Core Deposits

As promised in the last post, we will be discussing core deposits this time. Let’s begin with what a core deposit is. Core deposit amounts outstanding are stable and dependable. Core deposits can be depended on remaining on the balance sheet for an extended period of time – they are CORE. Depositors are attracted to the deposit for the service and convenience of the institution and not so much by the interest rate. The typical depositor is not really influenced much by the deposit rate. From the institution’s perspective, core deposits have rates that can be changed at any time in either direction often without notice. For this reason, core deposits are also called administered rate deposits.

The fact that they can have almost any rate and yet remain as a stable source of funding tells you that these deposits are extremely valuable to a financial institution. So these deposits are well worth tracking and trying to increase.

Not too surprisingly, the rate on these deposits is often very low, generally from 0%to 0.25%. When rates start rising again from their current floor levels, the rate on these deposits might not rise at all or they might change very slightly.

In essence, core deposits have two main characteristics:

1. In aggregate, the amount of the deposit is stable over a long period of time.
2. The rate paid on the deposit is also stable and unlikely to change over a long period of time.

Here’s a useful fact that really helps define a core deposit – core deposits are not variable. Variable deposits and core deposits are opposites of each other. Recall that a variable deposit’s rate is determined by another rate – usually the prime rate. Look at the second characteristic of core deposits and you can see that core deposits and variable deposits have opposite rate characteristics.

Just just because core deposits and variable deposits are opposites doesn’t mean that every account must be either variable or core. Just the opposite is true; most deposit accounts are a combination of the two; partly core and partly variable. A typical savings account will have a low rate today, but when rates start rising again, the savings account rate may go up too. It is very unlikely though, that the rate will go up as fast as the prime rate as it would for an account with a pure variable rate type. More likely, if the prime rate goes up 1%, the rate on a savings account will go up a portion of that 1%, say 0.10%. One useful way to look at this is to say the account is 10% variable. It’s tempting to say that the remainder is core, but be careful. A core deposit is non-variable, but it also has a balance that is stable over a long period. So, the non-variable portion might be core or, it might be non-interest rate sensitive (NIS).

In the last post we discussed how different interest rate types get modelled and interest rate sensitivity. Variable deposits have a straight forward modelling methodology, core deposits actually get modelled as fixed deposits, and NIS deposits are largely ignored - but we’ll talk about NIS accounts some more a little further down.

Here’s how you should determine how much of a deposit account is Core. Take daily or monthly balances for each deposit over two or three years. The very lowest level is definitely core, but that level may be too conservative. Chart the balances on a graph. If the amount has been bouncing around at about the same level, the lowest amount is probably reasonably accurate. If the deposit amount has been growing constantly, you will be better served by choosing a more recent low point; perhaps use the lowest level in the last 6-12 months, or use statistical techniques. Using statistics, you can find the deposit level that you can be 95% certain will be outstanding – that would be the core amount. If the chart is trending downwards, you might pick a core level that is even lower than the lowest point. The important thing to keep in mind is that your model will assume that the core amount will be outstanding for a considerable period of time – a portion of core deposits are assumed to be outstanding for years. You want to make sure that is true.

Take the core amount and divide by the current amount outstanding. Say that’s 75%. We can say the deposit is 75% stable. Now determine how much of the deposit is variable. Ask yourself this question – if rates go up 1%, how much will the rate on this account rise? If the answer is 20 basis points, then it is 20% variable. Remember, if an account is variable, it is not core. So, the most that this account can be is 80% core. You now have two values; the deposit is 75% stable and it is 80% non-variable. The core percent is the smallest value. If the deposit is 75% stable and 80% non-variable, then it is 75% core. So in this case, it is 75% core, 20% variable and 5% NIS.

As another example, say the deposit was 70% non-variable and 90% stable. That would be 70% core and the other 30% is all variable. There is no NIS component in this example.

Let’s look at chequing accounts. Chequing accounts can have very stable balances and the often pay no interest. In fact, some chequing accounts have never paid interest and likely never will pay interest. Are these accounts core or NIS? Recall that an NIS account has no interest rate, will never have an interest rate and is unaffected by changes in rates. It’s actually hard to tell if a chequing account is core or if it is NIS, as these deposits match the definitions for both. The distinction is important though, because the two are modelled very differently for interest rate risk.

