Tuesday, July 7, 2009

Gap Calculation, the Basics

Ok, so we are starting with the Gap interest rate risk calculation. Remember that there are two main models for calculating your Earnings at Risk (EAR) exposure. There is the gap model and there is income simulation.

Of the two methods, income simulation is the superior technique. The gap model has assumptions that are clearly incorrect in some circumstances. Gap assumes that the growth rate for all accounts is zero. Gap also assumes that any account that matures over the next year will roll over for exactly the same term and at exactly the same amount. For instance, a mortgage with a 6% rate that matures in the next month will be replaced with a new mortgage that matures in one month and has a rate of 6%. Clearly these assumptions are often wrong and that's the model's weakness. Income simulation can correctly model these assumptions and that is why it is a superior technique. Many believe that these frequently incorrect assumptions are the reason for the expression 'Gap is crap.' I disagree, in fact I think these assumptions are one of the gap model's strength.

More than any other interest rate risk model, income simulation is assumption driven. These assumptions are the income simulation technique's greatest strength and also its greatest weakness. Three main assumptions are made for each account - 1) growth, 2) maturity rollovers, and 3) a model of how each account's rates change with changing rates in the marketplace. These assumptions allow you to get a very accurate estimate of future profitability. That's why income simulation is ideal for annual budgets. The weakness is that there is a natural tendency for income simulation to assume away interest rate risk - that's why many income simulation models result in lower interest rate risk measures than gap models. But, is thsi the true measure of ineterest rate risk? That's a future blog topic.

So, income simulation has three main sets of assumptions. The gap model replaces the first two sets of assumptions with (perhaps) overly simplistic and frequently incorrect assumptions. Surprisingly though, these extremely simplified, incorrect assumptions are not a huge source of inaccuracy in the measure of interest rate risk. Many of these simplified assumptions effects on interest rate risk are minimal or they are cancelled out by similar assumptions on the other side of the balance sheet - net/net there is often not much actual effect on interest rate risk. Surprising, but true. And, because income simulation tends to assume away interest rate risk with these first two sets of assumptions, gap modelling can actually be superior to income simulation or, at the very least, gap results can supply a much needed reasonability test for income simulation results.

It's the third set of assumptions that can have a huge effect on the interest rate risk measure - the modelling of how each account's rates are affected by changing rates in the marketplace. Many gap models skip this modelling, and those gap models are indeed crap. It's my opinion that this third set of assumptions is the source of the expression that 'gap is crap'.

Like income simulation, gap models can make assumptions about how an account's rates change with market rate changes. Good assumptions here make the gap model's interest rate risk results approximate income simulation measures. These assumptions are the topic of the next post, but first we need to understand the basics.

First let's look at the rate shock. Interest rate risk models assume that current rates get shocked by a given amount, 1.00% is a standard. That interest rate shock is assumed to be immediate; it is assumed to be parallel effecting all points on the yield curve by the exact amount of the shock; it is assumed to effect all yield curves equally by the exact amount of the shock; and it is assumed to last for a full year without any other interest rate risk changes. Pretty extreme assumptions, but that is the basis for most interest rate risk modelling. (Although income simulation often looks at other rate scenarios, like 'interest rate ramps' where rates rise or fall at given constant rate for the full year.)

For interest rate risk modelling, all accounts are divided into three basic types - fixed, variable, and non-interest rate sensitive (NIS). Of the three, NIS accounts are the easiest to model because, as is suggested by their name, NIS accounts have no effect on interest rate risk. In fact, you can be largely ignore these accounts once you have used them to balance your account amounts. An example of an NIS account would be your fixed assets account containing items like the credit union's building and its furniture.

Variable rate accounts have the biggest effect on interest rate risk as measured by income simulation or gap models. Variable rate accounts have rates that change in lock step with prime rates (or some other market rate) - if the prime rate rises by 1.00%, the rate on these accounts also rise by 1.00%. A good example would be a variable rate mortgage.

Here's how the gap model handles these variable accounts. In the event of a 1% rate shock to the downside, a variable mortgage account's rate will also fall 1%. That means that the credit union's income will fall 1% for a full year for variable mortgages and that income change represents interest rate risk. The interest rate risk exposure amount would be the amount of variable mortgages times 1%. For $10 million dollars of variable rate mortgages, that would be $100,000 of interest rate risk. Simple, eh?

However, note that there might also be a variable deposit (perhaps an investment savings account) that also has a rate that moves in lock step with prime. A 1% rate rise, means that the credit union will lose 1% times the amount of the variable deposit. That offsets the variable mortgage account's income gain. In fact, a simplification would be to subtract the variable deposits amount from the variable mortgage amount and multiply that difference by the 1% rate shock.

In fact, you can take that simplification further and add all of the variable asset account amounts and subtract all the variable liability account amounts and multiply the difference by 1% to get the interest rate risk caused by all of the variable accounts. This difference between assets and liabilities is also called the gap - and that is where the gap model gets its name. If the gaps (between asset totals and liability totals) are all zero, there is no interest rate risk. And that is where the out-moded concept of matching came from - the idea being to match the amounts of assets with an equal amount of liabilities to eliminate interest rate risk. So, the gap model simplifies by concentrating only on the gaps.

Ok, now we have figured out the interest rate risk for NIS accounts (equals zero) and variable accounts (equals net variable gap multiplied by rate shock). That leaves fixed accounts. A fixed account is an account with a fixed rate of interest that doesn't change for a period of time. An example would be a fixed rate mortgage or a term deposit.

Modelling fixed accounts is a bit like modelling NIS accounts and a bit like modelling variable accounts. For the period until the term deposit matures, there is no interest rate risk and after that, it behaves like a variable account. For example, take a term deposit that matures in 5 months. There is no effect on interest rate risk for the first 5 months, but the full rate shock takes place for the final 7 months. So there is an effect on the estimated future income for those final 7 months. The formula to calculate that interest rate risk would be the amount of the mortgage multiplied by the rate shock (say 1%) multiplied by 7/12 (the final 7 months remaining of the next 12 months where interest rate changes can have an effect.)

And, once again you can simplify the process by take the gap between all the 5 month assets and all the 5 month liabilities and multiply that by 1% further multiplied by 7/12. This process must be repeated for all maturities with terms out to 12 month maturities.

What about items that mature beyond one year? Income simulation and gap models only look at the effects of interest rate changes on the next year's income. Anything maturing beyond 12 months has no effect on EAR. It's the great weakness of EAR models and why you really must measure EVR as well as EAR. Some credit unions believe that you can control risks beyond one year by gap matching, but that is really an old fashioned interest rate risk management technique that EVR handles much, much better.

Now we have measured the interest rate risk for all the possibilities - fixed, variable and NIS. Add up all the interest rate risks (some positive, some negative) and that is EAR as measured by the gap model. Big problem though - this gap measure truly is crap. This simple measure can be so misleading that it is quite possible that your credit union might look like you it is exposed to rising rates when your credit union is actually exposed to falling interest rates. In such circumstances, taking corrective actions to lower your credit union's interest rate risk exposure can actually increase your interest rate risk.

There are many complications to be considered. Most complications are related to that third set of assumptions used in income simulation - modelling how the account's rate changes with market rates. The next post discusses these complications and how to handle and measure them.

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