio profit. Only applicants with score >= threshold should be approved.
  3. Assume you have a historical dataset of 10,000 applicants with their scores, EADs, and revenues. Describe the analytical steps to find the threshold that maximizes sum(P) for the approved subset.

Constraints & Edge Cases

  • Assume Revenue and EAD are pre-calculated per applicant.
  • Consider cases where P is negative for high-risk applicants.
  • How would the optimal threshold shift if the company decides to prioritize market share (volume) over profit density?

Hints

Hint 1

Calculate the net profit for each individual applicant based on their specific risk and revenue profile.

Hint 2

Sort the applicants by their credit score and calculate the cumulative profit for every possible threshold cut-off point.

Hint 3

Since the number of applicants is finite, you can iterate through all unique score values present in your data to find the global maximum of cumulative profit.

Follow-up questions

  • If you want to test your threshold on a hold-out set, what metrics would you track besides total profit to ensure the model is stable?
  • How would you account for 'adverse selection' if the score distribution of applicants changes after you implement your new threshold?
  • Suppose we want to run an A/B test on this threshold. How would you design the experiment to minimize business risk while ensuring statistical power?