## Gap versus decayOne attempts to measure income sensitivity, the other is used to help determine value (Part 2)

Originally published 2/28/2007 © 2021 Olson Research Associates, Inc.

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Disclaimer: This is part two of two part post. Here is a link back to part 1.

In my prior post I stressed that when you look at a gap report you are trying to measure earnings sensitivity. To that end you need to gap non-maturity deposits in a way that's consistent with how they reprice. Earnings sensitivity measures are typically short-term measurements of interest rate risk. A typical gap report looks at the one-year cumulative gap percentage, a typical earnings simulation uses a one-year forecast.

To measure interest rate risk beyond one year you typically look at a balance sheet value simulation and measure the volatility of the bank's economic value of equity (EVE). In this type of analysis you calculate the value of all assets and subtract the value of all liabilities. The net left over is the economic value of equity (EVE). Calculating the value of standard instruments like a loan or CD is pretty straightforward. You have a maturity date, a rate earned or paid, you know if the principal amortizes or not, and you know if the rate resets or reprices. Given a discount rate you can use the standard present value formula to calculate the values of most of the bank's assets and liabilities.

We encounter a problem when we go to value the bank's non-maturity deposits however. What term to maturity should we use? By definition these deposits don't have a contractual maturity date. A common way to solve this problem is to assign a maturity structure to these deposits. This assigned structure is referred to as "decay". Some people think of decay as a measure of deposit turnover or run-off. How quickly or how slowly do the balances in these accounts shift? That's what decay is attempting to capture. It's import to understand however that these types of deposit balances shift (or don't shift) for reasons other than simply the rate paid. In fact in many cases convenience is more of a driving force for decay than the interest rate paid. This is why it is important not to confuse gap repricing and decay. Once we've assigned a maturity structure to these deposits using decay, we can then calculate the present value and complete the EVE analysis. In A/L BENCHMARKS we can model core deposit decay in one of several ways:

FDICIA305 Defaults
During the development of FDICIA305 (which ultimately gave us things like the BASEL 1 – Risk-Based Capital Standards) the examiners proposed a supervisory model that would measure interest rate risk for all banks. Part of the proposal included a standard default treatment of core deposit decay that slotted balances into what many consider to be a short-term “conservative” structure. This structure is shown at the right. You can see that most of the balance is slotted in the 3 to 12 month bucket, and no balances extend beyond 5 years. Using this approach the duration of core deposits tends to be from 1.5 to 1.9 years depending on the distribution of dollars across the various account types.

OTS NPV (TB-13a) Treatment
Following the major troubles for thrifts in the late 1980’s the Office of Thrift Supervision developed its Net Portfolio Value Model to help monitor long-term interest rate risk for thrifts. The NPV model also assigns a decay structure to the institution’s non-maturity deposits. The model uses an equation to project the demand deposit balance in each future month. For those of you who are interested the formula is shown at the right (taken from the OTS NPV documentation, chapter 6, page 6.D-3). Using this modeling approach deposit balances will decline over time and the rate of decline is influenced by the rate of interest being paid on the account relative to the 3-month LIBOR. This approach tends to produce core deposit durations from 1.8 years to 3.5 years. Several years ago many considered this to be too long and not conservative enough. However over the last seven or eight years this approach has gained more and more acceptance. This is a very commonly used approach for many thrifts, banks, and credit unions, especially those that run their own in-house A/L model.

Custom provided by bank
Another approach is for the bank to provide its own custom decay rates. These usually come in two flavors.

1. The S.W.A.G. This is by far the most common of the two custom methods. It’s usually just an estimate, and not supported by any data or analysis.

2. Closed account analysis. The bank analyzes its closed accounts over a period of a quarter and a year that were closed. They use the length of time the account was open, and the average balance of the account to determine the structure of decay.

Both custom methods tend to produce deposit durations that are much longer than FDICIA305 and the OTSNPV approaches. Typically 60% or more of the balances will be slotted in the over 5 year bucket. Average durations tend to be 4.2 to 5.0 years.

Other 3rd Party Data
Finally, there are companies that will analyze a bank’s core deposits to determine value (and therefore decay). There are a few specialty firms, but many brokers, correspondent banks, and accounting firms also provide such services. The data from these analyses are added to A/L BENCHMARKS usually in the form of a deposit decay rate download file. We’ve seen durations using 3rd party data that range from 1.2 years to over 6 years depending on the nature of the bank. This type of service tends to be very expense relative to the cost of modeling, especially for smaller banks. Another problem is that it is often very difficult to validate or back-test this type of data, making some wonder if it’s worth the cost.

Regardless of the which method a bank chooses, it’s important to remember that decay is not used in classic gap analysis. Decay is a technique used to define a maturity structure when one doesn’t exist.