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.

## Tuesday, July 7, 2009

## Wednesday, July 1, 2009

### Why Measure Interest Rate Risk?

So why measure interest rate risk? One obvious reason is that the regulators require you to measure it. Even if that wasn't the case, you should still measure your interest rate risk - using both measures EAR and EVR. Why?

The main reason you should be concerned about interest rate risk is that it can affect your bottom line more than just about anything else you can do as a credit union manager. This latest plunge in rates should have driven that lesson home. Since most credit unions are exposed to falling interest rates, most credit unions have lost money (lots of money) as the Bank of Canada drove rates down to their lowest possible level.

Was this loss of income preventable? Yes - it was entirely preventable. Even further, protecting yourself from falling interest rates usually increases income. To protect yourself from falling interest rates, you normally seek longer investments and shorter deposits. Longer investments typically have higher rates and shorter deposits typically have lower rates - hence more profits. So, not only could you have prevented the latest drop in income, you could have benefited from even more profits. You could have had your cake and eaten it too. With hind sight, a clear no brainer. That is why you should measure and control interest rate risk.

Some credit unions were forced to freeze their prime rate to prevent a further erosion of income. That too was entirely preventable. Your borrowing members could have had the entire reduction in interest rates. Today, you could be offering new clients a 2.25% prime loan on their mortgages. Member satisfaction and new member attraction is another reason why you should measure and control interest rate risk.

It is all hindsight now. Consider it a lesson learned. Start seriously measuring and controlling interest rate risk.

While on the topic of lessons learned, here's another. You can't consistently predict interest rates (although some people pretend they can). I didn't see anyone calling for this recession and I didn't see anyone calling for the dramatic plunge in interest rates to record low levels. That's why we endorse the philosophy of getting immunized from interest rate risk - then you don't care which way rates go. Then you can simply manage your credit union without worrying (or caring) about what the Bank of Canada will do next.

Get control of your interest rate risk and you can concentrate on serving your members. There is no better reason than that.

The main reason you should be concerned about interest rate risk is that it can affect your bottom line more than just about anything else you can do as a credit union manager. This latest plunge in rates should have driven that lesson home. Since most credit unions are exposed to falling interest rates, most credit unions have lost money (lots of money) as the Bank of Canada drove rates down to their lowest possible level.

Was this loss of income preventable? Yes - it was entirely preventable. Even further, protecting yourself from falling interest rates usually increases income. To protect yourself from falling interest rates, you normally seek longer investments and shorter deposits. Longer investments typically have higher rates and shorter deposits typically have lower rates - hence more profits. So, not only could you have prevented the latest drop in income, you could have benefited from even more profits. You could have had your cake and eaten it too. With hind sight, a clear no brainer. That is why you should measure and control interest rate risk.

Some credit unions were forced to freeze their prime rate to prevent a further erosion of income. That too was entirely preventable. Your borrowing members could have had the entire reduction in interest rates. Today, you could be offering new clients a 2.25% prime loan on their mortgages. Member satisfaction and new member attraction is another reason why you should measure and control interest rate risk.

It is all hindsight now. Consider it a lesson learned. Start seriously measuring and controlling interest rate risk.

While on the topic of lessons learned, here's another. You can't consistently predict interest rates (although some people pretend they can). I didn't see anyone calling for this recession and I didn't see anyone calling for the dramatic plunge in interest rates to record low levels. That's why we endorse the philosophy of getting immunized from interest rate risk - then you don't care which way rates go. Then you can simply manage your credit union without worrying (or caring) about what the Bank of Canada will do next.

Get control of your interest rate risk and you can concentrate on serving your members. There is no better reason than that.

### Earnings at Risk (EAR) from the beginning

As we have been discussing, EAR is a measure of interest rate risk that measures the effect that interest rate changes might have on your next year's income.

If we look at the measure a little closer, we realize that it more accurately can be said to be a measure of the effect on net interest income, or financial margin. That is because the main things that effect EAR are those balance sheet items with interest rates. So, non interest expenses and revenues (like salary expense or fee revenue) usually do not impact on the calculation of EAR.

