Interest Rate Gaps

INTEREST RATE GAPS The Gap concept has a central place in ALM for two reasons: (i) It is the simplest measure of exposure to interest rate risk. (ii) It is the simplest model relating interest rate changes to interest income. The interest rate gap is a standard measure of exposure to interest rate risk. There are two types of gaps: (i) The fixed interest rate gap for a given period: the difference between fixed rate assets and fixed rate liabilities. For fixed rate assets and fixed rate liabilities, the interest rate remains fixed during the reference period.

(ii) The variable interest rate gap: the difference between interest sensitive assets and interest sensitive liabilities. There are as many variable interest rate gaps as there are variable rates (1 month LIBOR, 1 year LIBOR etc.) Both the differences are identical in absolute value when total assets are equal to total liabilities. However, whenever there is a liquidity gap, they differ by the amount of liquidity gap.

Horizons need to be specified for calculating interest rate gaps. Otherwise, it is not possible to determine which rate is variable and which rate remains fixed between today and the horizon. The larger the horizon, the larger the volume of interest sensitive assets and liabilities because longer periods allow more interest rate resets than shorter periods. An alternative view of the interest rate gap is the gap between average reset dates of assets and liabilities. However, this is a crude measure of interest rate risk.

E xam p le: Fix ed R ate Liabilities200 Fixed R ate A ssets 400 V ariable R ate Liabilities 800 V ariable R ate A ssets 600 -----------1000 1000 ----------Fix ed interest rate gap +200 V ariable interest rate gap-200 Fix ed interest rate gap - V=ariable interest rate gap

Interest Rate Gap and Variation of Interest Margin The interest rate gap is the sensitivity of interest income when interest rate changes. ∆ IM = (VRA –VRL) ∆ I = Interest rate gap x ∆ I The above formula is an approximation because there is no such thing as a single interest rate. It however applies when there is a parallel shift of all interest rates or when the variable interest rate gap relates to a specific market rate. A major implication of hedging interest rate risk is the making of interest margin ‘immune’ to interest rate changes. It simply implies neutralizing the gap.

If VRA =300 VRL = 200 and the interest rate changes from 10% to 11%, the variation in interest margin will be (300200) x 0.01 = +1 Over a multi period horizon, sub-period calculations are necessary when interest rates rise, the cost increase depends on the date of rate reset.

Example End of Period Month 1 Month 2 Month 3 Variable Rate Assets 0 250 300 Variable Rate Liabilities 200 200 200 -----------------Cumulative gap -200 + 50 +100 Marginal gap -200 + 250 + 50 Monthly Changes in Interest Margin Month Cumulative Gap Monthly Variation of Interest Margin 1 -200 (-200 x 1% x 1/12) = -1/6 2 + 50 ( 50 x 1% x 1/12) = 1/24 3 +100 (100 x 1% x 1/12) = 1/12 ------1/24

• The variation can also be calculated using the marginal gaps: [ (-200 x3)+(250x2) + (50x1)] x 1% x 1/12 = (-600 +500 +50) x 1% x1/12 = -1/24

Interest Rate Gaps and Liquidity Gaps The interest rate gap is similar to the liquidity gap except that it isolates fixed rate from variable rate assets and liabilities. Another difference is that any interest rate gap requires us to define a period because of the fixed ratevariable rate distinction. Liquidity gaps consider amortization dates only while interest rate gaps require all amortization dates and reset dates.

• Both gap calculations require prior definition of time bands. Liquidity gaps consider that all amortization dates occur at some conventional dates within time bands. Interest rate gaps assume that resets also occur somewhere within a time band. In fact, there are reset dates in between the start and end dates. The calculation requires the prior definition of time bands plus mapping reset and amortization dates to such time bands. Operational models calculate gaps at all dates and aggregate them over narrow time bands for improving accuracy. For any future date, any liquidity gap generates an interest rate gap. A projected deficit of funds is equivalent to interest sensitive liability. An excess of funds is equivalent to an interest sensitive asset. However, in both cases, the fixed interest rate gap is the same. But pre-funding variable interest rate gap differs from post-funding gap. Variable Interest Rate = Variable Interest Rate – Liquidity Gap Gap (Post-funding) Gap (Pre- funding) While liquidity gaps include fixed assets and equity, these are excluded from interest rate gap.

