Background

Probably the most frequently used measure of interest rate risk is so called economic value or EV sensitivity.  This is an excellent tool for expressing the current level of open mismatch in the form of a single number and, as this number should be kept to the minimum required operationally to support customer flow, any observed increase should trigger immediate investigation and correction.

EV sensitivity, however, is not quite so good at estimating how much a firm would actually lose in the event of an adverse interest rate change.  This is because the calculation takes no account of any new business and, also, it assumes that whatever rate shock is being modelled will be reflected immediately and fully in the price all of the firm’s products – i.e. taking no account of varying pass through rates, any floors that may exist or the firm’s ability to re-margin. It is effectively a measure that assumes the firm is about to be liquidated and that the realisable value of its net assets would be directly impacted by a sudden change in rates.

Firms wishing to quantify more accurately how much, on a going concern basis, they could actually lose need to supplement EV value sensitivity with what is termed a net interest income (NII) sensitivity measure.

This article aims to set out, at a very high level, how such approaches tend to work.

The Method in Outline

The starting point is the obvious fact that the interest income or expense, generated by any given product, must be its projected volume multiplied by the projected interest rate that will apply to it.  Projecting NII is thus essentially a question of projecting both volumes and rates over some selected time period – say a year.

Let us consider a standard variable rate mortgage product which a firm usually re-prices monthly at SONIA plus a margin of 2%.  We need to estimate, at twelve monthly intervals, how much interest income this product will generate over the next year.

Looking firstly at projected volumes, the starting point is clearly the current balance sheet volume. Going forward, this must be reduced in respect of anticipated contractual repayments and customer prepayments. By the same token, the balance must be increased in respect of expected new business including the anticipated level of reversions from any fixed rate products coming to the end of their fixed terms.

As regards the interest rates that are likely to apply, the implied future level SONIA for each month may be readily calculated from the current yield (as forward/forward rate; to arrive at the final customer rate, simply add on the firm’s chosen margin of 2%.

The following table shows how this approach might, with monthly income being volume multiplied by customer rate divided by 12.   (Other numbers are purely illustrative.)

 

Month	Volume	Implied Risk Free Rate	Margin	Customer Rate	Monthly Income
1	1,000,000	4.25	2.00	6.25	5,208
2	950,000	4.50	2.00	6.50	5,146
3	975,000	4.75	2.00	6.75	5,484
4	1,000,250	5.00	2.00	7.00	5,835
5	1,100,000	5.00	2.00	7.00	6,417
6	1,250,000	4.75	2.00	6.75	7,031
7	1,275,000	4.50	2.00	6.50	6,906
8	1,300,000	4.25	2.00	6.25	6,771
9	1,350,000	4.00	2.00	6.00	6,750
10	1,300,000	4.00	2.00	6.00	6,500
11	1,375,000	3.75	2.00	5.75	6,589
12	1,400,000	3.50	2.00	5.50	6,417
Total					75,054

 

A similar process can be employed for each of the firm’s principal product lines, its liquid asset holdings, plus any swaps that the firm intends purchasing to hedge fixed rate products.

Obviously, the projected balance sheet as at the end of each month must balance, possibly using cash/wholesale market funding as the default balancing items (to the extent that reserves and other non-interest bearing items do not account for the imbalance).

Additionally, particularly on deposits, additional rules could be added to take account of any interest rate floors/caps that may exist as well as any changes to margin that the firm anticipates it would or could make.  Typically margins on deposits tend to be negative, but a firm could equally easily decide to apply a flat rate entirely independent of any benchmark market rate.

The final net income number, across all products, should broadly agree to the firm’s current management plan assuming the latter is based on the current yield curve – this is crucial because NII sensitivity is essentially “risk to plan”.

Then, in order to calculate simple NII sensitivity, the yield curve may be shocked thus altering the implied level of future market rates (e.g. SONIA or longer term swap rates for fixed products), and the calculation rerun.  The difference between the new NII estimate and the base case (or plan) estimate would be the NII sensitivity to the particular interest rate shock being considered.

Additional accuracy could then be achieved by having different volume and re-margining assumptions for each different rate scenario.  For instance, in a rising rate scenario prepayments might reasonably be assumed to decrease and the volume of fixed rate mortgages relative (to variable rate) might increase.

Similarly the amount of any rate change passed through to customers, or other re-margining, could also be made scenario dependent.

Some Caveats

While simple in concept, the potential richness of the approach can, however, if not properly managed, end up creating more problems than it solves, particularly if people decide to go to the nth degree in respect of:

• granularity of time periods (e.g. projecting weekly, or even daily, volumes and rates)
• granularity of product (e.g. modelling every single product as opposed to broad categories)
• extending the time horizon beyond what can be reasonably predicted
• an arrays of assumptions for every single combination of rate shock and product

For small firms particularly, it is important to start with a simple model and only gradually to add greater complexity and granularity.  If not, the final NII sensitivities just become a set of “numbers” whose derivation is impenetrable to all but the people responsible for the model itself (and even, sometimes, to them too!).

The key is to enhance any model only at a speed commensurate with senior management’s own appetite to improve the accuracy, and to ensure that each new enhancement is properly documented, is transparent in the outputs and, where assumptions are added, that these are properly approved and regularly reviewed.  In short, it is better to have a slightly inaccurate model that people understand and maintain as opposed to a model that is spuriously accurate but whose output no one can readily explain.

Another important aspect is to ensure that any NII sensitivity model is backtested against actual P&L outcomes.  This simply means comparing each month’s actual NII to what the model would have predicted as at the beginning of the month had the rate changes that actually occurred been input as shocks.  Any material difference would suggest that either plan volumes had proved to be inaccurate or that assumptions about the firm’s pricing response were incorrect.  In either case, this is valuable information suggesting that either the model should be corrected, or that the plan needs revising, or probably both.  Indeed, the results of backtesting are probably the surest guide as the direction in which any model can usefully be developed further as, by definition, such enhancements will be material whereas other suggested changes may, in practice, simply add complication and not significantly improve the quality of the information.