As a hypothetical example, a bank holds three positions. A long position in Japanese equity index futures loses 200 million yen for each 1% fall in stock prices. A yen interest rate swap receiving the fixed rate has a DV01 of 5 million yen. A long dollar, short yen position loses 30 million yen for each 1% the yen strengthens. In a stress testing scenario, stock prices fall 15%, rates fall 100bp and the yen strengthens 10%. What is the profit or loss when you multiply each sensitivity by the size of the move and add the results?
Quiz: Validation and Regulation
Last reviewed: September 26, 2026
This is a draft, shown for review before publication.
4 questions to check your understanding of the chapter “Validation and Regulation”. Choose an answer and select “Check answer” to see the answer and explanation. You can also open “Answer and explanation” to see the answer first.
Question 1
Answer and explanation
Answer: B
The profit or loss is −2.8 billion yen. In this approximation, you multiply the sensitivity to each risk factor (a driver of the position's value) by the size of its move and add the results. Stock prices fall 15%, so −200 million yen × 15 = −3 billion yen. A swap receiving the fixed rate loses when rates rise and gains when they fall. A 100bp fall in rates gives 5 million yen × 100 = +500 million yen. A 10% strengthening of the yen gives −30 million yen × 10 = −300 million yen. The total is −3 + 0.5 − 0.3 = −2.8 billion yen.
−3.8 billion yen comes from treating the fall in rates as a loss on the swap and adding −500 million yen. −2.2 billion yen comes from treating the stronger yen as a gain and adding +300 million yen on the currency position.
Conversely, in a scenario where stock prices rise 15%, rates rise 100bp and the yen weakens 10%, the result is a gain of +3 − 0.5 + 0.3 = +2.8 billion yen. This calculation is an approximation that assumes profit or loss is proportional to the size of the move. The assumption breaks down for positions whose prices do not move in proportion to the risk factors, such as positions that include options.
Learn more: Stress Testing
Question 2
Which statement correctly describes reverse stress testing?
Answer and explanation
Answer: D
Reverse stress testing first sets a size of loss that cannot be tolerated (such as a capital ratio below the regulatory minimum or a drying up of funding) and then searches for the scenario that leads to it. An ordinary stress test finds the loss from a scenario, whereas reverse stress testing works back from the loss to the scenario.
The other options describe other types of scenario. Applying the moves of a past crisis is a historical scenario. Moving only one risk factor is sensitivity analysis. Assuming an event with no precedent and moving many risk factors at once is a hypothetical scenario. These three work in the direction from a scenario to a loss.
Learn more: Stress Testing
Question 3
As a hypothetical example, a bank compares its daily profit or loss with its VaR (value at risk) in backtesting, using a one-day holding period and a 99% confidence level. The figures for five business days are as follows.
Day VaR measured at the end of the day (billion yen) Profit or loss for the day (billion yen) Day 1 1.0 0.2 Day 2 1.2 −1.1 Day 3 1.2 1.4 Day 4 0.8 −1.0 Day 5 1.0 −0.9 From day 2 to day 5, how many exceptions (days when the loss exceeded VaR) are there?
Answer and explanation
Answer: A
There are 2 exceptions. In backtesting, a day's profit or loss is compared with the VaR measured on the positions at the end of the previous day. The day 2 loss of 1.1 billion yen exceeds the previous day's (day 1) VaR of 1 billion yen, so it is an exception. The day 5 loss of 900 million yen also exceeds the previous day's (day 4) VaR of 800 million yen, so it is an exception. The day 4 loss of 1 billion yen is below the previous day's VaR of 1.2 billion yen, so it is not an exception even though it is a loss. Day 3 is a profit, so it is not counted.
The count of 1 comes from comparing profit or loss with the VaR measured on the same day. On that basis, only day 4 (1 billion yen > 800 million yen) is an exception, and day 2 (1.1 billion yen < 1.2 billion yen) and day 5 (900 million yen < 1 billion yen) drop out. The count of 3 comes from also counting the day 3 profit of 1.4 billion yen as exceeding the previous day's VaR of 1.2 billion yen. Exceptions count only losses; profitable days are not counted.
Learn more: Backtesting
Question 4
As a hypothetical example, a bank's VaR backtesting over the most recent 250 business days shows 6 exceptions (the larger of the counts with hypothetical P&L and actual P&L). Under the three-zone approach in Japan's capital adequacy notice (consolidated version updated on August 24, 2026), which statement correctly reads this result?
Answer and explanation
Answer: C
Six exceptions fall into the amber zone. The notice treats 0 to 4 exceptions over the most recent 250 business days as the green zone, 5 to 9 as the amber zone, and 10 or more as the red zone. The amber zone is a result that suggests a possible problem with the model but is not conclusive. The multiplier for 6 exceptions is 1.76, higher than the 1.50 of the green zone. A bank in the amber zone notifies the Commissioner of the Financial Services Agency, attaching a document describing the cause and its planned response.
If the model is correct and exceptions occur independently each day with a probability of 1%, the average number of exceptions over 250 days is 250 × 0.01 = 2.5. Even so, the probability of 5 or more exceptions is 10.78%, and of 6 or more is 4.12%. So 6 exceptions point to a problem with the model but are not conclusive. Having more than the average of 2.5 exceptions is common even with a correct model, but the green zone goes only up to 4. With a correct model, the probability of 10 or more exceptions is only 0.03%. The red zone is 10 or more and is not determined by whether the count is more than twice the average.
Learn more: Backtesting