Scenario analysis and sensitivity analysis: stress testing equity, interest rate, credit and currency risk

Advanced15 min read · updated 28 October 2026 · 14 sources

Scenario analysis asks: what happens to your portfolio if stocks fall 20%, interest rates rise by one percentage point and foreign currencies weaken against the dollar? It works with sensitivities (beta, duration, spread duration and currency exposure) or fully revalues the portfolio in the scenario. Here you will learn about the four main risks and their metrics, work through a stress scenario step by step and see why scenarios complement value at risk but do not replace it.

Sensitivity, scenario, stress test: the terms

A sensitivity analysis changes a single variable and holds everything else constant: how much does the portfolio lose if only interest rates rise by 100 basis points? A scenario analysis changes several variables at once to form a coherent picture, such as a recession with falling stocks, widening credit spreads and falling interest rates. A stress test is a scenario analysis with deliberately severe but still plausible assumptions. Value at risk answers a different question: it gives a loss that will not be exceeded with a certain probability, but it does not say which event would cause it.

Behind this lies an idea from bank risk management: every portfolio is a bundle of risk factors. If you know how strongly the value responds to each factor, you can calculate any scenario as the sum of factor move times sensitivity, at least approximately. For individual investors, four factors are enough: the stock market, interest rates, credit spreads and exchange rates.

The four main risks and their sensitivities

• Equity risk: beta measures how strongly a position moves with the stock market on average; for options, the derivative with respect to the price is called delta. A fund with a beta of 1.1 mathematically loses 11% when the market falls 10%.
• Interest rate risk: duration tells you by roughly what percentage a bond's price falls when its yield rises by one percentage point. The basis point value (DV01) converts this into dollars per basis point. Because short and long rates move differently, key rate durations as in Ho (1992) spread interest rate risk across maturity points; Litterman and Scheinkman (1991) found three patterns, level, slope and curvature, that explain almost all movements in the yield curve.
• Credit risk: spread duration measures the price loss when the credit spread over government bonds widens; CS01 is the amount in dollars per basis point. On top of this come two jump risks that no small sensitivity captures: default, in which roughly the face value times the loss rate is lost, and migration, i.e. a rating downgrade that makes the spread jump, especially at the boundary between investment grade and high yield.
• Currency risk: FX delta is the part of your assets held unhedged in a foreign currency. With a hedge ratio h, only the share 1 − h is exposed; hedging with forward contracts costs or earns roughly the interest rate differential between the two currencies (see currency risk and currency hedging).

Sensitivity analysis: changing one variable

The simplest question is: what happens if only one factor moves? For small moves, the linear approximation with the sensitivity is enough. For large moves it becomes inaccurate, because most securities do not respond linearly. For bonds, the curvature is called convexity, for options gamma. If you want an exact answer, you fully revalue the security with the new market data instead of adding up sensitivities.

Sensitivity analyses are quick and transparent, but they have one weakness: in crises, factors rarely move on their own. A rate shock of +100 bp with unchanged stock prices is a numerical experiment, not a scenario.

A scenario step by step

Take a balanced portfolio of $1,000,000 with stocks, government and corporate bonds and a share in foreign currencies. The figures are an example, not a recommendation:

The scenario is: stocks −20%, interest rates +100 bp, credit spreads +150 bp, foreign currencies −10%. A picture like this fits, for example, an inflation shock with recession fears in which stocks and bonds fall together.

Interest rates affect both types of bonds, the spread only the corporate bonds, whose yield therefore rises by 2.5 percentage points. Cash keeps its value. The portfolio's sensitivities in dollars are: $5,000 per percentage point of stock market move, $250 DV01, $75 CS01 and $3,000 per percent move in exchange rates. With these four numbers, you can estimate any further scenario in seconds.

Historical, hypothetical and reverse scenarios

• Historical scenarios apply the market moves of a real crisis to today's portfolio. Typical examples are the 2008 financial crisis, with collapsing stocks and exploding credit spreads but rising prices for safe government bonds, the 2020 COVID crash with a very fast collapse and a quick recovery, and the 2022 interest rate turnaround, in which stocks and bonds fell together. The advantage: the scenario actually happened and is internally consistent. The drawback: the next crisis will look different.
• Hypothetical scenarios describe an event that has not happened in this form before, such as a tariff war, a debt crisis in a large country or an oil price shock. They force you to think through the connections, but they are open to challenge: who decides how strongly credit spreads respond?
• Reverse stress tests turn the question around: which market moves would cause a specified loss, such as 20% of the portfolio or missing a financial goal? Banking supervisors expect them in order to find scenarios that could bring a bank down Basel Committee on Banking Supervision (2018). Glasserman et al. (2015) develop a method for finding the most likely combinations of factor moves behind a large loss.