Our chequing account example is clearly non-variable; so it might be core. Also, it usually has a balance outstanding that you can depend on lasting for an extended period of time. So, at least a portion of the chequing account meets the requirements to be classified as core. The value of core deposits is that they can be used to finance fixed assets. It seems reasonable to use chequing accounts to do just that. So, it is safe to model these as core.

And you can take that argument further and stretch it to other NIS liabilities. For instance, accounts payable could be core. In this case, as there is no rate involved, the only criterion is whether it has a dependable balance outstanding. If so, interest payable could be modelled as core. Same with accounts payable. And let’s go further still – what about assets? Asset accounts, by definition can never be a deposit, but are they not a perfect offset for a core deposit? For example, to the extent that core assets offset core liabilities, there is no interest rate risk and they can be ignored – effectively treated as NIS. If you are looking at NIS liabilities as possible core deposits, then you should also look at NIS assets.

Let’s step back for a minute and think about this. Core deposits are useful because they are long term sources of funding for fixed assets. We believe that NIS liabilities that have stable balances can also be used to finance fixed assets, so they are also core. Some NIS balances on the asset side are also stable in nature. Since they are on the asset side, they are kind of ‘contra-core’. To the extent that you have the contra-core asset balances, they offset/reduce the core balances. The reduced amounts get treated as NIS and are ignored by the interest rate risk measures.

And clearly, equity can be considered core. In fact, equity is a special case distinct from other core deposits because they have an additional feature that normal core deposits do not have. Equity is stable and has a rate that is controllable by the financial institution and the amount outstanding is completely under the control of the institution. A member can always leave and take their deposits with them, but the member can’t touch retained earnings. So, equity can be reliably used to finance long-term assets. 25-year assets can safely be financed with equity. So if your credit union does not offer mortgages with a term longer than 5 years because there are no deposits with a term longer than 5 years, you might want to reconsider. It is perfectly reasonable (even desirable) to finance long term assets with equity.

The core amounts of your deposits are essentially all the same, even though they originate from very different accounts. All core amounts have constant rates and are stable for extended periods. So, it is perfectly reasonable to lump them all together and model them as a group. This a simple sum for the principal amounts, and it is the weighted average rate for the rates. For example say one deposit has a rate of 0.50% and a $5 million core amount and another has $5 million core and a rate of 0%. Together you have $10 million core deposits with a rate of 0.25%.

So, here’s the process. Examine each variable and NIS account closely to see if it has core component – stable and non-variable. The more important (larger) an account is to your organization the more closely you should examine it. Large accounts might be graphed and perhaps statistically examined. Total all the core liabilities and subtract off total core assets. Now, subtract off core equity accounts as they are modeled differently. The remainder is the amount of core liabilities.

A word on terminology. This post is about core deposits, but clearly we have also included equity, non-deposits, and even assets. Clearly, ‘core deposits’ is a bit of a misnomer. Core liabilities might be better and we’ll use that term too, but we will also refer to them as core deposits as does the rest of the world.

You can see it is an involved process. If your interest rate risk consultant hasn’t taken you through this process, you can be pretty sure that your interest rate model is incorrect, especially for Economic Value at Risk (EVR) measures. And remember, deposit accounts can change over time. What looks completely non-variable today might look quite different tomorrow. You need to repeat the evaluation process- we suggest annually or biannually or on the occasion of extreme events. The recent interest rate crash to historical low levels is an excellent example of an extreme event where core deposits should be re-evaluated.

More on Gap Models

The last post briefly discussed the two models for the Earnings at Risk (EAR) measure of interest rate risk - the gap model and the income simulation model. We then went on to discuss the three types of accounts - fixed, variable and NIS. And then we discussed how each type of account gets modelled in the gap model. (We will cover the income simulation model later.) We concluded that there are many complications to consider, and that you would have a very poor measure of interest rate risk if these complications are not taken into account.

Let's start with a discussion with a simplistic look at interest rate risk. There was a time (early 1980's?) when interest rate risk was not measured. It was also a time when financial institutions made extra margin by extending loans along the yield curve - basically they would borrow short (say via a savings account) and then invest long (say via 5-year mortgages.) This was very profitable at first because long rates were much higher than short savings account rates, and a much of that extra spread made its way to the bottom line. Then we hit the eighties and interest rates soared. The rate on savings accounts also soared -sometimes to rates that were higher than those booked 5-year mortgages. Now that very profitable spread was actually negative, and the financial institutions lost money - some even went bankrupt.