• Interest Rate Gaps and Hedging Gaps can be easily used for hedging for the purpose of reducing interest income volatility. Hedging over a single period The interest rate gap can be neutralized by using funding or derivatives depending on the situation. For example, if the liquidity gap is +30 and the variable rate gap is +20 before funding, the bank can raise floating rate debt of 20 and the remaining debt of 10 at a locked in rate as of today (through a forward rate agreement). If the liquidity gap is + 30 and the variable interest rate gap is +45, after a floating rate debt of 30 is raised, there is an excess of 15 in floating rate assets. The bank is receiving excess floating rate revenue. This can be converted into a fixed rate revenue through an interest rate swap (IRS) whereby a fixed rate is received and a floating rate is paid.

• Hedging over Multiple Periods If the gaps over a three month period are –200, +50 and +100, a swap with a notional of 200 paying the fixed rate and receiving the floating rate would set the gap to zero at period 1. In the next period, a new swap with a notional of 250, paying the floating rate and receiving the fixed rate, neutralizes the gap. Actually the second swap should be contracted from date 0 and take effect at the end of month 1. This is a forward swap starting one month after zero. A third swap starting at the end of month 2 and maturing at the end of month 3 neutralizes the gap of month 3. Since the forward swap starting at the beginning of month 2 can extend to hedge the risk of month 3, the third new swap has a notional of only 50. The marginal gaps represent the notionals of the different swaps required at the beginning of each period, assuming that that the previous hedges stay in place.

Limitations of Interest Rate Gaps (i) There are volume and maturity uncertainties (as in the case of liquidity gaps). These are solved using assumptions and multiple scenarios. (ii) Implicit options on balance sheet and optional derivatives off balance sheet create convexity risk. (iii) Assets and liabilities have to be mapped to selected interest rates as opposed to using the actual rates of individual assets and liabilities. (iv) There are intermediate flows within time bands selected for determining gaps which need to be dealt with.

Mapping Assets and Liabilities to Interest Rates Interest rate gaps assume that the variable rate assets and liabilities carry rates following selected indexes. The process requires mapping the actual rates to selected rates of the yield curve. It creates basis risk if both rates differ. Sensitivities, which measure correlation between actual and selected rates, are used to correct basis risk. The technique is used for calculating ‘standardized gaps’. To calculate sensitivities, the average rate of return of a subportfolio can be regressed to the selected market index. Rate = a0 + a1 x index + random residual The coefficient a1 is the sensitivity of the loan portfolio rate with respect to the index. A variation of 1% in the market index generates a variation of the rate of loan portfolio of a1 %.

Intermediate Flows Gaps group flows within time bands as if they were simultaneous. In reality, there are different reset dates for liquidity flows and interest rates. A flow with a reset date at the end of the period has a negligible influence on the current period margin. However, if the reset occurs at the beginning of the period, it has a significant impact on the margin. For example, if there is a flow of 1000 at the beginning of the period and a flow of 1000, with an opposite sign at the end of the period. The periodic gap of the entire period will be zero. However, the interest margin of the period will be interestsensitive since the first flow generates interest revenues over the whole period and such revenues do not match the negligible interest cost of the second flow.

• The direct gap management or ‘gap plugging’ of margin may create errors. For example, if a cash inflow of 1000 has a duration of 270 days in the reference period (360 days) and outflow has a duration of 180 days, the outflow required is 1536 instead of 1000, assuming the interest rate shifts from 8% to 10%. Inflow at day 90 = 1000 (1.10270/360 – 1.08270/360) = -14.70 Outflow at day 180 = -1536 (1.10180/360-1.08180/360) = + 14.70