## Thursday, December 17, 2009

### More on Gap Models

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.

## Tuesday, July 7, 2009

### Gap Calculation, the Basics

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.

## Wednesday, July 1, 2009

### Why Measure Interest Rate Risk?

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

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.

## Wednesday, June 17, 2009

### Relative Measures

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

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.

## Wednesday, June 3, 2009

### Low Rate EAR solutions

The first step is measuring how much income you will lose. Here's how:

- Add up all your variable liabilities - those deposits that have rates that changed as the bank prime rate fell. Chances are that these consist mostly of the premium savings account and perhaps the floating side of a receive the fixed swap.
- Now total all your variable assets. Chances are that these are pretty rare. One example would be the floating side of a pay the fixed swap. (By the way, the floating side of swap is normally considered fixed not floating, but if the swap's reset period is 3 months or less, then it is close enough to floating for our purposes.)
- Take the difference between the total variable liabilities and the total variable assets. That difference is the source of your Low Rate EAR exposure.
- Now calculate how much is at risk. That is how much bank prime has dropped from the level where you froze rates. That would be the difference between your credit union' s prime rate and bank prime rate (currently 2.25%). For instance, if your credit union froze prime at 3.50%, there is 1.25% at risk.
- Calculate the dollar amount at risk per annum. That is the difference calculated in #3 multiplied by the percentage at risk calculated in #4.

That's how much income you will lose as the prime rate rises again to the level where you froze rates. So what to do?

Well, one choice is to do nothing about this Low Rate EAR and just concentrate on lowering your falling rate EAR that is currently masked. Here's the logic - you froze prime to prevent losing income from further drops in prime and that worked very well. Then there was a bonus as prime dropped further and you actually made more income as the rate on your premium savings account fell. That was great - the last blog called it found money. This is the income now at risk and it really means you will be back where you were when you froze prime - so why worry about it? You're just losing income that you weren't expecting to have.

Besides, there is no guarantee that when the prime rate starts to rise that the premium savings account rate will be forced higher. We saw that when prime rates were falling, that the premium savings account rate wasn't always in synch. Prime rate fell 4% whereas these rate only fell 2.00% to 2.50%. Perhaps the savings account rate will not rise when prime rate rises. However, there was a pretty good relationship between premium savings account rates and prime for the last few drops. Also, I think there is a pretty good chance that these rates will rise before prime does - in response to the economy turning and mortgage rates rising. (We saw the majors raised mortgage rates yesterday.)

Yeah, but what about solutions? We need something that will pay more when rates rise, but that will not be a burden when the normal EAR exposure to falling rates returns. That is difficult because many solutions that reduce Low Rate EAR will increase the normal falling rate EAR. Fixing one often makes the other worse.

A natural solution is to use your liquidity investments. Keep them short. When rate rise, their rates will also rise. If you have enough short investments to cover the difference calculated in #3, then you problem is solved. The shorter the term the better the match to your exposure. It would even be a good idea to sell longer investments and buyer shorter ones. Also, when rates rise to the extent that your normal EAR returns, you can reduce that exposure by investing longer. This really is the easiest/best approach to the problem, but chances are it is not enough.

Here's a very common thought process I hear about as an interest rate risk consultant. There is a price to pay when you keep your investments short. Shorter terms have lower yields than longer terms. So there is an immediate income loss if you invest short. Why not invest long and get the higher rate when you are pretty sure that rates will be stable for a while? Here's the problem - there is no telling when rates will start to rise again. When they do your credit union will lose income. A short investment will be able to offset that loss with higher rates on rollover.

If you have a one year term investment though, and rates rise say 1.00%, then you have to wait a year with a very low rate investment before your income will return. And remember that rates will not likely increase by 25 basis point increments - they cam down much faster and they will probably go up very quickly - perhaps as much as 2% in a couple of months. If you feel you can predict when rates will start to rise - go ahead and invest longer for more yield, but this is not recommended. We suggest terms of 3 months or less and again, shorter is better.