So from that experience financial institutions recognized and started to measure interest rate risk. It became conventional wisdom that you shouldn't finance long assets (like mortgages) with short liabilities (like savings accounts). It was much more sensible to match fixed mortgages with fixed deposits.

And here is where it starts to get complicated. One reason for this complication is that interest rate risk models give better results when cashflows are used instead of principal values. When entering data into the interest rate model, cashflows provide a much more accurate interest rate risk measure than principal values. What does that mean? Here's an example:

Let's say a credit union has $5 million in 60 month mortgages and $5 million in 60-month deposits. In our little interest rate risk story, this position would be considered matched and no credit union would lose money on that position simply because interest rates changed. Given our gap model so far, that would have zero interest rate risk. All of which is wrong, wrong, wrong. The error is that this example uses principal values, not cashflows. The 60-month mortgage pool really has a cashflow every month - the members make a payment each month and each payment consists of some interest and some principal. Each principal and interest payment is a cashflow. Plus, mortgages allow prepayments and any pool of mortgages will have some prepayments, and each prepayment is also a cashflow. That means that cashflows will be spread from 1 month to 60 months, unlike the principal amount – where there is just one term – all at 60 months. Depending on the average amortization period of the mortgage pool and the rate of prepayments, the principal amount left in the 60th month might only be $2.5 million (one-half the total principal) or even less.

And what about the 60-month deposits? What if the 5 year fixed deposit pool accrued interest and paid interest at maturity. If that was the case there would only be 1 cashflow on the maturity date and that cashflow amount would be larger than the $5 million principal amount because of the accrued interest paid on maturity.

So the position does have interest rate risk. All those monthly mortgage payments have no matching liability. And the maturing deposit is likley only half covered. And because asset cashflows tend to happen sooner than liability cashflows, this interest rate risk exposure is to falling rates. In other words, the credit union with a 5-year mortgage portfolio and a matching 5-year deposit portfolio is considerable more exposed to falling rates than you might think.

Also recall that EAR measures (both gap and income simulation) completely ignore maturities beyond 1 year. Once again the mortgage portfolio will have cashflows in the first year - the payments and prepayments from 1 month through to 12 months. But the deposit portfolio will have no payments less than 1 year - an exposure to falling rates. And, incidentally, EVR is even more exposed to falling rates because the long items are badly mismatched in the 60-month term.

In fact, because assets (loans) tend to pay more frequently than liabilities (deposits), using principal values generally tends to underestimate falling rate exposures. (You could also express this as overestimating rising rate exposures, but this is really just the flipside of the first statement - an underestimate of a falling rate exposure also means an overestimate of rising rate exposures and vice-versa. To save the confusion, we will just discuss the effect on falling rate exposures, but remember, there is also an opposite effect on rising rate exposures.)

We also need to adjust slightly our earlier statements on how to calculate the interest rate effects of the various types of accounts. For fixed accounts (specifically, for a five-month maturity) we said, "...take the gap between all the 5 month assets and all the 5 month liabilities and multiply that difference by 1% further multiplied by 7/12." This needs to be adjusted to - take the gap between all the 5 month asset cashflows and all the 5 month liability cashflows and multiply that difference by 1% further multiplied by 7/12. Principal values are only an estimate of the cashflow amount. Sometimes the principal amount is a good estimate (they are pretty good for variable accounts), but sometimes it is terrible estimate as shown in our example above.

One more point - remember the horribly mismatched portfolio that caused financial institutions to go bankrupt – the 5-year mortgages funded by savings accounts? Well today, that might actually be a better match than the 5-year deposit. Say the savings account pays a very small rate (0.10%), that it has paid that rate for a decade and is expected to pay that rate for the foreseeable future. Obviously this is not a variable account. In fact, it is what is called a 'Core Deposit'. Core deposits are a big topic worthy of a complete post all by itself (the next one), but for now here is how these accounts are modelled. They are treated like fixed deposits and spread from one month out to your credit union's maximum maturity. If you look at the first year (where EAR is affected), the mortgage cashflows offset by the savings account cashflows is at least a partial match - certainly there is a better match than the fixed deposits which have no cashflows in the first 12 months.

