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Measuring Interest Rate Risk Static Gap Analysis • Calculate the gap between rate sensitive assets and rate sensitive liabilities over a given horizon (i.e. 0-90 days, 1 year) • Assets or Liabilities are rate sensitive if: – It is an interest paying demand deposit. – It matures within the horizon or there is partial or interim principal payment – Interest Rate changes by contractual terms – Interest Rate changes according to some base rate Static GAP • Difference between dollar value of risk sensitive assets and risk sensitive liabilities within some time bucket. • Cumulative GAP measures the GAP for a time horizon of today until the end of some date. • Cumulative GAP measures the effect of a permanent change in interest rates on income over that horizon. ∆NII = GAP*∆i Example Assets Yield Liabilities Yield Rate Sensitive 500 8.00% 600 4.00% Fixed Rate 350 11.00% 220 6.00% Nonearning 150 100 /Nonpaying Equity 80 1000 1000 GAP -100 NII 41.3 NIM 4.86% Assets Yield Liabilities Yield Rate Sensitive 500 9.00% 600 5.00% ∆NII = Fixed Rate 350 11.00% 220 6.00% GAP*∆I Nonearning/ 150 100 Nonpaying Equity 80 =-100*.01 1000 1000 GAP -100 =1 NII 40.3 NIM 4.74% Steps for GAP Analysis • Make Interest Rate Forecast • Select a series of Time Buckets – Specific periods of time in the future • Allocate all rate sensitive assets and liabilities into time buckets • Calculate periodic GAP and cumulative GAP for each time bucket. • Calculate effect of change in interest rate on net income. Rate sensitivity reports …classifies a bank’s assets and liabilities into time intervals according to the minimum number of days until each instrument can be repriced. Hang Seng Bank 2005 Less than 3-6 Months6Months- More than Nonearning/ Trading Assets 3 months 1 Year 1 Year Nonpaying Book Total Cash& Short-term Funds 56807 3505 5539 2347 68198 Placings w/ Banks 11211 3101 1919 16231 CD's Held 20539 2366 4318 6348 19 33590 Investment Securities 63977 7027 11253 53821 1947 1866 139891 Advances to Customers 222916 14781 6182 5349 2546 99 251873 Other Assets 1857 896 97 313 33984 1695 38842 Total Assets 377307 28171 27274 65831 44016 6026 548625 Liabilities & Equity Deposit Accounts 417652 5617 3242 7476 29429 463416 Deposts from Banks 8018 514 99 8631 Other Liabilities 3446 18 21954 7123 32541 Minority Interests 852 852 Shareholders Funds 43185 43185 Internal Funding of the Trading Book 1196 -1196 0 Total Liabilites 430312 5635 3242 7476 95934 6026 548625 GAP -53005 22536 24032 58355 -51918 Cumulative GAP -53005 -30469 -6437 51918 0 Weakness of GAP • Cannot capture interest rate risk within buckets. • Focuses on small interest rate changes in short- run. • May be changes in spreads between different base rates and asset/liability rates. • Does not allow composition of assets and liabilities to change – Non-interest paying liabilities may disappear if rates rise. – Debtors typically have an option to repay funds early. Earnings Sensitivity Analysis • Forecast different interest rate scenarios. • Forecast changes in volume and composition effects of interest rate scenarios. Cumulative Gap only measures interest risk if changes in interest rate have even effects across assets and liabilities • Because interest rates changes may be temporary, they may affect of the shape of the yield curve. If rate sensitive assets and liabilities have different maturity structures, cumulative gap may not • Consider the case where short-term interest rates go up by 2% for 6 months and return to previous level for subsequent 6 months. Assets Yield Liabilities Yield Rate Sensitive 500 600 Demand 200 9.00% 600 5.00% 6 Months 300 8.00% Fixed Rate 350 11.00% 220 6.00% Nonearning/ 150 100 Nonpaying Equity 80 1500 1600 GAP -100 NII 37.3 NIM 2.76% Managing the GAP • Calculate periodic GAPs and match rate sensitive assets and liabilities at certain intervals. • Match long-term assets with non-bearing liabilities • Use off-balance sheet transactions to hedge interest risk. Present Value of a Stream of Income is equal to the sum of the present value of each component • Examples 1. Coupon Bond C C C C FACE PRICE .... C BOND (1 y ) (1 y ) 2 (1 y )3 (1 y)T (1 y)T 2. Fixed Payment Loan PAY PAY PAY PAY .... (1 y ) (1 y ) (1 y ) 2 3 (1 y )T 3. General T Xt PVt 1 y t t 1 Changes in interest rates, change in bond prices • Bond prices are inverse to interest rates which determine bond yields. A rise in interest rates reduces bond prices. A fall in interest rates increases bond prices. • % effect of a permanent change in interest rates results in a change in price/present value proportional to T. 1 Par log(1 y ) log( ) T P0 y 1 log P0 1 y T How does a change in the discount factor affect present value? PV T 1 Xt yt y 1 y t t 1 T Xt 1 t 1 y 1 y t t 1 PV T PVX t y Xt t PVX t PV t 1 PV 1 y 1 y t T PVX t duration t A way to measure the maturity structure of t 1 PV an income stream is to calculate what PV PV duration percentage of the present value of an y income stream comes from different 1 y maturity dates Duration also To sum up this measure, calculate a measures the weighted sum of the years until final sensitivity of the maturity using these percentages as income stream to weights. changes in the interest This measure is called DURATION of the rate. income stream. Duration Gap • Market Value of equity should be the gap between the present value of assets and the present value of liabilities NWMV = APV – LPV NW A L A L L NW A L A A A A L A • Use the duration of assets to calculate the y effect of a change in interest rates 1 y NW L duration A duration L DGAP A A Immunization • Banks may deal with interest rate risk by structuring assets and liabilities so as to close the duration gap as much as possible. • Firms conduct simulation series to calculate the effect of different interest rate scenarios on balance sheets.

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posted: | 8/29/2012 |

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