There are two measurement tools for EAR - gap and income simulation.

Income simulation is the better of the two approaches, but it is more complicated and asumption bound. Income simulation works by modelling the income statement and then seeing how the chnaging of rates affects the bottom line. It's a superior approach because it takes into account current yield curves and product growth. Obviously, both of those involve assumptions - what rate do you apply to mortgages maturing 6 months from now? Or how fast do you assume your premium savings account is going to grow. The answers will impact on your interest rate risk.

One of the problems with income simulation is that you can assume your interest rate risk away. For instance, assume you are exposed to falling rates. Falling rate exposures can be corrected by increasing the amount of fixed term mortgages (long assets) or variable deposits (short liabilities). So, if your model assumes a fast growth rate in these items - presto, no interest rate risk.

Income simulation assumptions are also work intensive. Every product must be mapped to how interest rate chnages affects that product's rate. Also you must specify that product's gowth rate and it's rollover assumptions. When a product like a fixed term mortgage matures, what term does the borrower renew at? One year? Five years? You must specify. Its very labour intensive.

Gap calculations were the financial industry's initial approach to interest rate risk. Gap is income simulation, without the growth rate, interest rate, and rollover assumptions. So its much simpler to calculate. That is actually a strength over income simulation, because you can't assume your interest rate risk away with gap.

However, gap's assumptions are pretty extreme. Gap assumes no growth and it assumes that anything that matures will rollover to the same maturity and to the term. So a mortgage with a remaining term of 3 months and a rate 3% over the current market is assumed to rollover to a three month term with the same very high rate (plus or minus the shock rate). Those are the exact assumptions that get corrected by using income simulation. Taht is why income simulation is the stronger approach.

There is an expression - Gap is crap - and there certainly is some truth to that expression. However, if done correctly, gap provides a very useful answer. We'll explore both opinions (useful or crap) in the next few posts.

If we look at the measure a little closer, we realize that it more accurately can be said to be a measure of the effect on net interest income, or financial margin. That is because the main things that effect EAR are those balance sheet items with interest rates. So, non interest expenses and revenues (like salary expense or fee revenue) usually do not impact on the calculation of EAR.

There are two measurement tools for EAR - gap and income simulation.

Income simulation is the better of the two approaches, but it is more complicated and asumption bound. Income simulation works by modelling the income statement and then seeing how the chnaging of rates affects the bottom line. It's a superior approach because it takes into account current yield curves and product growth. Obviously, both of those involve assumptions - what rate do you apply to mortgages maturing 6 months from now? Or how fast do you assume your premium savings account is going to grow. The answers will impact on your interest rate risk.

One of the problems with income simulation is that you can assume your interest rate risk away. For instance, assume you are exposed to falling rates. Falling rate exposures can be corrected by increasing the amount of fixed term mortgages (long assets) or variable deposits (short liabilities). So, if your model assumes a fast growth rate in these items - presto, no interest rate risk.

Income simulation assumptions are also work intensive. Every product must be mapped to how interest rate chnages affects that product's rate. Also you must specify that product's gowth rate and it's rollover assumptions. When a product like a fixed term mortgage matures, what term does the borrower renew at? One year? Five years? You must specify. Its very labour intensive.

Gap calculations were the financial industry's initial approach to interest rate risk. Gap is income simulation, without the growth rate, interest rate, and rollover assumptions. So its much simpler to calculate. That is actually a strength over income simulation, because you can't assume your interest rate risk away with gap.

However, gap's assumptions are pretty extreme. Gap assumes no growth and it assumes that anything that matures will rollover to the same maturity and to the term. So a mortgage with a remaining term of 3 months and a rate 3% over the current market is assumed to rollover to a three month term with the same very high rate (plus or minus the shock rate). Those are the exact assumptions that get corrected by using income simulation. Taht is why income simulation is the stronger approach.

There is an expression - Gap is crap - and there certainly is some truth to that expression. However, if done correctly, gap provides a very useful answer. We'll explore both opinions (useful or crap) in the next few posts.

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