There are two lessons here. One, cashflows are what should be modelled, not principal values. And two, how an account reacts to changes to interest rates is key. The savings account in this example does not change much with interest rate changes, and so it would not have caused nearly the problems that savings account did in the 1980's. Ironically, the mortgages funded by such savings accounts have a much lower EAR than the case where mortgages are funded by similar term deposits.

Core deposits are another complication. Since they are covered more extensively in the next post, I'll just say this: Core deposits are really important to model correctly, especially for EVR. The effect of treating core deposits as variable deposits tends to underestimate falling rate exposures - both EAR and EVR. Its a big mistake, and it is a common mistake.

The next complication is interest rate floors. As a minimum, your interest rate risk model should not allow negative interest rates. That means you should not let rates fall lower than 0.00%. So, if your savings account has a rate of 0.25% and your rate shock is 1%, then this account’s rate would move to 0%, not negative 0.75%. As this mainly effects deposit accounts (because they tend to have lower rates), an interest rate risk model allowing negative rates will tend to underestimate falling rate exposures.

More recently, we have seen where interest rate floors can also affect assets accounts. The current level of prime is at a minimum - it cannot go lower. So asset accounts with a rate based on prime (i.e. variable accounts) cannot drop further. That means there are currently no falling rate exposures for variable loan accounts. Rates can't drop any more - in effect they are 'floored out'. That is an adjustment to your model - now when the rate shock is applied to your variable assets, the rate is unchanged. This can have a huge effect on interest rate risk. Not adjusting for floors on assets tends to result in an overestimate of falling rate exposures. (This is the first complication that overestimates the falling rate exposures.) And again, it is a common mistake to not apply these floors.

And before we leave floors, some credit unions stopped dropping their prime rates before prime bottomed out at the Bank of Canada - say at 3.50% prime. Those credit unions have higher floor rates on their variable assets, which also needs to be modelled. For a credit union that ceased dropping primes, the model should not allow rates to go any lower. And, to be even more complicated, the model must now adjust for what the credit union will do when interest rates start rising again. Will a variable loan account that has had its rates frozen for the last one percent of Bank of Canada bank rate drops, start raising their rates when the Bank starts raising them, or will they leave their variable loan rates constant until their prime is the same as the major banks, or will they do something in between? Whatever the answer, it is important that your interest rate risk model incorporates that answer, or the results could be substantially incorrect. There is a recommended further discussion in my May and June 2008 posts on Low Rate EAR.

Another complication has to do with accuracy. There are a number of unavoidable approximations made when estimating interest rate risk. Core deposit modelling is an excellent example of unavoidable approximations. So, because there are already inaccuracies in the model, it is important that it interest rate risk model reduces estimation error wherever possible.

Remember this? "...take the gap between all the 5 month assets and all the 5 month liabilities and multiply that difference by 1% further multiplied by 7/12." The truth is that there will be many maturities during the month of July, but relatively few will fall exactly on July 31, which the 7/12 implicitly assumes. A more accurate number would be 6.5/12, which assumes that items maturing in July are spread evenly over the month. Even better, the 7/12 should be replaced by the number of days between Jan 1 and July 16th divided by the number of days in the year (yes, incorporating leap years). For 2009 the 7/12 should be replaced with 0.539726027397 (compared to the .5833333 that 7/12 equates to) taken to as many decimals as possible. Further, it is even better if the exact maturity date is used (rather than July 31, or any one single day in the month) for each loan and deposits and gaps are calculated for every day of the year instead of only monthly.

Yes, these are only small errors, but the whole process has many assumptions and estimations. In my opinion it is best to avoid estimation errors where possible in order to get the very best calculation possible. Modern computers make most avoidable approximation errors inexcusable. Many models simply use the 7/12. In my opinion, that is inexcusable. Equating variable accounts to fixed accounts with a 0 to 3 month maturity - also inexcusably inaccurate.

Many models accept aggregate data as opposed to transaction level data. Do you input 60 entries for your mortgages or do you enter thousands representing every single mortgage outstanding at the credit union? Clearly, its more accurate to use every single transaction if possible. Any aggregation will likely reduce accuracy.

