# 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!

• I think you should state the end-use (i.e. purpose) for which you would like to apply non-parallel IR shock. Is it for RNIR (risk not in VaR)? – bhutes Jul 18 at 2:45
• No, not exactly. I have different Interest Rate scenarios like flattening, steepening, normal yield curve, inverted yield curve. First I am trying to understand how I can move on from the current state - do I look at history and pick the periods that match my scenarios and derive the shock or is there another approach (potentially interest rate modelling). Then how can I extend these scenarios to ETFs, stocks, FX, etc. in my portfolio. Does it make sense? I am open to hear you out on RNIV though. – AK88 Jul 18 at 3:03
• It isn't my area of expertise - so, better to wait for another reply. I have seen model parameters being extracted from historical data and those parameters being used in a model, which otherwise calibrates to "today's market", e.g. a jump-size and jump-frequency being extracted from historical data, then a jump-diffusion model is calibrated to correctly reprice today's vanilla option prices utilizing historical jump-size and jump-frequency and a volatility (adjusted downwards compared to no-jump model vols). – bhutes Jul 18 at 3:58
• Do you have access to the pricing models of the products? – Magic is in the chain Jul 18 at 11:26
• To re-price the instruments after applying the shock? – AK88 Jul 18 at 14:29

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!

• +1 and thanks for your inputs. Regarding the first paragraph -- if I do not have the Interest Rate as a pricing factor, then these securities won't change at all. What would be ideal is to reflect any change in the Interest Rates in those investments as well. For example, I do not have a specific pricer for the shares of Microsoft - I just take the observed market price to see my day-to-day P&L. However, changes in Interest Rates are going to affect Microsoft. How do I figure that out? – AK88 Jul 18 at 17:22
• The second paragraph still seems unclear to me. If the subject curve is non-US curves (e.g. Australian Government curve), can we still extrapolate Lehman scenario, for example? – AK88 Jul 18 at 17:22
• Added further details on equity. If the scenarios observed in one market are not too unrealistic for another market then you can use these as hypothetical scenario or at least to inform the scenarios construction. – Magic is in the chain Jul 18 at 18:48
• OK, since we don't have a cash flow model, I can safely ignore the first two approaches. Re third point, are you saying equity duration? How would you estimate that if there is no interest rate component? The most viable option to me seems the fourth option, but I am not really sure what maturity/tenor to regress stocks to -- is it 2Y or 5Y? Is it all KRD tenors? How about multicolinearity? So on and on ... – AK88 Jul 18 at 19:35
• For duration please google empirical duration of equity, it was trending a while back! I would use just one benchmark rate for equity, – Magic is in the chain Jul 18 at 19:39