Consistency: correlations and plausibility

A scenario is only as good as its internal logic. If stocks fall 20%, credit spreads usually widen; whether interest rates rise or fall depends on whether an inflation shock or a growth shock lies behind it. A scenario that moves only stocks and holds everything else constant usually understates the losses on corporate bonds. And it says nothing about whether government bonds protect you or fall too.

A common approach: you set the most important factors and put the others at their conditional expectation, derived from volatilities and correlations. Kupiec (1998) proposed calculating stress scenarios with the same conditional distributions that underlie VaR. Breuer et al. (2009) show that this approach maximizes the plausibility of the scenario and measure plausibility with the Mahalanobis distance: the further a scenario lies from normal conditions, measured in terms of volatilities and correlations, the less plausible it is.

With several factors, the same rule applies in matrix form. You specify the shocks s for a group S of factors and set all other factors U to their conditional expectation. With a single specified factor, the formula shrinks to correlation times the ratio of volatilities times the shock, which is exactly the calculation above. How unusual the scenario as a whole is can be measured by the Mahalanobis distance of the factor vector; the conditional expectation makes it as small as possible for the given shocks.

Be careful with the correlations themselves: in crises they differ from those in calm periods. Longin and Solnik (2001) find that the correlation of international stock markets rises in bear markets but not in bull markets; Ang and Chen (2002) find something similar for stock portfolios. Forbes and Rigobon (2002) show that part of the measured increase is a statistical effect of higher volatility. For stress tests, this means that correlations from a calm estimation period make scenarios too mild.

Supervisory stress tests as an example

Banks have long been required to run stress tests. After the financial crisis, the Basel Committee on Banking Supervision (2009) published principles intended to remedy the weaknesses of previous practice. The nine principles from 2018 that apply today call for, among other things, clear objectives, good data, suitable models and scenarios that are severe but plausible Basel Committee on Banking Supervision (2018). Two recent examples:

• EU: in the 2025 EU-wide stress test, the EBA (2025) ran 64 banks covering 75% of EU banking assets through three years. The adverse scenario was designed by the European Systemic Risk Board and the ECB; in it, the CET1 ratio fell by 370 basis points to 12%, with losses from credit, market and operational risks of €547 billion.
• US: in the 2026 stress test of the Federal Reserve (2026), 32 large banks had to withstand a severe global recession with unemployment of up to 10%, house prices falling 30% and commercial real estate prices falling 39%. Losses exceeded $708 billion, and the aggregate capital ratio fell by 1.6 percentage points; all banks stayed above their minimum requirements.

For investors, these tests are useful above all as a template. They show how thoroughly a severe scenario is described: with paths for growth, unemployment, real estate, interest rates and stocks over several years, not just with a single shock.

Scenarios and value at risk

Value at risk and expected shortfall condense the entire loss distribution into one number with a probability, while scenarios describe individual events without a probability. Berkowitz (2000) criticized that stress tests therefore usually sit alongside the risk model: nobody knows how important a scenario is, and the two results cannot be combined into a single risk measure. His proposal: include scenarios with probabilities in the risk model.

In practice, both are used side by side. VaR tells you how big an ordinary bad month is; the stress test tells you what a specific, very bad event costs. If the scenario loss is far above the expected shortfall, the estimation period probably contains no comparable crisis. How VaR and volatility are distributed across positions is explained in the article risk contribution.

Advanced: nonlinearity and cross effects

• Taylor expansion: the linear calculation is the first term of a Taylor series. The second contains convexity and gamma as well as cross derivatives between factors, in the example the stock × currency effect of $6,000. For options, volatility (vega) and time value come on top.
• Key rate scenarios: parallel shifts are rare. For a steeper curve, you multiply the key rate duration by the change in rates at each maturity point and add them up; the basics are in the articles yield curve and bond math.
• Default and migration: for credit portfolios, scenarios are calculated with default probabilities and rating transitions rather than spreads alone. Losses then come in jumps and hinge on a few issuers. This is another reason why diversification across issuers matters so much for bonds.
• Measuring plausibility: the Mahalanobis distance d = √(xᵀ Σ⁻¹ x) of the factor moves x defines an ellipsoid of equal plausibility. Breuer et al. (2009) search within it for the scenario with the largest loss. This is at the same time a systematic reverse stress test.
• Multi-period scenarios: supervisory scenarios unfold over several years. Then coupons, reinvestment, rebalancing and liquidity matter too: if you have to sell in a crisis, paper losses become permanent.