Interest rate swaps are another possibility. If you pay the fixed on a swap, the floating side will be like a variable rate that will rise when prime rates ascend again. That will hedge Low Rate EAR exposures. And, fixed pay swaps are a great idea right now because they effectively lock in these low rates for the long term. A five year fixed pay swap is like a five year deposit in that it locks in the rate for five years. But, and its a big BUT, this will also increase you normal EAR exposure to falling rates. (And your falling rate EVR exposure too.) You will also find that the amount you are paying is higher than the amount you are receiving - a loss that starts the moment your swap starts. And there is some pretty ugly accounting for swaps these days. However, this is an effective hedge for Low Rate EAR and a great way to lock in long term rates, so it is a good approach provided that the effects on the normal falling rate EAR and EVR are manageable. Otherwise, a pay fixed swap is not recommended.

Is there a way to get BA (not prime) based loans on your books? These would work, but they also will impact your normal falling rate EAR adversely. Can you convince members to convert their premium savings deposits to longer term deposits (preferably longer than one year) in this environment? Probably a hard sell and again, it will add to your normal falling rate EAR So there really are not many good solutions For Low Rate EAR.

Here's one more approach. As prime rates start to rise, can you also increase the rates on your variable assets? That too is a tough sell to members, as these rates didn't fall when prime fell so how will you explain that to the members affected? Even increasing your prime a portion of the prime rate increase would help. If prime was to increase 1.00%, you could cut this Low Rate EAR in half if you could raise you prime rate by 50 basis points. One way to help sell this would be to promise to get credit union prime back to the levels of bank prime by increasing less than the banks after bank prime reaches the level where you froze rates. Of course that means you would still lose the full amount of annual income calculated in step #5 above, but you have spread the losses to a period where you have higher income.

Finally, you can increase margins the old fashioned way - by increasing spreads on variable loans. This too will offset losses from Low Rate EAR. That is what the banks have done and that is one way they are able to make money with a 2.25% prime rate.

So, the two best methods are to shorten investment terms and to increase loan spreads. Other methods impact member relations or add to the normal EAR that will return when rates rise. They should only be considered with that in mind.

## Monday, June 1, 2009

### How Low Rate EAR works

- Low Rate EAR changes dramatically when prime changes.
- Low Rate EAR only applies to credit unions that froze their prime rate at higher levels.
- Low Rate EAR can have a big effect on your profitability.
- Normal EAR is still there, lurking in the background. It will return in full when credit union prime is 1.00% higher than the level where credit union prime rate was frozen. So, you definitely want keep measuring it.

Next time strategies to manage Low Rate EAR. Promise.

## Friday, May 15, 2009

### Low Rate EAR

Let's be careful with our terms here. What is an exposure to interest rates? If your organization has an exposure to interest rates, that means it will lose something (earnings or economic value) when interest rates change. Of course, interest rate changes could also mean that you gain something (earnings or economic value), but that is not an exposure. Exposures only concern themselves with the downside, favourable results are not a concern - so favourable results are not an exposure.

For the credit unions that froze their prime rates, interest rates rising to higher levels was not an exposure. And rates falling was not an exposure either, after prime was frozen. But their EAR was not zero. They would make more income (or economic value) when rates rose and, somewhat surprisingly, some credit unions would make more income when rates fell - substantially more.

To see why, we have to take a closer look at a very popular demand account - the premium savings account. The simple fact is that the rate on premium savings accounts is too high. In normal market conditions, no deposit rate should be higher than the swap curve, which is the same as the BA curve for terms under one year. Why? Because the swap curve is roughly where the major banks can borrow (or invest) as much money as they desire. Why pay a retail investor more for their $1,000 deposit than the rate where you can borrow millions, even billions of dollars? That should mean the rate for this account should be under 0.50%. And yet the rate persists as a full percent higher. Even the major banks offer premium savings account deposit rates higher than 1.00%.

So why is the rate on premium savings accounts so high? Most likely it is competition - everyone is offering high savings account rates, so not doing so likely means losing market share. But why is anyone paying such high rates? The premium savings account was practically invented by ING. They raised tons of money with this account and used those funds to finance loans - mostly mortgages. So they tend to watch the spread between 5 year mortgages and this savings account rate. So, this rate tends to change with 5 year mortgage rates rather than prime. Mortgage rates remained stubbornly high, as prime rates fell. And so did the rate on the premium savings account remain stubbornly high.

