Scenario and factor stress tests for a multi-asset portfolio: rate shock, equity drawdown and inflation surprise
Turn three macro scenarios into euro losses for a five-asset portfolio using portfolio beta and duration contribution, and compare the results with a written loss limit.
What you will learn
- Historical, hypothetical and factor stress tests.
- How to compute portfolio beta and duration contribution.
- How to run a rate shock, an equity drawdown and an inflation surprise through a multi-asset portfolio in euros.
- How to compare results with your drawdown budget.
Explanation
A stress test asks what the portfolio would lose if a specific thing happened; it complements volatility, which describes normal days, with a view of bad weeks. A historical scenario replays a past episode (course "Market History"). A hypothetical scenario is a story you write ("rates up 150 basis points, equities down 8 percent"). A factor stress shocks one risk factor and lets each asset respond through its sensitivity. We use the factor approach because it needs only two sensitivities you already know.
Equity beta is the sensitivity of an asset's return to the broad equity market (course "Stocks & Fundamental Analysis"). Modified duration is the sensitivity of a bond's price to a parallel yield change: price change ≈ −duration × yield change (course "Bonds & Fixed Income in Depth"). At portfolio level we use two aggregates:
portfolio beta = Σ wi × βi (over the equity sleeves)
duration contribution = w(bonds) × duration(bonds), so euro loss per 100 basis points ≈ portfolio value × duration contribution × 1 %.
A basis point (bp) is 0.01 percentage points. For large yield moves convexity (the curvature of the price–yield relationship) softens the loss slightly; with convexity 60 and a 150 bp rise the correction is 0.5 × 60 × 0.015² = +0.675 points. We leave it out of the table to keep the test conservative.
The three standard scenarios and their assumptions:
- Rate shock: yields rise in parallel; bonds lose duration × move; equities fall modestly through lower multiples; gold falls as real yields rise; cash is flat.
- Equity drawdown: the market falls; each equity sleeve falls beta × move; government bonds and gold gain slightly from the flight to safety (the 2008 and 2020 pattern).
- Inflation surprise: yields rise more than in scenario 1, equities fall as multiples and real earnings suffer, gold rises. Bonds and equities fall together: the 2022 pattern, when the stock–bond correlation flipped (lesson 2).
Each assumption is a judgement, so state it in the table. The value lies not in precision but in comparing scenarios with each other and with the loss limit from your drawdown budget (lesson 5).
Worked example
Hypothetical example: €500,000: global developed equities 55 percent (beta 1.0), emerging-market equities 10 percent (beta 1.2), euro government bonds 25 percent (modified duration 7), gold 5 percent, cash 5 percent. Written limit: no scenario may cost more than 25 percent. Fees, taxes, currency effects and convexity are excluded.
Aggregates: beta = 0.55 × 1.0 + 0.10 × 1.2 = 0.67; duration contribution = 0.25 × 7 = 1.75 years; loss per 100 bp ≈ 500,000 × 1.75 × 1 % = €8,750.
| Sleeve (value) | Rate shock +150 bp | Equity drawdown −35 % | Inflation surprise |
|---|---|---|---|
| Global equities (€275,000) | −8 % → −€22,000 | 1.0 × −35 % → −€96,250 | −15 % → −€41,250 |
| EM equities (€50,000) | −10 % → −€5,000 | 1.2 × −35 % = −42 % → −€21,000 | −15 % → −€7,500 |
| Euro gov. bonds (€125,000) | −7 × 1.5 % = −10.5 % → −€13,125 | +5 % → +€6,250 | −7 × 2.0 % = −14 % → −€17,500 |
| Gold (€25,000) | −5 % → −€1,250 | +5 % → +€1,250 | +10 % → +€2,500 |
| Cash (€25,000) | 0 | 0 | 0 |
| Total | −€41,375 (−8.3 %) | −€109,750 (−22.0 %) | −€63,750 (−12.8 %) |
The equity drawdown is the binding scenario at −22.0 percent, inside the 25 percent budget with little room. For a 15 percent limit the quickest lever is the equity share: with beta 0.67 a 35 percent fall costs about 23.5 percent before offsets, so equities would need to drop to roughly 40 percent of the portfolio. The inflation scenario shows why "bonds protect equities" is regime-dependent: here they add €17,500 to the loss.
Common mistake
Practice activity
On paper: €300,000 with 50 percent global equities (beta 1.0), 20 percent small caps (beta 1.3), 25 percent bonds (duration 5), 5 percent cash. (a) Portfolio beta and duration contribution? (b) Euro loss in an equity drawdown of −30 percent with bonds +4 percent? (c) Euro loss in a rate shock of +200 bp with both equity sleeves −10 percent? Which scenario breaks a 20 percent limit?
Show solution
(a) Beta = 0.50 × 1.0 + 0.20 × 1.3 = 0.76. Duration contribution = 0.25 × 5 = 1.25 years.
(b) Global: 150,000 × −30 % = −€45,000. Small caps: 60,000 × −39 % = −€23,400. Bonds: 75,000 × +4 % = +€3,000. Total −€65,400 = −21.8 percent: breaks the 20 percent limit.
(c) Bonds: 75,000 × (−5 × 2 %) = −€7,500. Equities: 210,000 × −10 % = −€21,000. Total −€28,500 = −9.5 percent: within the limit.
Limitations: betas are historical averages and rise in crashes; convexity, currency moves and losses beyond the scenario are ignored.
Key takeaways
- Two aggregates summarise most multi-asset risk: portfolio beta (Σ w × β) and duration contribution (w × duration).
- Run rate shock, equity drawdown and inflation surprise, stating every assumption.
- Compare the worst scenario with your written limit; the equity share is the fastest lever.
- Include the scenario in which your main hedge fails; in 2022 that was bonds.
Next step
Next: leverage inside a portfolio, from leveraged ETFs and volatility drag to margin loans and the debate about borrowing when young.
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