Maximize credit card portfolio profit
Overview
This question evaluates competence in credit-risk quantification, portfolio profitability analysis, approval decisioning and experiment design for a Data Scientist role, requiring estimation of expected credit loss, per-account economics, cutoff-based approval rules, and validation planning within an analytics & experimentation domain.
Credit Card Approval and Profit Optimization (12‑month horizon)
Context
You receive 10,000 credit card applications per month. Applicants are grouped into risk bands with given portfolio share and annual probability of default (PD). You can estimate expected credit loss (ECL) using:
- EAD (exposure at default) = 80% of credit limit
- LGD (loss given default) = 90%
Revenues and costs per approved account (12‑month):
- Interchange revenue = 1.8% of annual spend
- Expected annual spend per approved = $6,000
- Variable servicing cost = $24/year
- Acquisition cost = $50 per approved
- Baseline credit limit = $2,500
Risk bands (share of applicants; PD):
- A: 10%; PD = 0.2%
- B: 20%; PD = 1%
- C: 30%; PD = 3%
- D: 25%; PD = 6%
- E: 15%; PD = 10%
Assume PDs are 12‑month, spend is not constrained by the baseline limit, and other revenues (e.g., interest) are ignored.
Tasks
- Compute, for each band, the expected credit loss (ECL) per approved and the expected profit per approved over 12 months.
- Choose an approval cutoff (approve A…?, B…?, etc.) that maximizes total monthly profit for 10,000 applicants. Report the monthly portfolio ECL and the approval rate under your cutoff.
- If limits can vary by band (e.g., halve D and E limits), recompute and state whether the optimal cutoff changes.
- Outline a safe experiment to validate the decisioning policy before full deployment.
Solution
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