# Copyright 2014 by Diane S. Docking1 Interest Rate Risk Management: DGAP.

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Copyright 2014 by Diane S. Docking1 Interest Rate Risk Management: DGAP

Learning Objectives Define the duration gap measure of interest rate risk Understand the process of DGAP management Copyright 2014 by Diane S. Docking2

3 Duration GAP Why look at Duration GAP? ISGAP does not fully take into account the effect of changing interest rates on bank’s capital. Immunize Financial Institution Balance sheet

Copyright 2014 by Diane S. Docking4 Duration Gap Analysis Recall: The basic equation for determining the change in market value for assets or liabilities is: % Change in Value = – DUR x [Δi / (1 + i)] or Change in Value = – DUR x [Δi / (1 + i)] x Original Value

Copyright 2014 by Diane S. Docking5 Immunizing a Bank’s Balance Sheet Use duration to immunize bank assets and liabilities, in effect the capital. Duration is an attractive measure because it is _____________across assets and liabilities. If duration of capital =, the bank will not be affected by changes in interest rates.

Copyright 2014 by Diane S. Docking6 Dollar-Weighted Average Duration of an Asset Portfolio Where: w i = the dollar amount of the i th asset divided by total assets D Ai = the duration of the i th asset in the portfolio

Copyright 2014 by Diane S. Docking7 Dollar-Weighted Average Duration of a Liability Portfolio Where: w i = the dollar amount of the ith liability divided by total liabilities D Li = the duration of the ith liability in the portfolio

Copyright 2014 by Diane S. Docking8 Leverage-Adjusted Duration Gap (DGAP K ) where: TA or A= total assets of an investment portfolio or a bank K = total capital of the bank or net worth of the investment portfolio TL or L = total liabilities of an investment portfolio or a bank

Copyright 2014 by Diane S. Docking9 Duration Gap DGAP models focus on managing net worth (capital) or the net market value of the portfolio, recognizing the timing of all individual cash flows. Management’s goal is to stabilize or increase net worth or the value of the portfolio. If Fund/Bank expects interest rates to increase (decrease), then it will want a negative (positive) DGAP

Copyright 2014 by Diane S. Docking10 Change in the Value of a Bank’s Capital

Copyright 2014 by Diane S. Docking11 Example: DGAP - Financial Institution Balance Sheet Given the average duration items from First National Bank’s Balance Sheet (see next slide), calculate the following: 1. Dollar-Weighted average duration of assets? 2. Dollar-Weighted average duration of liabilities? 3. What is the bank’s Leverage-adjusted Duration GAP of capital? 4. Suppose interest rates decrease from 6% to 4.5%. What is the bank’s dollar change in capital?

Duration of First National Bank's Assets and Liabilities Example: IDGAP - Financial Institution Balance Sheet 12 Copyright 2014 by Diane S. Docking Assume Macaulay duration

Example: DGAP - Financial Institution Balance Sheet 13 Copyright 2014 by Diane S. Docking

14 Example: DGAP - Financial Institution Balance Sheet \$  in K if rates decrease: New Capital is: 5 mill. – 1.470283 mill. = _______________ In probable violation of capital ratios.

Copyright 2014 by Diane S. Docking15 Impact of Changing Interest Rates on a Portfolio’s or Bank’s Capital

Copyright 2014 by Diane S. Docking16 Problems with Duration Gap Analysis 1. Finding Assets and Liabilities of the Same Duration Can be Difficult 2. Some Assets and Liabilities May Have Patterns of CFs Not Well Defined 3. Customer Prepayments May Distort the Expected Cash Flows in Duration 4. Not a Linear Relationship Between Prices and Interest Rates 5. Any duration analysis assumes that the yield curve is flat and shifts in the level of interest rates imply parallel shifts of the yield curve. In reality, the yield curve is seldom flat, and short-term and long-term interest rates have different volatilities or shifts over time.

Copyright 2014 by Diane S. Docking17 Problems with Duration Gap Management 6. Overly aggressive management that “bets the bank.” This happened to First Pennsylvania Corp. in late 1970s. With rates high at the end of an expansion, it bought long-term securities with short-term borrowed funds (negative dollar gap, positive duration gap). However, instead of rates falling, they shot up further, causing both negative NIMs and losses on equity leading to bankruptcy. Moral: don’t bet the bank on interest rates! 7. Average durations of assets and liabilities drift or change over time and not at the same rates. At one point the duration gap may be 2.0 but one year later it may be only 0.5. Some experts advise rebalancing to keep the duration gap in a target range over time.

Example: Immunize Financial Institution Balance Sheet 18 Copyright 2014 by Diane S. Docking 90/360 See next slide

Duration Calculation 19 r m = 5.00% Calculation of monthly payment Loan Amount100,000.00 Annual Interest Rate5.00% Loan Period in Years30 Number of Payments360 Monthly Payment536.8216 tCFPVCF at 5.0%/12t x PVCFDuration 1536.82534.5941 2536.82532.37591,064.7518 3536.82530.16691,590.5007 4536.82527.96702,111.8681 5536.82525.77632,628.8814 355536.82122.679143,551.0918 356536.82122.170143,492.5520 357536.82121.663243,433.7481 358536.82121.158343,374.6835 359536.82120.655643,315.3611 360536.82120.155043,255.7843 100,000.000013,718,611.771811.4322years Copyright 2014 by Diane S. Docking

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