Stress Testing

The risk management unit reports the losses from stress testing to senior management alongside the results of VaR.

Why VaR alone is not enough

Stress testing is used alongside Value at Risk (VaR) because VaR has two limits. VaR is a statistical estimate from past observed data, and it is calculated on the assumption that the past repeats. So when the market environment changes and the shape of the distribution of price moves changes with it, VaR does not reflect this. VaR also shows losses only up to a confidence level (such as 99%), and it does not capture the tail losses beyond that level (tail risk)¹.

Many financial institutions were already running stress tests before the global financial crisis. In practice, though, these tests mostly reset VaR assumptions, for example by raising the confidence level or ignoring correlations, or applied a few past shocks as a formality. The results were not used in management decisions either². Even scenarios that were called "severe" before the crisis typically produced loss estimates within one quarter's earnings³. The crisis also showed that statistical relationships estimated from past data, such as correlations, cannot be relied on in stressed markets⁴.

From this experience, stress testing took on the role of complementing methods based on past data, such as VaR, and showing risk from a different angle⁵. The Financial Services Agency's "Comprehensive Guidelines for Supervision of Major Banks, etc." (hereafter, the supervisory guidelines) note that VaR can come out too low when the track record is short or the data are unreliable. The guidelines ask banks to strengthen their risk management methods, including stress testing⁶.

Calculating VaR with data from a stress period (stressed VaR) and looking at the average of losses beyond VaR are covered in Expected Shortfall.

Types of scenarios

Stress test scenarios are classified by how many risk factors (the drivers that move the value of positions) they move and how the size of the moves is set⁷.

The examples in the table come from a Bank of Japan training document and from the provisional translation of the Basel Committee on Banking Supervision's "Principles for sound stress testing practices and supervision" (May 2009)⁸⁹. The 200bp rise in rates in the hypothetical scenario has the same size as the one in the sensitivity analysis. The difference is that it is assumed in connection with an event⁷. Historical scenarios are objective, while hypothetical scenarios let you set assumptions freely⁸. In the global financial crisis, however, scenarios based on past events failed to capture the risks of the new products at the center of the crisis, and past experience also understated how deep and long the stress would be¹⁰. Hypothetical scenarios are used to capture events that have never been experienced before¹⁰.

Sensitivity analysis does not consider the relationships or spillovers among risk factors. In return, it gives a quick, rough picture of where the positions are vulnerable¹¹. Moving risk factors one at a time can miss the effect of their moving together. So in some cases it helps to combine it with scenario analysis, which moves several risk factors at once⁹.

Worked example with W Bank's positions

Consider a hypothetical example in which W Bank compares the profit and loss (P&L) of its trading positions under each scenario. W Bank holds the following three positions.

W Bank's 1-day VaR (99% confidence level) is 500 million yen. The P&L of the positions is approximated by multiplying each risk factor's sensitivity by the size of its move and adding up the results.

$$\Delta V \approx \sum_{i} S_i \times \Delta x_i$$

$\Delta V$ is the change in the value of the positions, $S_i$ is the P&L when risk factor $i$ moves by one unit (1% for stock prices and the exchange rate, 1bp for interest rates), and $\Delta x_i$ is the size of the move in risk factor $i$ in the scenario.

Sensitivity analysis

First, move only one risk factor. For stock prices and interest rates, the table shows the P&L for moves in both directions.

A 30% fall in stock prices and a 300bp rise in rates each produce, on their own, a loss of six times the 1-day VaR. W Bank's positions are vulnerable both to falling stock prices and to rising rates.

Historical and hypothetical scenarios

Next, move all three risk factors at once. Consider a hypothetical example in which a historical scenario that applies moves resembling a past crisis (the values are hypothetical) is compared with a hypothetical scenario in which stock prices fall and rates rise at the same time.

In the historical scenario, rates fall while stock prices fall, and the gain on the interest rate swap offsets part of the loss on stocks. In the hypothetical scenario, stock prices and rates move against the bank at the same time. So even though stock prices fall less than in the historical scenario, the interest rate swap adds to the loss. Hypothetical scenarios also consider situations in which price correlations between positions break down¹². In both scenarios the loss is five to seven times the 1-day VaR, and looking at VaR alone would not reveal a loss of this size.

The calculation in this example is only an approximation that multiplies sensitivities by the size of the moves. It assumes that P&L stays proportional to the size of the move even when risk factors move a lot. This assumption breaks down for positions whose prices do not move in proportion to the risk factors, such as positions that include options. For banks that use internal models, the capital adequacy notice requires stress scenarios to capture the linear and nonlinear characteristics of prices¹³. Sensitivity analysis and scenario analysis can also be used to check model assumptions, such as whether linear relationships still hold when extreme values are put in¹⁴.