The chart to the left shows the Bank prime rate and ING's savings and 5 year mortgage rates. It may not be obvious (you get a clear picture by clicking the graphic), but prime rates fell 4% while mortgages rate only fell 2.15% and the prmium savings rate only fell 2.25%. That was very bad news for many credit unions. Many credit unions finance their variable rate assets with variable rate deposits, like the premium savings account. While their variable rate returns on prime-based assets fell off a cliff, the savings account rate only fell half as much. In fact, the chart shows how the savings rate was almost touched the prime rate at one point - for almost a month there was only 30 basis points difference between prime and the savings account rate, as compared to the more normal 2 or 3 percent. (You can see that the relationship between mortgage and savings account rates stayed relatively in synch for the entire period.) It was only when mortgage rates started to crack, that there was any relief on the savings account rates. That's the reason for the high savings account rate - it is tracking the 5 year mortgage rate rather than short term rates like BAs or prime.

No wonder, many credit unions took the unusual step of freezing prime to preserve income. Let's say the credit union froze their prime at 3.50%. Since then, the prime rate has fallen 1.25% and the premium savings account rate has fallen 1.20%. That represented a gain in income for these credit unions. The variable asset rates were stuck, but the variable liability rates continued to fall. That created interest rate risk. Now when prime rises, the variable asset rates will stay constant as they did on the way down. But chances are the savings account rates will also rise. And, in many cases, there is nothing to hedge this expense that is due to interest rates changing. That is a rising rate EAR exposure.

And this is a very unusual interest rate risk.

- The magnitude of this EAR will vary as prime rates rise, such that this EAR will be zero again when bank prime equals the credit union's prime. The magnitude of normal EAR does not change significantly with interest rates.
- This EAR is an exposure to
**rising**rates, whereas credit unions are normally exposed to**falling**rates. The falling rate exposure still exists, but is currently hidden by the low rate environment. Eventually, rates will rise again and the falling rate exposure will be there again. - This new EAR is pretty tricky to hedge.

So we now have two types of EAR. We need to give this new form of EAR a name to avoid confusion with the completely different normal EAR. As this EAR will only occur when rates are low, we'll call it Low Rate EAR. So we have normal EAR and, now, Low Rate EAR.

What to do about Low Rate EAR next.

## Monday, May 11, 2009

### New EAR and Masked EAR

- It seems that the prime rate will not go down anymore. The Bank of Canada indicates that a 2.25% prime rate is the floor; we will not see prime at 2.00%.
- Most credit unions have a falling rate exposure. That falling rate exposure is now $0 because rates likely will not drop any further. In other words, most credit unions now have no Earnings at Risk (EAR) interest rate risk.
- The Bank of Canada forecasts rates will stay at these levels for a year. If true, credit unions will have zero falling rate interest rate risk for the next year.

So falling rate exposures have been eliminated, but that doesn't mean they should be ignored. When rates rise again, they will come back. Instead of relaxing, take this time as an excellent opportunity to optimize (or eliminate) your EAR interest rate risk.

EAR falling rate exposures is temporarily hidden, but when rates rise again it will reappear. Depending on your credit unions shock test and depending how quickly the Bank of Canada raises rates this might be a step-wise process. Here's a few cases:

- If the shock test at your credit union is 25 basis points, the next rise in rates will immediately bring back all of your falling rate EAR.
- If the shock test is 50 basis points and the next move in rates is 25 basis points higher, your falling rate EAR will be one-half of normal. The next move higher after that brings all your EAR all back.
- If the shock test is 100 basis points and the next move in rates is 25 basis points higher, your falling rate EAR will be one-quarter of normal. Each quarter point move higher adds another quarter of EAR exposure.

