Historical stress testing: how to apply past crises to your portfolio today

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A historical stress test applies the market moves of a real crisis to today's portfolio: what would the financial crisis, the COVID crash or the 2022 interest rate turnaround have done to your current positions? There are two ways to do this: by replaying the returns of the time, or via factors and betas, which can also take funds without prices from that period through the crisis. Here you will get to know both approaches, work through an example and see where the method reaches its limits.

Why historical scenarios?

Historical scenarios have one big advantage over invented ones: they really happened. Nobody has to decide how much credit spreads widen in an equity slump or whether safe government bonds gain; the crisis supplies an internally consistent bundle of moves. That is why they are standard in risk management, alongside hypothetical scenarios and the reverse stress test. The Basel Committee's principles call for scenarios that are severe but plausible Basel Committee on Banking Supervision (2018). For investors, a historical stress test answers a very tangible question: would I have come through the last big crisis with my current portfolio?

The drawback is just as obvious: the next crisis will look different from the last one. If you only recalculate 2008, when government bonds cushioned losses, you underestimate a year like 2022, in which equities and bonds fell together (see stock-bond correlation). Breuer et al. (2009) criticize exactly this: hand-picked historical scenarios overlook plausible but damaging combinations that have never occurred, and a scenario that is dangerous for one portfolio can be harmless for another. Historical tests are therefore one building block, not a complete stress test.

Two approaches: replay or factors

The direct approach is the replay: you take the monthly returns of each current position in the crisis window and run the portfolio through with today's weights, usually reset to the target weights every month. This is accurate, provided all positions already existed at the time. But for an ETF launched in 2018, there are no prices from the financial crisis. A proxy helps here, such as the index the ETF tracks or a similar older fund.

The second approach works via factors. First you measure how strongly each position reacts today to a handful of market factors: the stock market, interest rates, exchange rates, commodities and credit spreads. These sensitivities, the betas, are estimated by a regression of the monthly returns of recent years on the factors (factor regression). Then you measure how the factors moved in the crisis window and multiply: beta times factor move, summed over all factors and positions. Long series exist for the factors; for the positions, the last few years are enough.

The two approaches complement each other. The replay shows what happened to exactly these securities, including everything no factor captures. The factor calculation shows what the positions' current behavior would mean in a crisis of this pattern, and it breaks the loss down into contributions: how much comes from the stock market, how much from interest rates, how much from the dollar. If the two differ widely, it is worth looking for the cause: a fund that has changed since the crisis, a proxy that does not fit, or a risk outside the factors.

Worked example: a crisis with a young ETF

A $200,000 portfolio consists of three ETFs: 50% global equities, 30% US Treasuries and 20% a thematic ETF that has only existed since 2018. The betas come from a regression over the last 60 months. The moves in the crisis window are assumed, rounded values of the kind that can occur in a severe crisis: global equities −40%, ten-year Treasury yield −1 percentage point, foreign currencies +10% against the US dollar.

A replay of the returns would only be possible here with a proxy for the thematic ETF. If you use the equity index for this, you underestimate its risk: with a beta of 1.3, it falls by 48% in the model instead of 40%. The factor approach, by contrast, uses what recent years reveal about the ETF and transfers it to the crisis. Conversely, it reveals nothing about risks that were not visible in those years, for example if the thematic ETF falls further in a real crisis than its beta suggests because of a lack of liquidity.

The right window

How strongly a crisis bites in the test depends on the window. The usual choice is the stretch from the stock market's peak to its trough, measured at month-ends. A window that is too long dilutes the slump with months of recovery; one that is too short misses consequences that only came later, such as rising credit spreads after the first crash. With monthly data, a slump that recovers by the end of the month does not show up at all. Black Monday in October 1987 falls within a single month, the dotcom crash lasted from 2000 to autumn 2002, the financial crisis from autumn 2007 to early 2009, and the COVID crash only from February to March 2020. Fix the windows before you calculate, not afterward.

Crises differ above all in how the factors move together. That is why it pays to test several types:

• Equity crash with a flight into government bonds: equities fall, interest rates drop, safe bonds rise, as often happens in recessions and as in the financial crisis.
• Interest rate shock: yields rise quickly, long-dated bonds lose, equities come under pressure; examples are the taper tantrum of 2013 and the interest rate turnaround of 2022.
• Liquidity crisis: almost everything falls at the same time because investors need cash, including corporate bonds and, at times, gold; that is how the first weeks of the COVID crash played out.
• Currency shock: for US investors with foreign assets, the dollar matters. If it rises in the crisis, it amplifies losses on foreign assets; if it falls, it softens them.