Reverse stress testing

Reverse stress testing first fixes an unacceptable outcome (such as a capital ratio below the regulatory minimum, funding running out, or insolvency) and then asks what events would lead there¹⁵. An ordinary stress test derives a loss from a scenario. A reverse stress test works backward from the loss to the scenario. The Bank of Japan training document includes an example that lays out stock price moves and rate moves in the rows and columns of a table and checks whether the bank's financial strength would hold up¹⁶.

Suppose W Bank allocates 5 billion yen of risk capital to its trading positions and looks for the combinations of stock prices and rates at which the loss reaches that amount (the exchange rate is assumed not to move).

The values in the table are P&L in billion yen. Stock prices alone must fall 50% for the loss to reach 5 billion yen. If rates rise 100bp, a 40% fall in stock prices reaches it, and if rates rise 200bp, a 30% fall does. A 30% fall in stock prices is the size that occurred in the historical scenario in the previous section. The remaining question is whether a 200bp rise in rates could come on top of it. W Bank discusses whether that combination could occur, and if it decides that it could, it reviews its positions and limits.

Reverse stress testing prompts a bank to consider scenarios beyond its normal business environment, and it can also reveal weaknesses or inconsistencies in hedging strategies¹⁷. It is especially useful for businesses that look too profitable for their risk under conventional risk management models, for new products and markets that have not been through a severe crisis, and for positions that lack a two-way market¹⁷.

How scenarios are built and the workflow

The risk management unit is at the center of stress testing. It decides how to choose scenarios and how severe the stress should be by exchanging information and discussing them with senior management and the front office (sales and trading)¹⁸. The views of relevant experts (risk managers, economists, traders, and others) are gathered, and the unit responsible for running stress tests challenges them before settling on the design¹⁹.

Based on the supervisory guidelines (for major banks), the capital adequacy notice, and the Bank of Japan training document, the workflow is roughly as follows.

Figure description

The board of directors sets the basic approach, the risk management unit listens to concerns and drafts the scenarios, and senior management verifies the results and uses them in risk management decisions, in that order. The box numbers are the step numbers below; step 3, the calculation of profit and loss, is not in the figure.

1. The board of directors sets the basic approach for stress testing. The board or a similar body reviews the settings regularly; the guidelines say "at least once each period" (our translation) (supervisory guidelines)²⁰.
2. The risk management unit hears the concerns of senior management and works with the front office to identify events that would hurt the organization and whether their likelihood is rising, and then drafts scenarios (Bank of Japan training document)²¹.
3. The scenarios are applied to the positions and the P&L is calculated. The bank sets up its systems to calculate the results of historical scenarios and reverse stress tests regularly, so that senior management can see them at any time alongside 99% VaR (Bank of Japan training document)²².
4. Senior management examines and analyzes the results and uses them in specific risk management decisions (supervisory guidelines)²³.
5. If weaknesses are found, the bank promptly takes measures to address them (the notice requires this of banks that use internal models)²⁴.

In the approach of the Bank of Japan training document, it is realistic to start with mild stress scenarios that are likely over short periods and move on to severe stress scenarios that are unlikely over long periods. At the same time, likely scenarios such as the economic outlook can be easier to discuss with management, while scenarios severe enough to push the bank into crisis can also open a discussion with management²⁵.

The choice of scenarios, the reasons for it, and the assumptions are documented, and the effectiveness of the stress testing framework is assessed regularly from an independent standpoint²⁶. Because expert judgment is involved, independent control functions such as the risk management unit and internal audit take part²⁷.

How the results are used

Stress test results serve as one input for setting risk limits and are also used in discussions of long-term business plans. They are built into the capital planning and liquidity planning processes as well³⁰. The capital adequacy notice has requirements for banks that calculate the capital for market risk (called the "market risk equivalent amount" in the notice) with internal models. The results must be used in discussions at the board of directors or a similar body at least once a month, in assessing capital adequacy, and in setting limits²⁴.

How limits are set differs by institution³¹. For example, one approach allocates risk capital after looking at stress test results and manages overall market risk with a VaR limit. Another assumes certain moves in rates and stock prices as stress scenarios and builds up individual limits from them³¹. In the approach of the Bank of Japan's document on building a market risk management framework, what matters more than the form of risk capital allocation or limit setting is that the organization can give a reasoned explanation of how it confirmed that its financial strength is sufficient³².