Having said all that, chances are good that no matter your shock test level, the next move in rates will bring all of your EAR exposure back. Why? The Bank of Canada has engineered rates all the way down to what it calls the effective lower bound - in effect, as low as they can. This would obviously be tremendously inflationary in a normal economy, and one of the main functions of the Bank of Canada is to keep inflation within a tight range. On the other hand, we are in such a bad recession right now that the Bank has lowered rates to the very lowest level it can go. Any rise in rates now could make things worse and could squelch any emerging economic growth. So the Bank won't move rates higher until it is convinced that the economy is rebounding. But, when the economy does seem to be coming back, it will want to move quickly to keep inflation in check. For those reasons, the first rate change is unlikely to be a quarter-point move - more likely it will jump a half percent or more.

If that is correct, the next move in rates will bring back all of your credit union's falling rate EAR. So, it is definitely not a good idea to ignore it. That's why you should take this time of zero EAR to get this masked/hidden exposure under control.

Another thought. As mentioned last time, most interest rate risk models have a 0.0% interest rate floor. This prevents the possibility of negative interest rates. Given the Bank of Canada's last statement, this now seems incorrect. The floor should be set at .25%, which roughly where the current over night rate is. 0.25% is where the Bank of Canada has set the floor. Also, clearly the floor is much higher for variable rate assets. For loans at the prime rate, the floor is 2.25%. If there is a loan with spread over prime, the floor would be 2.25% plus the spread. Some savings account rates are already below 0.25%. For those cases, the floor is the current rate.

Next post we will cover the very interesting ramifications for those credit unions that froze their prime rate at higher levels.

## Saturday, May 9, 2009

### Ramifications of Zero EAR

First up - all the credit unions with a falling rate exposure. In our experience this is the vast majority of credit unions. Even those credit unions that carefully measure and control their interest rate risk likely have falling rate exposures, so that they can take advantage of the eventual runup in rates.

The latest Bank of Canada statement (well worth reading here) had some very interesting statements. Here's one:

*With monetary policy now operating at the*

**effective lower bound**(emphasis mine) for the overnight policy rate, it is appropriate to provide more explicit guidance than is usual regarding its future path so as to influence rates at longer maturities. Conditional on the outlook for inflation, the target overnight rate can be expected to remain at its current level until the end of the second quarter of 2010 in order to achieve the inflation target. The Bank will continue to provide such guidance in its scheduled interest rate announcements as long as the overnight rate is at the**effective lower bound**.The Bank is calling current interest rates the ' effective lower bound'. The main rate that the Bank of Canada uses in monetary policy is the overnight rate, or the rate for a one-day loan from the Bank of Canada. The major banks and other financial institutions then set their prime rates based on that rate. So indirectly, the Bank of Canada sets prime rates. The current target overnight rate is 0.25% and it is this level that the Bank is calling the effective lower bound.

The Bank of Canada changes its targeted rate in 1/4% increments. So, at 0.25%, there is only one more downward move that is possible. (Negative interest rates are an interesting concept, but who will lend and then pay the borrower interest - it just won't happen.)

The bank is taking this negative rate fact one step further by calling 0.25% the effective lower bound. This is a statement that overnight rate won't drop any further. Why can't it go to 0.0%? Because of the simple fact that those with money may not lend if they cannot get a return and that would be the case at 0.0% interest. A 0.0% interest rate could jam the money markets, stopping the flow of funds. This could reduce credit availability, which is exactly what the Bank has been trying to improve since the credit crunch. So, the Bank will not drop its overnight rate any further. And thus, 0.25% is the effective floor for interest rates.

Now for ramifications. If you have a falling rate exposure, your EAR is now zero. The risk of rates falling any further is close to zero, because the Bank of Canada will not drop its rate any more and so prime will not go down anymore. Hopefully your interest rate risk advisor advisor is telling you this so you can report a zero interest rate exposure to your regulator.

That means a prime of 2.25% is also the floor. There won't be a 2% prime. And this is true for all your variable interest rates - all their interest rates are at effective floors. Their rates will not drop any further. This has considerable meaning for interest rate risk measurement. Most models will not allow rates to fall below zero, but they will assume that car loans at 6% can still go down. Ignoring credit spreads, that is now incorrect.