What research shows

Research on stress tests revolves around two questions: how do you connect scenarios with probabilities, and how do you find scenarios that are both severe and plausible? According to Kupiec (1998), historical VaR covariances with a conditional normal distribution deliver usable loss estimates in many stress periods, contrary to the widespread assumption that VaR models are useless for stress. Berkowitz (2000) called for assigning a probability to every scenario. Breuer et al. (2009) criticize hand-picked scenarios: if you rely only on history, you overlook plausible but damaging scenarios that have never occurred, and a standard scenario can be dangerous for one portfolio and harmless for another. Glasserman et al. (2015) provide the statistics to derive the most likely loss scenarios from data.

It is also well documented that diversification weakens in crises because correlations rise in falling markets Longin and Solnik (2001). It follows that scenarios should not be derived solely from the correlations of calm years. A detailed treatment of VaR methods, their validation and stress tests is given by Jorion (2007).

Limitations and common mistakes

• Not a maximum loss: a scenario is one possibility among many. The next crisis can hit other factors or turn out more severe.
• Scenarios that are too mild: if you only replay the last crisis, you overlook new risks. Anyone who ran only the 2008 scenario, in which safe government bonds gained, underestimated a year like 2022, in which stocks and bonds fell together.
• Linear instead of revalued: for options, leveraged products and large rate shocks, the linear calculation is misleading.
• Inconsistent combinations: stocks −30% with unchanged credit spreads is hardly plausible; correlations from calm years make scenarios too mild.
• Outdated sensitivities: beta and duration change with prices, interest rates and rebalancing. A stress test applies to today's portfolio.
• Missing liquidity: scenarios usually calculate at market prices. If you have to sell in a crisis, you pay wider spreads or find no buyer.

How Portfolio Lab calculates

The Risk page has the Scenarios tab for this. For each position, it estimates betas to seven factors (global equities, euro rates, US rates, US dollar, crude oil, gold and credit) from monthly returns and uses them to calculate hypothetical shocks, either in isolation or with the conditional expectation for the other factors. The templates are equity crash, rate shock, stagflation, dollar weakness and credit crisis. In addition, it applies twelve historical crises, from Black Monday to the 2025 tariff shock, to today's portfolio and, in the reverse stress test, searches for the move in one factor that triggers a specified loss. The details are in the scenario methodology.

For your own scenarios, Portfolio Lab provides the building blocks. In the Backtest, the Crisis periods tab shows how the portfolios came through nine built-in crises: from the 1973/74 oil crisis through Black Monday, the Asian and Russian crises, the dotcom crash and the financial crisis (11/2007–03/2009) to the euro debt crisis, the COVID crash (01–03/2020) and the 2022 interest rate turnaround (01–10/2022), each with the return and maximum drawdown over the period. A crisis only appears if the data cover it completely. This is a historical scenario with the backtest's weights, not a revaluation of today's portfolio.

For the sensitivities, the Risk factors tab in the Look-through shows the interest rate duration per currency, key rate durations at the maturity points from 1 to 30 years, the spread duration by issuer type and the equity beta from a regression over the last 60 months against global equities. These are exactly the numbers you plug into the linear calculation above. The Risk page calculates value at risk and conditional VaR for one month at 95% or 99%, parametric and historical, breaks them down by position and shows the risk by factor as well as by region, country, sector, currency and asset class. On the Macro page, you can analyze how portfolios performed in recessions, inflation bands, interest rate phases or with an inverted yield curve. More in the risk factors methodology.

Long monthly series for the most important factors are available as asset classes: global equities, German Bunds and US Treasuries with ten-year maturities, US dollar corporate bonds, gold and crude oil. If you place them next to your positions in the Grid, the correlation matrix on the Risk page shows how closely they move together over your period, giving you the ingredients for the conditional expectation. How to apply past crises to a portfolio today, even with funds that have no prices from that time, is explained in the article historical stress test.

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