What happens to the loss estimate if the positions are changed after looking at the results? Suppose W Bank cuts the DV01 of its interest rate swap from 10 million yen to 5 million yen and leaves the other positions unchanged. Using the same formula as in the previous section, only the P&L from rate moves is halved.

In the scenario where rates rise, the loss shrinks from 5 billion yen to 4 billion yen. In the historical scenario where rates fall, the swap gains less, so the loss grows from 3.5 billion yen to 3.75 billion yen. In this example, halving the swap's DV01 halves both the losses and the gains from rate moves.

Based on the results, a bank separates risks it can reduce in an emergency from risks that are hard to reduce, and decides in advance how to respond³³.

The Bank of Japan's document on building a market risk management framework describes a case in which a stress scenario showed the possibility of large losses or insolvency, yet senior management did not react. To avoid this, when risk cannot be reduced right away, the bank prepares a concrete action plan that sets out what will trigger risk reduction and how the risk will be reduced³⁴.

In a stress period, funding markets and asset markets can become tightly linked, and pressure can hit both at the same time. Stress tests also consider this simultaneous pressure and how falling market liquidity affects the valuation of positions³⁵.

Supervisory expectations

In Japan, the supervisory guidelines list stress testing as a point of focus for market risk management. Stress tests analyze not only historical scenarios that apply major past crises or the largest past losses, but also hypothetical scenarios. The bank sets several hypothetical scenarios that assume domestic and overseas economic developments with a large impact on the assets it holds¹². Senior management must be in a position to examine and analyze the results thoroughly and use them in specific risk management decisions²³. The recovery plans of global systemically important banks (G-SIBs) and other banks designated by the Commissioner of the Financial Services Agency under the capital adequacy notice include stress tests that assume stress higher than usual and reverse stress tests. These are items related to the triggers for activating the plan³⁷.

The capital adequacy notice sets the stress testing requirements for banks that calculate the market risk equivalent amount with internal models. The stress scenarios include the following:

• Scenarios the Commissioner of the Financial Services Agency sets out as needed
• Historical scenarios that consider price moves and sudden falls in liquidity in past stress periods
• Scenarios that put extreme values on volatility and correlations
• Hypothetical scenarios that assume the largest loss that could arise from the characteristics of the bank's own positions

The results are reported to directors and others on a daily basis and to the board of directors regularly¹³.

The international approach is set out in the Basel Committee's Principles. The Principles of May 2009 contain 15 principles for banks, including linking stress testing to management decisions, offering a view that complements VaR and other measures, and including reverse stress testing³⁸. In October 2018, the Basel Committee published "Stress testing principles"³⁹.

The authorities also run stress tests of the financial system as a whole. In its Financial System Report, the Bank of Japan runs macro stress tests that assume stress events and assesses whether financial institutions have enough loss-absorbing capacity. The April 2026 report used two downside scenarios, including one that assumes stress on the same scale as the collapse of Lehman Brothers, and covered 106 banks and 247 shinkin banks⁴⁰.

Notes

1. Bank of Japan Financial System and Bank Examination Department, Center for Advanced Financial Technology, "ストレステストとシナリオ分析" (Stress testing and scenario analysis, in Japanese) (basic seminar, July 2017; hereafter, the Bank of Japan training document), pages 3–4, "１．ＶａＲの限界" (1. Limits of VaR). ↩

2. The same document, pages 5–6, "金融危機以前：VａＲへの過信" (Before the financial crisis: overconfidence in VaR) and "金融危機以前：形骸化したストレステスト" (Before the financial crisis: stress testing as a formality). ↩

3. Basel Committee on Banking Supervision, "健全なストレス・テスト実務及びその監督のための諸原則" (Principles for sound stress testing practices and supervision; provisional Japanese translation by the Financial Services Agency) (May 2009; hereafter, the Principles), page 5, "ストレス・シナリオの選択" (Selection of stress scenarios) (in Japanese). ↩

4. The same document, page 4, "ストレス・テスト手法" (Stress testing methodologies). ↩

5. The same document, page 10, Principle 2. ↩

6. Financial Services Agency, "主要行等向けの総合的な監督指針" (Comprehensive Guidelines for Supervision of Major Banks, etc.) (October 2026), III-2-3-3-2(2)⑤ (page 125) (in Japanese). ↩

