**Relationship between earnings-at-risk and EVE-at-risk**

*Originally published 8/30/2007 © 2021 Olson Research Associates, Inc.*

What's the most misunderstood concept in interest rate risk measurement? There is probably a six or seven-way tie for first place on that list. Certainly one concept that's tough to grasp is the relationship between net interest earnings-at-risk (EAR) and EVE-at-risk. Specifically, why do they often seem to contradict one another? How can the bank have earnings exposure to rates down, but EVE exposure to rising rates (or vice versa)?

Often the two measures do seem to contradict one another. This is the biggest reason many bankers dismiss the EVE-at-risk measurement as a useless measurement. However things are not always as they seem. In a previous post I gave a pretty simple example of why you need a longer term measurement of IRR.

In his book Interest Rate Risk for Banks, the author Leonard Matz, addresses both the conceptual and practical relationships between EVE and EAR. Understanding both gives a much clearer understanding of why the differences occur.

**The conceptual relationship between EVE and EAR**

As with any measurement or modeling approach consistency is key. Without it the results are much less reliable (or believable).

Conceptually, it is easy to relate the rate sensitivity of net income to the rate sensitivity of economic value. For any single interest rate scenario, the EVE should approximately equal the present value of the annual net incomes for all future years. Suppose we use both an income simulation model and an EVE simulation model. Both models should incorporate the same assumptions. Suppose we use the income model to project net income for all future years and we then take the present value of every one of those projected income amounts. If we use the same discount rates to calculate the present value that we used in the economic model, the present value of the future net incomes should be close to the calculated EVE...they should be close, but not identical. Having a better understanding of why these two measures differ will help you grasp what each measure is telling you about risk.

There are four reasons why the present value of the income flows for all future periods won't necessarily equal the EVE, even when the same discount rates are used.

1) Banks have more assets than liabilities. Because a bank has equity the present values of asset cash flows will exceed the present values of the liability cash flows.

2) Most EVE calculations include only balance sheet cash flows. There may be, and usually is, some rate sensitivity to non-interest income and expense cash flows.

3) Earnings are calculated using accrual accounting, while EVE uses only cash transactions. Take for example a zero coupon bond. Net income recognizes monthly accretion of the discount. EVE on the other hand captures the income as the present value of a cash-flow at final maturity.

4) EVE calculations do not include cash flows resulting from future business. If new business is added at the prevailing market rates of interest this is not a problem. However, for floating-rate instruments with caps & floors, and more importantly for core deposits, this discrepancy will produce irreconcilable differences between EVE and EAR.

*Pages 5.32-5.34, **Interest Rate Risk Management for Banks**, Leonard Matz, 2007*

**The practical relationship between EVE and EAR**

So does EVE relate to earnings-at-risk in practice? To quote the author again, the answer is "**not even close**." The biggest reason why is that we don't measure earning-at-risk by adding up the present values of all future earnings flows. In the case of A/L BENCHMARKS we only look at a one-year time frame (you have the same problem even if you look at a two or three year time frame).

Just because the present value of all future earnings might equal the economic value of equity, that doesn't mean that the rate risk sensitivity of the current periods earnings relates in any way to the sensitivity of EVE. EVE reflects the sensitivity of all periods, while EAR is measured for just a single defined period. If the risk sensitivity for any one year is similar to the total risk exposure for all years it will be nothing more than a coincidence. * In fact, even the direction of rate risk exposure - whether we suffer from rising rates and benefit from falling rates or vice versa - may be different for the next year than it is for all future years.* (emphasis was added by the author, not by me!)

Measuring the EVE-at-risk of financial institutions is not a "new" practice. The OTS was measuring EVE years before the Joint Policy Statement on Interest Rate Risk was issued in 1996. Starting in the late 80's the OTS was measuring the EVE-at-risk for all thrifts in the country. Market interest rate movements in 1993, and in 1994 presented the OTS with an interesting opportunity.

For both years (in 1993 rates fell significantly, and in 1994 rates rose sharply) the OTS attempted to find a correlation between their calculated EVE-at-risk and the thrift's change in earnings. What they found were some pretty weak correlations.

The OTS study found that the economic model was not even very good at predicting the direction of the earnings rate risk exposure. When prevailing rates rose in 1994, 59% of thrifts in the OTS study experienced a decline in their net interest margins. For that group of thrifts, in early 1994, the OTS's model indicated that 87% would experience a decline in EVE if rates rose. In other words the model was directionally correct in predicting the earnings risk for 87% of those thrifts.

On the other hand, for thrifts whose net interest margin actually rose in 1994, the model only identified 20% of them as being subject to an increase in EVE if prevailing rates rose. In other words, the model was directionally incorrect at identifying the earnings risk for 80% of those institutions.

In short, it is very important to remember that your rate risk exposure for the next month, quarter, year or two years may not even be in the same direction as the entire rate risk exposure in all of your balance sheet positions. EVE sensitivity tells us the amount of our rate risk exposure, but it tells us absolutely nothing about the timing of the risk.

A change in prevailing rates causes an immediate and very real change in the value of our assets and liabilities. However, that same change does not impact the earnings of the bank immediately. Instead, earnings are affected at the time the instruments reprice. The earnings impact may occur on the day rates change, or many years in the future.