Correlation Budget Portfolio Model

CORRELATION BUDGET PORTFOLIO MODEL

Inspiration

Optiver Track Team: Arman Behera, Arthur, Aditya Kumar Singh, Orion Bhattacharya

WHAT IT IS A method for buying carbon credits at the lowest cost while making sure the tonnes actually arrive, even when project failures are linked. It uses only statistical and deterministic models. No large language models are used to select projects.

THE PROBLEM

Goal: 100,000 tonnes of expected delivery within a $1,000,000 budget, chosen from 4,355 projects.
Projects can fail, and failures are correlated. Projects that share a country, developer, registry or project type are less independent than projects with no shared exposure.
Picking the cheapest credits alone tends to produce a concentrated, fragile portfolio.

HOW IT WORKS

Project risk. A risk rating sets a base failure probability: AAA 1%, AA 2%, A 4%, BBB 7%, BB 12%, B 20%, CCC 35%, Unrated 15%. A past reversal multiplies it by 1.5.
Expected delivery. A buffer pool recovers 50% of lost credits, so survival = 1 - p x (1 - recovery). Expected delivery = sum of (tonnes bought x survival).
Correlation budget. For country, developer, project type and registry, compute a Herfindahl-Hirschman Index (HHI) from delivery-weighted shares. Combine them: C = 0.50 x HHI(developer) + 0.30 x HHI(country)
- 0.25 x HHI(type) + 0.15 x HHI(registry) The portfolio must keep C at or below 0.15.
Group caps. No developer above 10% of expected delivery, no country above 20%, no project type above 25%, no registry above 35%.
Time-decaying shocks. A recent failure temporarily raises its group's risk, then fades with a 180-day half-life: shock = baseline + delta x exp(-lambda x days_since_failure) Starting uplifts: developer 10 pp, country 6 pp, type 5 pp, registry 4 pp.
Optimise and stress-test. Choose the cheapest portfolio that meets a delivery reserve (110,000 to 130,000 tonnes), the correlation budget and the caps, then simulate country, developer, registry and project-type shocks.

CONSTRAINTS

Budget under $1,000,000; target 100,000 tonnes.
Cap of 10,000 tonnes per project. (A 10-tonne cap would allow only 43,550 tonnes across 4,355 projects, so it could never meet the target.)
Optional universe filters: whitelist or blacklist countries and providers, and a minimum risk rating.

KEY CAVEAT The dataset warns that failures are correlated but has too few dated failures to estimate correlations directly. The alpha weights and shock sizes are therefore policy assumptions, to be shown with sensitivity tests rather than treated as observed facts.

NEXT STEPS

Run sensitivity analysis on the alpha weights and C_max.
Keep a dated event log of failures (the workbook records only whether a reversal happened, not when).
Finalise the portfolio and validate it with scenario simulation.

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