Stress Testing Yield Curves Against Equity Market Shocks

# How to estimate the change in risk free yields curve based on equity returns?


# How to estimate the change in risk free yields curve based on equity returns?












In the context of stress-testing, what possible methods are there to estimate the change in the risk-free yields curve based on a hypothetical equity return ? I'm trying to estimate the change in european risk-free yield curve based on the return of EUROSTOXX50 index.

## Answer by Dimitri Vulis (score 0, accepted)

https://quant.stackexchange.com/a/80538

If you're trying to create a comprehensive library of unlikely, but plausible adverse market stress scenarios, then looking at the history is a good start, but isn't nearly enough. If you just look at historical daily correlations over a few years, you'll see no material correlation between equity prices and interest rates. You should look at more than the last few years, and nor only to EUR and its predecessor XEU, but at other markets as well. For example, with USD, a growth in asset prices, including equities, alarmed the central bank (here https://www.federalreserve.gov/boarddocs/speeches/1996/19961205.htm for example), then the interest rates went up, then some asset prices went down, it all happened rapidly, although not in one day. If your portfolio is sensitive to interest rates and spreads, then you shouldn't assume that a large move in equities would cause a single interest rate scenarios. Rather, you should have many. You can also run Monte Carlo-like simulations, letting various market factors move many historical standard deviations, and letting correlations vary from 1 to -1, and see which scenarios cause large negative P&L to your portfolio. You should also tier the stress scenarios, so you can have larger limits for losses caused by less likely scenarios, and by fewer scenarios in your library. A human expert is needed to think of unlikely scenarios that may happen, even if they haven't happened in the past. Inventing stress scenarios is still more art than science. Backing up expert judgment with data analysis is useful, but not a replacement.

## Answer by Sane (score 0)

https://quant.stackexchange.com/a/80513

Non-exhaustive list of approaches that you might want to consider:

Econometric Models (e.g., VAR Models): Apply a Vector Autoregression (VAR) model or similar econometric techniques to forecast changes in the yield curve based on changes in equity returns. These framework is useful for capturing the dynamic relationships between equity returns and the yield curve. Econometric models can help you understand how these variables interact over time.

Macroeconomic Models: Incorporate equity return scenarios into a macroeconomic model to observe how they might influence economic conditions and subsequently the risk-free yield curve. These models are particularly useful for capturing indirect effects through macroeconomic variables.

Factor Models: Useful if you want to understand the common underlying factors driving both equity returns and interest rates, but they may be less direct compared to the aforementioned methods.