The nature of accounts is another complication. All accounts must be classified as NIS, variable rate, or fixed rate, but the truth is that sometimes it is hard to tell. Which account type is a standard on-demand savings account - NIS, variable or fixed? The truth is that such accounts are sometimes a bit of all three account types and sometimes they are just one, and sometimes a combination of two types – there are an infinite number of possibilities. For instance, if the rate never changes, and the rate is never going to change no matter what happens, then it is 100% NIS. If the rate is tied directly to prime and moves in lock step with the prime rate then it is variable. And if it is determined that it is a core deposit, then it is really fixed. And, more typically, it is a little bit fixed, and a little bit variable, and a little bit NIS. For instance, say the savings account rate moves slightly with prime – say when prime moves 1.00% it’s rate moves 0.10% - then it is 10% variable. And if it is also determined that the savings account is 85% core, then it is 85% fixed and it must also be 5% NIS. The important thing is that each account needs to be properly modelled, because small differences can have a big effect. This takes effort and work, but in my opinion it is really well worth it.

One final complication needs to be discussed and that is interest rate sensitivity. The interest rate on some variable accounts is only partially based on prime. Like in the example above, where the account is determined to be 10% variable. The best way to model such an account is to give it an interest rate sensitivity of 10%. But that account is also 85% core. That means that 85% of the balance is going to be removed and spread out over various fixed terms. The remaining 15% of the savings account is 67% variable (10% divided by 15%) and that is how the interest rate sensitivity of that account should be modelled - 67% interest sensitive. Another example is the case where the credit union stopped lowering its prime at 3.50%. Going forward, they have decided that they will not keep their prime steady when the Bank of Canada starts to raise rates again – rather they will increase their prime at 50% of the Bank of Canada increase until their prime is equal again to the major banks. How to model that? Answer, give the account a 50% interest rate sensitivity.

Also note that it is quite possible that the interest rate sensitivity is different for downward movements in prime than it is for upward moves, and should be modelled accordingly. That means that at least two interest rate sensitivities should be tracked for each variable account.

Some complications are just not worth modelling. You always have to weigh the benefit of obtaining the extra information against the cost of getting it. Sometimes it’s just not worth the time and effort - core deposits are an excellent example of this. There are outfits in the states that will model your core deposits and give you very precise ways that they should be treated in your interest rate risk model, but their models require years of information, which can be hard to come by, and their analyses are not inexpensive. Even if you gather your data and pay for such an analysis, you are still left with the fact that the analysis is based on historical information, which might not be relevant going forward. I’m of the view that a straight forward, rational, consistent approach can give comparable results for much less time and expense.

In summary

• Accuracy is important and should be a key objective of the model. There also must be a reasonable balance between the cost of obtaining more accuracy and the benefit of having it.

• A gap model that does not account for the many complications of interest rate modelling is likely worthless.

• Not modelling many of complications tends to result in an underestimate of falling rate exposures. This is surely one of the main reasons that credit unions tend to have an exposure to falling rates.

• A gap model that incorporates these many complications will give results that are not radically different from for the income simulation model.

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.

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.

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.

Relative Measures

So far, we have been talking about interest rate risk measurements in terms of dollars of risk to earnings or economic value. The problem with absolute dollars is that it is hard to compare the amount to previous risk levels at your credit union or to risk levels at other credit unions. For instance, $50,000 of EAR interest rate risk is quite different for a credit union with $10 million of total assets as compared to a credit union with $100 million of total assets. We need a method to compare these two credit unions.

For this reason, we usually divide the dollar amount of interest rate risk by the total assets. For the example above, that would be an EAR of .005 for the $10 million credit union and .0005 for the $100 million credit union.

These small numbers are awkward to work with, so we normally talk in terms of 'basis points of assets'. A basis point is one percent of one percent - or .0001. An example will make this more clear. If we are talking about a rate of 5.53%, adding one basis point to 5.53% would make 5.54%.

To change our .005 and .0005 to basis points of assets you multiply by 10,000. For the $10 million credit union that gives an EAR exposure of 50 basis points. That is a very high level of exposure. For the $100 million dollar credit union, the EAR exposure is 5 basis points of assets. That is a low level of exposure.

$100,000 of EAR interest rate risk is very meaningful to you. That means if the rates change adversely by the shock amount, your credit union will suffer a loss of income of $100,000. That is critical information no matter how big your credit union is. However, to get a feel for the relative size of this exposure, we need to divide by the assets and then multiply by 10,000 to get the exposure in terms of basis points of assets. As we just demonstrated, $100k of EAR exposure can be either very high or low - depending on the size of the credit union.

By the way, this is how the regulators want you to report your exposure - at least in Ontario.

