Scenario methodology: how Portfolio Lab runs stress tests

Advanced10 min read · updated 27 October 2026 · 9 sources

The Scenarios tab on the Risk page is a stress test for today's portfolio: it calculates what a shock to equities, interest rates, the dollar, crude oil, gold or credit spreads would do, how historical crises carry over to this portfolio and which move in a factor would trigger a given loss. It is based on a linear factor model estimated from monthly returns. This page describes what the code in core/scenarios.py actually calculates.

Data and factors

The basis is the same data as on the rest of the Risk page: monthly returns of completed months in the base currency from the settings, for all positions over their common period, at the target weights of the selected portfolio (positive weights only, scaled to 100%). Positions with a short history are extended by their proxy from the grid. In addition, there are seven factors as monthly series that the app already uses elsewhere. The code loads each series individually over its full available history, so that one short factor does not cut off the others.

The asset class returns are calculated in the base currency; for euro investors, Global equities therefore also includes exchange rate movements, and the regression separates out the dollar through its own factor. For the credit factor, the exchange rates cancel out except for a small cross term, because both asset classes are quoted in the same currency. With the US dollar as base currency, the dollar factor is dropped. If a series is missing when the data is retrieved, the page calculates without this factor and names it in a note. The interest rate series come from central bank statistics; where only monthly averages are available, they fill in only the period before the month-end values begin.

Deliberately left out of the model are euro credit spreads (the euro corporate bond series only starts in 2009), the slope of the yield curve, other currencies such as the pound, yen or Swiss franc, volatility and inflation. For these risks, either there is no long monthly series in the app, or they would overload the model at 60 months. You can recognise positions that depend mainly on them by their low R².

Regression per position

For each position, the code estimates a least squares regression of the monthly returns on all selected factors with an intercept, over the last 36, 60 or 120 common months or the entire common history; the default is 60 months, as on the rest of the page. At least 36 months are required, and at least three times as many months as there are coefficients. With all seven factors, that makes 24, so the minimum stays at 36. A factor whose series ends before the last month or is too short within the period is dropped, with a note.

The portfolio betas are the weighted sum of the betas. They match exactly a regression of the portfolio return, whose R² the page also shows. For each beta there is a t-statistic based on the classical standard errors. If the factors explain less than 50% of the variation of a position or of the portfolio, a note appears: in that case, every scenario captures only part of the risk. Closely related factors such as equities and credit, or euro and dollar interest rates, share the effect between them (multicollinearity). Individual betas then fluctuate strongly, but their sum in the scenario is well determined. If you want more stable betas, choose fewer factors.

Hypothetical scenarios

A scenario consists of shocks to one or more factors, such as equities −30% or euro rates +2 percentage points. For the remaining factors, there are two modes. Isolated, they stay at zero. With correlations (default), they take their conditional expectation, as proposed by Kupiec (1998) for stress tests: for jointly normally distributed factors with zero mean, this is the move you would expect on average if the shocked factors take exactly the specified values. The covariance matrix Σ is the sample covariance of the factors over the regression period.

Alphas are not included: a shock is a deviation from normal conditions, not a month with the usual return; the code also sets the factor means to zero. Each factor value comes with its z-score fₖ/σₖ in monthly standard deviations, and the scenario as a whole with its Mahalanobis distance. According to Breuer et al. (2009), the conditional expectation is the most plausible of all possible completions of the remaining factors: its Mahalanobis distance is the smallest. Kritzman and Li (2010) use the same distance as a measure of financial turbulence. If you want to model the causes and consequences of a scenario explicitly, you can use Bayesian networks (Rebonato 2010); Portfolio Lab sticks with the simpler conditional expectation.

If a portfolio value is entered, all impacts are also shown as amounts. As a measure of uncertainty, the page shows the portfolio's residual volatility for one month. Five templates set typical shocks: Equity crash (equities −30%), Rate shock (euro rates +2 percentage points), Stagflation (equities −20%, euro rates +1.5 percentage points, crude oil +50%), Dollar weakness (US dollar −10%) and Credit crisis (credit −6%). Shocks of down to −95% are allowed for equities and crude oil, and of up to ±5 percentage points for interest rates.

Historical crises

For each stored crisis window, the code measures the move of each factor from the end of the month before the first month to the end of the last month: returns compounded as Π(1 + fₜ) − 1, interest rate changes summed. These moves act on today's portfolio through today's betas, exactly like a hypothetical scenario that specifies all factors. This means that even a fund without prices from that period can be run through the crisis. If a factor is missing even a single month in the window (crude oil goes back less far as a monthly series than the other factors), its conditional expectation given the available factors is used instead. Windows without any factor series or with months after the last completed month are dropped. Supervisory principles call for scenarios that are severe but plausible (Basel Committee on Banking Supervision 2018). Twelve windows are stored, from Black Monday to the 2025 tariff shock:

If all positions have returns for every month of the window, the actual replay is shown alongside: Π(1 + Σ wᵢ rᵢₜ) − 1, reset to the target weights every month as in the risk decomposition, with proxies as in the grid. The difference between model and replay comes from the positions' residual risk, the alphas, compounding over several months (the model applies the betas to the whole move over the window) and the fact that the betas come from today's estimation period. For long windows such as the dotcom crash, it is therefore usually larger.

Reverse stress test

For a chosen factor j, the reverse stress test looks for the shock that moves the portfolio by a specified loss L; the default is 20%, the permitted range 0.5% to 90%. Because the model is linear, there is a closed-form solution. With correlations, the whole factor vector moves in direction c, i.e. per unit of factor j, each remaining factor moves by its regression slope on factor j; isolated, only the factor itself moves.

The page calculates this for all factors and marks as reachable whatever lies within the factor's permitted range. If the portfolio does not react at all in a given direction, there is no solution. A linear reverse stress test only finds the size of the shock along a fixed direction; Glasserman et al. (2015) show how to determine instead the most likely combination of factor moves behind a large loss.

Limitations

• Linear: the model has no convexity. For large interest rate moves, a bond loses less and gains more than the linear calculation suggests (see Scenario analysis); options, leveraged products and portfolio insurance strategies react quite differently from what their beta implies.
• Estimation period: betas and correlations come from the selected months. Correlations often rise in crises Longin and Solnik (2001); Kim and Finger (2000) therefore estimate separate correlations for stress periods. Correlations from calm years make scenarios too mild.
• Signs can flip: whether interest rates fall or rise in an equity crash depends on the period. In years with inflation shocks, equities and interest rates move together differently than in years with growth shocks.
• Monthly data: the model does not see slumps within a month that recover by the end of the month. Historical windows measure from month-end to month-end.
• No probability: a scenario states a loss, but not how likely it is Berkowitz (2000). The Mahalanobis distance only ranks scenarios by plausibility; probabilities come from value at risk.
• Choice of factors: risks outside the seven factors, such as individual stocks, sectors or emerging market currencies, end up in the residual risk. A low R² indicates this.

This page describes how Portfolio Lab calculates; past results are not a forecast. All terms in the glossary.