How do you design and implement a single-factor stress test for a portfolio?

Question

AcadiFi · Accepted Answer

A single-factor stress test examines how a portfolio's value changes when ONE risk factor is shocked by a large amount while all other factors either remain unchanged or move according to their historical correlations with the stressed factor.

## The Process

**Step 1: Select the risk factor**
Common choices: interest rates, credit spreads, equity index level, oil price, FX rate, implied volatility.

**Step 2: Determine the shock magnitude**
This can be:
- **Historical** — based on an actual extreme move (e.g., the 10Y Treasury yield moved +150 bps during the 2022 tightening)
- **Hypothetical** — a scenario that hasn't occurred but is plausible (e.g., oil price drops 40% due to demand collapse)
- **Regulatory** — prescribed by the regulator (e.g., EBA stress test assumptions)

**Step 3: Full revaluation**
Reprice EVERY position in the portfolio under the stressed factor. This is "full revaluation" as opposed to using sensitivities.

## Worked Example

Redstone Capital manages a $200M portfolio of corporate bonds and equity options. The risk committee wants a single-factor stress test: "What happens if credit spreads widen by 200 bps?"

**Portfolio composition:**

| Position | Notional | Spread Duration | Spread Sensitivity |
|---|---|---|---|
| Whitmore Corp bonds (BBB) | $80M | 4.5 | -$3.60M per 100bps |
| Ashford Inc bonds (A) | $60M | 6.2 | -$3.72M per 100bps |
| Vanguard Equity options | $40M | N/A | -$0.15M per 100bps |
| Redstone CDS protection (short risk) | $20M | 3.0 | +$0.60M per 100bps |

**Apply +200 bps shock:**

| Position | P&L Impact |
|---|---|
| Whitmore Corp | -$3.60M x 2 = -$7.20M |
| Ashford Inc | -$3.72M x 2 = -$7.44M |
| Equity options (via correlation) | -$0.15M x 2 = -$0.30M |
| CDS protection (hedge) | +$0.60M x 2 = +$1.20M |
| **Total** | **-$13.74M** |

The portfolio would lose approximately **6.87%** under this scenario.

```mermaid
flowchart TD
    FACTOR["Single Factor: Credit Spread +200bps"] --> P1["Whitmore Bonds
-$7.20M"]
    FACTOR --> P2["Ashford Bonds
-$7.44M"]
    FACTOR --> P3["Equity Options
-$0.30M"]
    FACTOR --> P4["CDS Hedge
+$1.20M"]
    P1 --> TOTAL["Portfolio Impact
-$13.74M (-6.87%)"]
    P2 --> TOTAL
    P3 --> TOTAL
    P4 --> TOTAL
    TOTAL --> ACTION{"Breach Limit?"}
    ACTION -->|"Yes"| REDUCE["Reduce Exposure
or Increase Hedges"]
    ACTION -->|"No"| MONITOR["Continue Monitoring"]
```

## Single-Factor vs. Multi-Factor Stress Tests

- **Single-factor** is simpler and isolates the impact of one driver, but ignores correlations breaking down
- **Multi-factor** (e.g., rates up + spreads widen + equities down simultaneously) is more realistic but harder to calibrate
- Best practice: run both and compare results

For more stress testing methodology, check our FRM Part I course.

How do you design and implement a single-factor stress test for a portfolio?

Master Part I with our FRM Course

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