Whether the exposure is high medium or low is somewhat subjective. We benchmark exposures in terms of a 1.00% shock. Using a 1.00% rate shock for EAR, we say 5 basis points or less is a low exposure, 6 to 10 is a moderate low exposure, 11 to 15 is a moderate high exposure, and over 15 is a high exposure. For EVR, we say 20 basis points or less is a low exposure, 21 to 35 is a moderate low exposure, 36 to 50 is a moderate high exposure, and over 50 is a high exposure.

One more note. Some practitioners divide by total capital instead of total assets. This makes some sense as capital is available to protect the institution should an adverse event occur - and an adverse interest rate move is a good example. This approach especially makes sense if your capital is relatively low. In that case you want to know what effect the change of rates will have on your capital. As an example, a credit union with lots of EAR exposure (say over 15 basis points of assets) should be much more concerned if their capital low are low than if they have lots of capital.

Interest Rate Risk - From the beginning

Let's step back and review interest rate risk from the beginning.

There are two types of interest rate risk measurements - Earnings at Risk (EAR) and Economic Value at Risk. In some ways they are polar opposites to each other, and yet they are also good complements of each other. A strength in one measure is a weakness in the other and vice-versa.

Both measures work with an assumed change in interest rates. There are numerous ways to do this, but the most common (and easiest) method is to assume that all interest rates change at once by exactly the same amount. That's called a parallel shock in interest rates.

The next question is how big a change? A one percent change is kind of the standard. Shocks greater than are pretty rare, but two percent is sometimes used as a worse case scenario. Many credit unions use smaller shocks for reporting to their regulators. 25 and 50 basis point parallel rate shocks are pretty common.

Other common rate changes include 'ramps' which mean a constant and steady change of rates over a period of time. 'Tilts' are like ramps, but the shorter rates move at a different pace or direction than the longer rates, resulting in a tilting of the yield curve. Ramps and shocks imply all rates move the same way - this assumption can also be relaxed. In fact, the possibilities are infinite - it's deriving some meaning from the results that frequently means using simple parallel shocks, or perhaps ramps.

Earnings at Risk (EAR)
This is the simpler of the two measures to understand. It measures how many profits the organization will make or lose for a given change in interest rates. The results from an EAR analysis are quite simple to understand. If rates move like this, profits over the next year will rise (or fall) by this many dollars. That kind of statement hits home to many credit union managers.

The measurement process is relatively simple, and closely related to doing a margin budget. Calculate how much you will earn/pay on each asset/liability based on current or forecasted interest rates. The total of earnings less payments is net interest income. (So far, that's analogous to a margin budget.) Now assume those rates change and recalculate net interest income. The difference between the two results is the EAR in dollar terms.

Economic Value at Risk (EVR)
Unfortunately, this form of interest rate risk has many names and even different methods of calculating it. Having stated that, they all ultimately translate into pretty much the same thing. So, to keep it simple, we'll just stay with EVR.

Economic value is somewhat similar to other valuation terms of an organization - market value or stock price, book value, liquidation value, going concern value. Basically you are trying to derive the value of the credit union. Subtracting liabilities from assets is one technique - that's the accounting book value. Economic value goes one step - it is calculated by subtracting the present value of all the liabilities less the present value of all the assets.

An EVR measurement states how much the economic value of the credit union will change for a given change in rates. Taking the present value involves an interest rate - in this case the rate on the specific asset or liability. And like EAR, you calculate a new economic value after changing the rates by a given amount. The difference between the two economic values is your EVR.

Comparison of EAR and EVR
EAR is concerned with risks to the next year's net interest income. EVR is concerned with risks to economic value of the credit union. It's something like owning a stock or bond. EAR is similar to a concern about risks of loss on interest or dividends. EVR is similar to a concern about risks of loss on the market price of the stock or bond.

EAR only considers the next year's income, so items with a maturity beyond 1 year have no effect on EAR. Variable items have the biggest effect on EAR. The shorter the term of a fixed item, the bigger the effect on EAR. The longer the term of a fixed item, the smaller the effect, such that after one year there is no effect on EAR.

EVR considers all items on the balance sheet, but variable items have almost negligible effect. The longer the term of a fixed item, the bigger the effect on EVR. The smaller the term of a fixed item, the smaller the effect on EVR.

So, to properly consider all the terms exposed to interest rate risk, you need to use both measures.