Capstone project · Finance · about 210 minutes
How bad can a bad day get? A tail-risk review
Audit three years of daily fund returns, show why a normal model understates extreme losses, estimate historical Value-at-Risk and expected shortfall with honest uncertainty, test diversification under stress, and recommend how an endowment should size its liquidity buffer.
The brief
Wadi Sahm Endowment Trust (a fictional charitable endowment) holds SAR 120 million in three funds run by an invented manager, Meridian Dunes Capital: SAR 50 million in the Income fund, SAR 40 million in the Balanced fund and SAR 30 million in the Growth fund. The trust pays scholarships monthly and has commitments it must meet even in a market crash, so it keeps a cash liquidity buffer sized to "a very bad trading day" — today calculated as a one-day 99% normal (parametric) Value-at-Risk.
The investment committee has asked the risk team — you — for an independent review before it renews the policy:
- What do the return distributions actually look like? Is the normal model behind today's buffer a reasonable description of the funds' daily risk?
- How big is a very bad day? Estimate one-day Value-at-Risk (VaR) and expected shortfall (ES) by more than one method, with an honest statement of how precise those estimates are.
- Does holding three funds protect the trust when it matters? Look at correlation in calm and turbulent periods.
- What should the buffer be? Cash in the buffer earns less than the invested portfolio; the committee's planning assumption is a carry cost of 3% per year of the buffer. A buffer that is too small risks a forced sale in a falling market. Weigh both.
Stakeholders. The committee chair (wants one defensible number), the treasurer (pays the carry cost), and the scholarships office (needs payments never to be interrupted).
The data. asset_returns contains 750 trading days (2022-01-02 to 2024-11-14, Sunday–Thursday trading) of daily percentage returns for the three funds. The dataset is synthetic: it was generated to behave like real fund returns (fat tails, volatility clustering, a crash day), but the funds, the manager and the trust are invented. Nothing here describes a real market, and nothing in this project is investment advice — it is a review of how risk is measured, not a view on what to buy or sell.
Your deliverable is a risk review paper for the investment committee, built in the report workspace as you work through the six stages.
Dataset
Daily returns of three funds
750 rows · one row = one trading day · synthetic data
| Date | Income fund return (%) | Balanced fund return (%) | Growth fund return (%) |
|---|---|---|---|
| 2022-01-02 | 0.127 | -0.19 | 0.935 |
| 2022-01-03 | 0.145 | 0.287 | 2.042 |
| 2022-01-04 | -0.097 | -0.218 | -0.934 |
| 2022-01-05 | 0.004 | -0.305 | 0.727 |
| 2022-01-06 | 0.295 | 0.228 | -0.136 |
| 2022-01-09 | -0.199 | -0.216 | -0.017 |
Included with a Formula Quest membership
This capstone has 6 stages and 23 graded tasks, ending with a written report.
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