One of the big mistakes in early interest rate risk models was that they allowed negative interest rates. Say your Plan 24 savings account rate was 0.15% and your interest rate risk model used a shock rate of 50 basis points, the model assumed your Plan 24 rate could go to -0.35%. An impossible negative interest rate. (It's dangerous to use the word impossible these days when discussing interest rate movements, so let's say impossible, unless you think that your members will pay you when they invest their money). So interest rate risk models quickly incorporated a 0.0% rate floor. The effect was a huge jump in the EAR measure. Here's why. If interest rates dropped 0.50%, asset rates would fall 0.50% (reducing income), but Plan 24 rates could only fall 0.15% (not reducing expenses). Overall resulting in a drop in expected income - EAR interest rate risk. Further model refinements would prevent the 0.15% rate from falling at all. And that modification resulted in even more falling rate EAR.

And now that is true on the asset side. And that suggests a big drop in falling rate EAR. Falling rate exposures are now zero, as stated above. But falling rate exposures will be low even when rates start rising again. Say rates go up 0.25%. Now they can drop 0.25% again, but if your rate shock is at 0.50%, then EAR falling rate exposure is still cut in roughly in half.

At BiLd Solutions, we like to use a 2 percent shock/change in rates as a worst case scenario. Obviously, these floors have implications for this measurement. Prime will have to be 4.25% (up 2 percent from the current floor) before the full 2 percent worst case drop in rates is possible.

That's a lot to digest. More on this topic next time.

## Thursday, April 30, 2009

### Zero Interest Rate Risk

(For some reason, the regulators seem more concerned about EAR interest rate risk than they are about EVR. In Ontario for instance, credit unions don't even report EVR to the regulators. So, they have no idea what risks lurk in the long end of their credit unions' portfolios. Sorry - one of my pet peeves.)

Having stated that EVR is important, this blog is only about EAR. There is something you can do to completely eliminate this interest rate risk at your credit union. Well, you can if you are exposed to falling interest rates - and 90% of credit unions are.

It's pretty simple. One, have your variable asset rates tied to the credit union prime rate not the prime rate at the major banks. And two, do not drop your prime rate when the major banks do. Voila, your EAR is now zero. Now when interest rates fall, your asset rates stay constant but your variable liability rates will still fall. That's why EAR is zero.

Won't the members scream? I am told they do not and that has been true for years, not just this crazy interest rate cycle.

For these loans, a member can refinance without penalty. Won't your credit union become uncompetitive? Yes, the major banks have been dropping prime in lock-step (pretty much) with the Bank of Canada, so their prime will be lower than yours. But they have also been increasing spreads as quickly as they can. Retail line of credit spreads have jumped. Remember those prime minus 0.75% variable closed mortgage rates from a few years ago. Now they are more like prime plus 0.75%. So, no - you likely will not be uncompetitive. Should a member check your rate against the competition, chances are good that you are OK.

I should have written this blog about 6 months ago because now it is too late. We are now sitting at the bottom of the interest rate cycle. (In fact, the all time bottom. In fact, the absolute bottom.) If you freeze your variable rates now, it won't matter because the Bank of Canada is now done. They've reached their 'lower effective bound'. Still, there is always next time. And, if you are really hurting, conceivably you could raise variable asset rates and then freeze them. Or, perhaps more palatable, you could increase spreads instead of increasing your prime.

Here's an interesting thought. Given that the Bank of Canada has (more or less) stated that they will not drop rates any further, every credit union in Canada has had its falling rate exposure eliminated.

And, many credit unions did freeze the rates on their variable loans. They did it to protect income, but they also achieved zero EAR interest rate risk. Now there are some big ramifications. More on that next time.

Oh, and by the way - this 'freezing your variable asset rates' strategy has no effect on EVR.

### My First Post

Topics will usually be centred around Accounting/Finance. There will likely be a heavy emphasis on interest rate risk. Hopefully you will find an idea or two that will save or make your credit union some money because that is what BiLd Solutions is all about.

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Thanks for your time. Let me know what you think.