7. The Principles, pages 5–6, "ストレス・シナリオの選択" (Selection of stress scenarios) (in Japanese). ↩ ↩²

8. The Bank of Japan training document, page 11, "３．ストレステストとシナリオ分析" (3. Stress testing and scenario analysis), page 10, and pages 14–15. ↩ ↩²

9. The Principles, pages 11–12, Principle 3 (in Japanese). The examples of reverse stress testing are on page 16, Principle 9. ↩ ↩²

10. The same document, page 6, "ストレス・シナリオの選択" (Selection of stress scenarios). ↩ ↩²

11. The same document, pages 5–6, "ストレス・シナリオの選択" (Selection of stress scenarios). ↩

12. The supervisory guidelines, III-2-3-3-2(2)⑥ (page 125) (in Japanese). ↩ ↩²

13. Financial Services Agency, "銀行法第十四条の二の規定に基づき、銀行がその保有する資産等に照らし自己資本の充実の状況が適当であるかどうかを判断するための基準" (Standards for determining whether a bank's capital adequacy is appropriate in light of the assets it holds, under Article 14-2 of the Banking Act, our translation; FSA Notice No. 19 of 2006, consolidated version updated on August 24, 2026), Article 273 (pages 447–448) (in Japanese). ↩ ↩²

14. The Principles, page 12, Principle 3 (in Japanese). ↩

15. The Principles, page 16, Principle 9 (in Japanese). ↩

16. The Bank of Japan training document, page 10 and page 16, "（例）リバース・ストレステスト" (Example: reverse stress testing). ↩

17. The Principles, page 17, Principle 9 (in Japanese). ↩ ↩²

18. The Bank of Japan training document, page 30, "リスクコミュニケーションの充実を図る動き" (Moves to strengthen risk communication). ↩

19. The Principles, pages 11–12, Principle 3 (in Japanese). ↩

20. The supervisory guidelines, III-2-3-3-2(2)⑦ (page 125) (in Japanese). ↩

21. The Bank of Japan training document, pages 12–13, "金融危機の教訓①" (Lessons of the financial crisis 1) and "金融危機の教訓②" (Lessons of the financial crisis 2). ↩

22. The same document, page 14. ↩

23. The supervisory guidelines, III-2-3-3-2(2)⑨ (page 125) (in Japanese). ↩ ↩²

24. The capital adequacy notice (the same standards as Article 273 above), Article 272-6, items 4 and 5 (pages 441–442) (in Japanese). ↩ ↩²

25. The Bank of Japan training document, pages 17, 19, and 21. ↩

26. The Principles, pages 12–13, Principle 4, and page 13, Principle 6 (in Japanese). ↩

27. The same document, page 14, Principle 6. ↩

28. The same document, page 13, Principle 5. ↩

29. The same document, page 4, "ストレス・テスト手法" (Stress testing methodologies). ↩

30. The same document, pages 9–10, Principle 1. ↩

31. Bank of Japan Financial System and Bank Examination Department, Center for Advanced Financial Technology, "市場リスク管理態勢の整備" (Building a market risk management framework, in Japanese) (September 2019), page 16, "市場リスク全体枠：設定の考え方" (Overall market risk limit: how to set it), and pages 21–22, "（事例①）" (Case 1) and "（事例②）リスクを許容し管理する枠組み" (Case 2: a framework for accepting and managing risk). ↩ ↩²

32. The same document, page 16. ↩

33. The Bank of Japan training document, page 24. ↩

34. Bank of Japan Financial System and Bank Examination Department, Center for Advanced Financial Technology, "市場リスク管理態勢の整備" (Building a market risk management framework, in Japanese) (September 2019), page 11. ↩

35. The Principles, page 17, Principle 10 (in Japanese). ↩

36. The Bank of Japan training document, page 31, "リスクコミュニケーションの充実を図る動き" (Moves to strengthen risk communication). ↩

37. The supervisory guidelines, III-11-2-2(1)③ロ (page 341) (in Japanese). ↩

38. The Principles, pages 9–19, "銀行向けの諸原則" (Principles for banks), Principles 1, 2, and 9 (in Japanese). ↩

39. Financial Services Agency, "バーゼル銀行監督委員会による『ストレス・テストの諸原則』の公表について" (Publication of "Stress testing principles" by the Basel Committee on Banking Supervision, in Japanese) (October 23, 2018). ↩

40. Bank of Japan, "金融システムレポート" (Financial System Report) (in Japanese), April 2026, page 72, "２．マクロ・ストレステスト" (2. Macro stress testing), and footnotes 44 and 45. An English version of the report is available: "Financial System Report (April 2026)". ↩