Implementing Reverse Stress Tests with Scenario Parameters

# What research exists regarding implementation of reverse stress testing?


# What research exists regarding implementation of reverse stress testing?












I need to implement a reverse stress testing model (definition here)

I have searched around and cannot find anything substantial on the topic. Does anyone know of any good papers/references regarding actual implementation? Please don't post links to Basel docs.

## Answer by Finance Mentor (score 1)

https://quant.stackexchange.com/a/1467

Within the Insurance and Portfolio Management Industry there is a concept called Probability of Shortfall as well as Probability of Ruin. There were a number of papers (not on the internet) that I remember seeing on shortfall as part of my actuarial courses.

They evaluate how a certain product or strategy would impact a reduction in surplus or equity beneath some target level.

So if we take a similar approach here, you could start by identifying market shocks in isolation as well as in combination that would bring your regulatory capital below the minimum requirement. At work I run an ALM simulation for clients where I track what strategies lead to what probabilities of shortfall.

Not sure if this helps.

## Answer by Dimitri Vulis (score 0)

https://quant.stackexchange.com/a/84023

(I decided to add an answer this very old question because Googling still doesn't find a good explanation of what people do practically.)

The basic principle is that you start with the outcome (for example, losing some amount of money due to market risk), and you solve for scenarios (market moves) that might lead to this unacceptable loss. When there are multiple such scenarios, plausible assumptions about interconnectedness help select fewer scenarios defined using fewer parameters, ideally just one parameter.

I'll illustrate this principle with a couple of simple examples.

As a trivial example 1, consider 100 shares of some stock that is now trading at \$10. The mark to market is \$1,000. Under what scenarios can this position lose \$400 or more? Clearly, if the stock price falls 40% (\$4) or more.

Example 2 Consider a portfolio of multiple stocks, possibly long or short, as well as stock index futures. Clearly, there are many moving parts, and many ways to lose money. We can, for example, assume, like in a single-index CAPM, that stock price $P_s$ changes have no idiosyncratic (not explained by the beta) movements, but rather are fully explained by their betas $\beta_s$ to the index, which we know. Now the index remains the only moving part, and we can solve for the index movement $m$ that would lead to the unacceptable loss. Further, if we also know or assume the volatilities of each stock's idiosyncratic movement $\sigma^i_s$, we can build a reasonably realistic/conservative stress scenario described by a single parameter $m$, where the index moves by $m$ standard deviations, and each stock's price moves by $m\beta_s$ and further up if we're short, or down if we're long, by $m\sigma^i_s$. Note that we don't guarantee that the index movement is consistent with the movement of its component stocks. We can then solve for $m$ that would result in the unacceptable loss.

Example 3 Consider a portfolio of bonds or similar fixed-income instruments, possibly in different currencies, and assume that we know how much each instrument price will change if interest rates change. Assume that all interest rates, in all tenors and currencies, move in parallel, or, almost equivalently, are explained by their historical 1st principal component (PC1). This is a realistic assumption for a large shock. Then once more we can solve for the shock to the interest rates that would lead to the unacceptable loss, and we can express the size of the shock in basis points, or standard deviations of PC1.

If we are concerned about losses due to non-parallel curve shape change, we can also solve for a shock to the historical PC2, in terms of standard deviations, that would lead to an unacceptable loss for this scenario.