Lesson 16 of 20 · 6 min
Stress testing versus forecasting
A forecast asks what will probably happen; a stress test asks what happens if something specific does.
These two exercises look similar and answer different questions, and mixing them up produces analysis that satisfies nobody.
A forecast attaches probabilities to outcomes: this is likely, that is unlikely. Its usefulness depends entirely on those probabilities being roughly right, which for tail events the earlier lessons showed they are not.
A stress test does something different. It stipulates a scenario without claiming it is likely, and computes the consequence. If collateral falls 35 percent and correlations go to one, what is my loan-to-value, is the threshold breached, and what does the cure require? No probability is needed to answer that, which is the point: the answer is robust to being wrong about likelihood.
For a leveraged position, the stress test is usually the more useful exercise, because the question that matters is not how likely is a 30 percent decline but what happens to me if there is one. The second question has a definite answer computable from Track 1's arithmetic, while the first has an answer that depends on a tail estimate nobody can defend.
A minimal stress test for a pledged portfolio, all of it arithmetic:
- Pick a decline: 20, 30, 40 percent of collateral value.
- Recompute collateral value, applying beta if the decline is stated in market terms.
- Recompute the balance including accrued interest to that date.
- Compute loan-to-value on the basis your agreement specifies.
- If the threshold is breached, compute the shortfall and multiply by 1 ÷ (1 − threshold) to get the required sale.
Key terms
- Stress test
- Computing the consequence of a stipulated scenario, without assigning it a probability. Robust to being wrong about likelihood.
- Scenario
- A specific, internally consistent set of conditions. Chosen for severity and relevance rather than for likelihood.
- Reverse stress test
- Working backwards from a failure to the conditions that would cause it. Asks what would have to happen rather than what if.
Worked example
Three declines, three consequences
Collateral $600,000, balance $300,000, threshold 70%. Interest ignored for clarity.
- 20% decline
- Collateral $480,000, LTV 62.5%
- 30% decline
- Collateral $420,000, LTV 71.4%
- 30% decline: required sale
- $20,000
- 40% decline
- Collateral $360,000, LTV 83.3%
- 40% decline: required sale
- $160,000
- Probabilities used
- None
No breach. Headroom now 10.7%.
Breach. Shortfall $6,000.
$6,000 × 3.33.
Breach. Shortfall $48,000.
$48,000 × 3.33.
Five lines of arithmetic produced the full consequence map, and not one of them required a forecast.
Check yourself
Why is a stress test often more useful than a forecast for someone with a pledged portfolio?
Saved in this browser only. No account, nothing sent anywhere.
Educational only. Nothing in this lesson is investment, legal or tax advice, or a recommendation to enter into any transaction. Figures are illustrative and computed from the inputs stated in the lesson.