When data are missing

Not only funds but also factors have gaps: some series begin later than the crisis you want to test. There are then two clean ways out. Either you leave the factor out of the scenario, or you set it to its conditional expectation: the move you would expect on average given the observed factors and the correlations. Kupiec (1998) proposed this approach for stress tests that are meant to be consistent with a VaR model; Breuer et al. (2009) show that, of all possible completions, it is the most plausible.

With a single observed factor, the formula shrinks to correlation times the ratio of the volatilities times the move. If the stock market falls by 40%, crude oil and equities have a correlation of 0.3 and crude oil is twice as volatile as equities, the expected oil move is 0.3 × 2 × (−40%) = −24%. That is an estimate, not a substitute for data: in crises especially, individual markets often deviate far from the average.

What the research shows

According to Kupiec (1998), historical VaR covariances with a conditional normal distribution deliver usable loss estimates in many stress periods, contrary to the widespread view that VaR models are no good for stress. Caution is needed with correlations: Longin and Solnik (2001) find that the correlation of international stock markets rises in bear markets, but not in bull markets. Kim and Finger (2000) therefore estimate separate correlations for stress periods from a mixture of two normal distributions, one for calm days and one for hectic ones; in their example, correlations change markedly under stress for four of 18 markets (correlation breakdown).

How unusual a crisis window was can be measured. Kritzman and Li (2010) use the Mahalanobis distance of returns as a measure of financial turbulence: it is large when markets fluctuate strongly or move against their usual correlations. A historical scenario with a large distance is a genuine outlier; one with a small distance shows more what can happen in a bad year anyway. Berkowitz (2000) reminds us that scenarios without probabilities stand alongside the risk model. Rebonato (2010) links the causes and consequences of a scenario using Bayesian networks to assign it a probability.

For advanced readers: compounding, rebalancing and shifting betas

• Compounding: applying a beta to the whole move of the window is linear. Two months of −20% each add up to −36% together; a position with a beta of 0.5 loses 18% calculated linearly, but 19% compounded month by month. With long windows the difference grows.
• Rebalancing: a replay with monthly rebalancing buys more in a falling market. In a long bear market such as 2000 to 2002, it therefore tends to lose more than buy and hold, and after a sharp crash with a rapid recovery such as 2020, rather less (see rebalancing).
• Shifting betas: betas from the last 60 months describe current behavior. In the crisis itself, betas and correlations often rise; a factor model from calm years then underestimates the losses.
• Scaling: a historical scenario can be read as a direction and stretched: 1.5 times the financial crisis is a harsher but equally consistent scenario. This is how you link historical scenarios with the reverse stress test.
• Non-linearity: options, portfolio insurance strategies and leveraged products do not react linearly. For them, the replay, if necessary with full revaluation, is better than the factor calculation.

Limits and common mistakes

• Only the past: a historical test shows what happened, not what can happen. Supplement it with hypothetical scenarios (see scenario analysis).
• Unsuitable proxies: a proxy with too little risk makes the replay too mild. Check the proxy's beta and volatility against the real position over the years they share.
• Conveniently chosen windows: if you set the window so that your own portfolio looks good, you are testing nothing. Fixed windows defined in advance are more honest.
• Forgetting the currency: for US investors, what counts is the crisis in dollars. The same crisis can have looked very different in dollars and in euros (see currency risk).
• Overlooking residual risk: the factor model explains only part of the fluctuation. With individual stocks, sector and thematic funds, a large residual risk remains that is not contained in the scenario.
• Correlations from calm years: conditional expectations from calm years make the scenario too mild, because correlations usually rise in crises.

How Portfolio Lab calculates it

In the Crisis periods tab, the Backtest shows how the portfolios came through nine stored crises, with the return and maximum drawdown over each period; a crisis only appears if the data cover it completely. This is a replay using the weights and rebalancing of the backtest. You can extend positions with a short history using a proxy in the Grid; the app's asset classes often go back decades as monthly series and are well suited for this.

The transfer via factors is calculated by the Scenarios tab on the Risk page: for twelve stored crises, from Black Monday to the 2025 tariff shock, it measures the move of equities, interest rates, the US dollar, crude oil, gold and credit spreads in the crisis window and applies them to your positions via the currently estimated betas, including to funds without prices from that time. If all positions have prices for the whole window, the actual replay is shown alongside. The details are in the scenario methodology.

On the Risk page, the historical value at risk shows the worst months of the selected period with today's weights, and the correlation matrix of the positions shows which building blocks fall together. In the Look-through you will find the equity beta of each position, from a regression over the last 60 months against global equities, as well as interest rate and spread duration. This lets you follow the factor calculation from the example by hand for the most important factors.

This article explains a method; it is not investment or tax advice. Worked examples are simplified and rounded. All terms in the glossary.