How to stress test a portfolio with your own scenario

Most portfolio tools offer one kind of stress test: pick a past crisis and replay it. That answers a real question — how would this allocation have handled 2008 or March 2020 — but not the one investors usually ask, which is about the next shock, not the last one. What if semiconductors fall 35%? What if long Treasuries lose 15% while the dollar firms? Those are scenario stress tests, and the Stress Lab in MEDGE is built for them.

Two kinds of stress test

The shortcut that double-counts

The quick way to run a custom scenario is to estimate the portfolio’s beta to each factor with a separate regression, multiply each beta by its shock and add up the products. It looks reasonable and it is wrong whenever the shocked factors are correlated — which, for equity indices, sectors and styles, is almost always.

A deliberately simple illustration. Take a fund that tracks the S&P 500 exactly, so its beta to the S&P 500 is 1. Assume, for the example, daily volatility of 1.1% for the S&P 500 and 1.4% for the Nasdaq 100, with a correlation of 0.92 between them. The fund’s beta to the Nasdaq 100, estimated on its own, is 0.92 × 1.1 × 1.4 / 1.4² ≈ 0.72. Now set the scenario S&P 500 −30%, Nasdaq 100 −35%.

The fix: treat the shocks jointly

Model daily returns as jointly normal with covariance Σ. Given shocks s on a set of benchmarks S, the expected move of any other asset a is the conditional expectation μ_a = Σ_aS Σ_SS⁻¹ s, and what the shocks do not explain has variance h·(σ²_a − Σ_aS Σ_SS⁻¹ Σ_Sa) over a horizon of h days. This is exactly the coefficient vector of a multiple regression of the asset on all shocked benchmarks at once, so correlated shocks share the effect instead of stacking it. It also gives the implied move of every benchmark you did not shock — which is how a scenario like "semiconductors −35%" becomes a full picture of the market.

• ·Work in log returns and convert back, so a −50% shock stays meaningful.
• ·Add a small ridge to Σ_SS when shocked benchmarks are nearly collinear (an S&P 500 fund and the S&P 500 itself).
• ·Build the portfolio band from the residual covariance of the holdings, not from each holding separately.

Estimate relationships on the right market

Correlations are not constant. In sell-offs equities move more together and some hedges weaken; in strong markets dispersion rises. A scenario about a bear market should use relationships estimated on bear-market days. MEDGE classifies each session by the S&P 500’s trend over the previous three months, splits the sample into thirds, and blends each third with the full history in proportion to its size, so a few extreme days cannot dominate. Running the same shocks under bear, neutral and bull relationships is itself informative: a large spread means the answer depends on conditions that may not hold.

Check the scenario, not only the result

• ·Plausibility: the Mahalanobis distance of the shocks, s′(hΣ_SS)⁻¹s, follows a chi-square distribution under normality. It ranks how extreme the combination is. Normal tails understate real extremes, so read it as a ranking.
• ·Coherence: for each shock, compute what the other shocks imply for it. A shock several standard deviations away from that — S&P 500 −25% with Nasdaq 100 +20% — assumes the usual relationship breaks. That can be the point of the scenario, but it should be deliberate.
• ·Historical analogues: find the past windows in which the shocked benchmarks moved most like the scenario, measured in standard deviations, and compare what each holding actually did with what the model expects.

Read the holdings

The portfolio number tells you whether the loss is tolerable. The holdings tell you what to do about it. For each holding, compare its scenario move with its closest index, its sector and its country peers; check whether its sensitivity to the index rises in bear phases, how much of the index’s down days it captures, and whether it gave way in the index’s worst historical months. Then rank everything — inside and outside the portfolio — by how it fares in the scenario and how much it offsets the risk you already hold, and try the change: in the Stress Lab a weight edit updates the outcome instantly.