Stress Testing Portfolios with Non-Parallel Interest Rate Shocks

# Applying Interest Rate Shock to Equities, FX, etc


# Applying Interest Rate Shock to Equities, FX, etc












I am looking for resources on practical applications of non-parallel Interest Rate shock for a portfolio that contains different types of investments. Specifically:

- how to identify the tenors and how to identify the shock amount for each tenor;

- after identifying the tenors and non-parallel shocks, how to reflect this shock to equities, FX, commodities and other investments;

Will provide more details if required. Thanks!

## Answer by Magic is in the chain (score 1)

https://quant.stackexchange.com/a/46693

First assume you have been given/you know the shocks scenarios. Ideally you would have these scenarios in term of shifts/movements- e.g., curve shifts by $a+bT$. So what I would do is to price the products using the current market interest rate data. Then apply the shifts to the curve and then re-price the products. The change in price is the main object of interest.

Now let’s say you don’t have scenarios and you need to come up with realistic scenarios. You can look at the historically observed shifts and pick some sample scenarios based on say quantile/some other measure depending on the objective and the portfolio exposure. Additionally you can look at the significant historical events - shifts observed at Lehman’s event for example, or when Fed announced rate cuts. Or you can get the regulatory stress scenarios- EBA/PRA.

And lastly let’s assume you have been given the scenarios but the tenor is different or the different pricing functions you got use different tenor structure. Then the easiest way would be to interpolate/extrapolate the shifts using say linear interpolation.

The above should work for products that have interest rate as a pricing factor. But equity is going to be interesting. Very idiosyncratic behaviour is expected as different equities (or sectors or value/growth segments) will have different exposure to interest rate risk. Additionally there might be implicit impact - cut in interest rate might be associated with recession, or change in interest rate might lead to changes in the leverage (borrow more if debt is cheaper). With the caveat aside, here are some potential alternatives:

If you have the cash flow models, then you can always estimate the impact of the shock by applying the shocks to the assumptions relating to interest rate. A second alternative would be to use the CAPM relationship, but people have been reporting mixed results. Third approach would be to estimate 'empirical duration' and then estimate the impact of the shock by multiplying the shift by the duration. Fourth approach would be to establish some regression/econometric relationship between the changes in the interest rate and the changes in the equity, and then infer the impact of interest rate via the estimated relationship. This could also be based on filtered historical scenarios as an alternative.

Hope this helps!