# Effective Duration in Core Studies

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Effective duration is an important measure of the value and hedging power of non-maturity deposits, which is why we include this measure in our core analysis studies. The article on hedging interest rate risk by Tom Farin eloquently explains why it is superior to other tradition measures of non-maturity “life” or duration.

The calculation of effective duration is fairly simple. It is technically just:

De = – % Market Value Change / Rate Change

The way we apply this to core analysis study data is by using the market value numbers for each rate shock scenario. We calculate the market value in a given rate environment by discounting the principal and interest cash flows for each month using the related FHLB borrowing rate for that term. The principal cash flows are the differences between the remaining dollar balances after applying the standard decay and the surge decay rate assumptions to the existing balances. So given these values for rate shock scenarios:

Rate Environment – Flat (0%)

Market Value = 2,000,000

Rate Environment – +1%

Market Value = 1,900,000

The effective duration for the +1% rate scenario would be calculated as:

-((1,900,000 – 2,000,00)/2,000,000) / .01 = 5.0

Note that effective duration is the relative change in market value. So if market value changes by 1% with a 1% change in market rates, effective duration is 1. Recall also that effective duration is more useful than cash flow duration because it considers pricing betas. In non maturity deposit terms, effective duration considers betas and lags, where weighted life and cash flow duration do not – because they only consider principal cash flows and fixed interest expense.

It is important to note that effective duration is not a measure of the life of a financial product. We often confuse duration with time, mostly because standard Macaulay duration is an estimate of the life of the fixed cash flows of an instrument. But with non maturity deposits, there are no contractually fixed cash flows – there are only estimates of decay rates and price responses. Remember that effective duration is really a measure of price sensitivity. We express duration in “years” as a shorthand way of comparing different instruments.

To avoid getting confused by the idea of a lifetime of a deposit, it is easier to remember the typical relationships between rates and value. For an asset, when market rates go up, price (market value) typically goes down and vice versa. So it is with liabilities, when market rates go up, market value typically goes down. This is a good thing for a seller of liabilities (a bank) because it hedges against asset prices going down.

Asset market values decrease with a rise in rates primarily because the discount rate goes up, but the corresponding cash flows are fixed or sticky. Fixed coupon bonds provide the easiest understanding of this. When you discount a future cash flow at a higher rate, you get a lower market value.

So effective duration is measuring the extent to which the value of our deposit product is going to react to rate changes.

Negative effective duration occurs when market value changes in the same direction as rates. How can a liability’s market value increase as rates increase? It can happen in two ways – if principal cash flows accelerate via more rapid decay, and if interest cash flows increase by an amount close to the weighted cost of funds using the discount curve. Specifically we might see negative duration when:

1. We have lots of surge and low beta.

2. We have a high beta, especially with no lag.

Think of negative duration not as negative time, but rather as a bad hedge. As a measure of hedging power, this is somewhat intuitive. If I have an account with a lot of surge balances and a low beta, my surge balances leave for higher rates in rising rate environments, further reducing the value of the deposits. Similarly, a high beta is intuitively less of a hedge – interest expense rises faster. So a negative effective duration is similar to a low effective duration – both are bad hedges for assets with larger effective durations.

Negative duration bothers us only because we think that a duration of zero is significant. But there is nothing magical about an effective duration of zero. It only means that there was no change in market value with a change in market rates. It isn’t any kind of mathematical equilibrium, it is really just a coincidence. You can’t solve for an effective duration of zero with variable rate non maturity instruments, nor can you predict what it is dependent on – there are too many factors. So there is nothing special about the difference between an effective duration of plus 0.50 or minus 0.50 other than the -0.50 effective duration indicates a somewhat worse hedge.

by Darryl Mataya