Chapter Seven AssetLiability Management Determining and Measuring Interest

Chapter Seven Asset-Liability Management: Determining and Measuring Interest Rates and Controlling Interest-Sensitive and Duration Gaps Mc. Graw-Hill/Irwin © 2008 The Mc. Graw-Hill Companies, All Rights Reserved

Asset-Liability Management The Purpose of Asset-Liability Management is to Control a Bank’s Sensitivity to Changes in Market Interest Rates and Limit its Losses in its Net Income or Equity Mc. Graw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved. 7 -2

Historical View of Asset-Liability Management • Asset Management Strategy • Liability Management Strategy • Funds Management Strategy Mc. Graw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved. 7 -3

Interest Rate Risk • Price Risk – When Interest Rates Rise, the Market Value of the Bond or Asset Falls • Reinvestment Risk – When Interest Rates Fall, the Coupon Payments on the Bond are Reinvested at Lower Rates Mc. Graw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved. 7 -4

Yield to Maturity (YTM) Mc. Graw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008

Bank Discount Rate (DR) Where: FV equals Face Value Mc. Graw-Hill/Irwin Bank Management and

Market Interest Rates Function of: • Risk-Free Real Rate of Interest • Various Risk Premiums – Default Risk – Inflation Risk – Liquidity Risk – Call Risk – Maturity Risk Mc. Graw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved. 7 -7

Yield Curves • Graphical Picture of Relationship Between Yields and Maturities on Securities • Generally Created With Treasury Securities to Keep Default Risk Constant • Shape of the Yield Curve – Upward – Long-Term Rates Higher than Short-Term Rates – Downward – Short-Term Rates Higher than Long. Term Rates – Horizontal – Short-Term and Long-Term Rates the Same Mc. Graw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved. 7 -8

Net Interest Margin Mc. Graw-Hill/Irwin Bank Management and Financial Services, 7/e © 2008 The

Goal of Interest Rate Hedging One Important Goal of Interest Rate Hedging is to Insulate the Bank from the Damaging Effects of Fluctuating Interest Rates on Profits Mc. Graw-Hill/Irwin Bank Management and Financial Services, 7/e 7 -10 © 2008 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

Interest-Sensitive Gap Measurements Interest-Sensitive Assets – Dollar Interest. Sensitive Gap = Interest Sensitive Liabilities Relative Interest -Sensitive Gap Interest Sensitivity Ratio Mc. Graw-Hill/Irwin Bank Management and Financial Services, 7/e 7 -11 © 2008 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

Interest-Sensitive Assets • Short-Term Securities Issued by the Government and Private Borrowers • Short-Term Loans Made by the Bank to Borrowing Customers • Variable-Rate Loans Made by the Bank to Borrowing Customers Mc. Graw-Hill/Irwin Bank Management and Financial Services, 7/e 7 -12 © 2008 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

Interest-Sensitive Liabilities • Borrowings from Money Markets • Short-Term Savings Accounts • Money-Market Deposits • Variable-Rate Deposits Mc. Graw-Hill/Irwin Bank Management and Financial Services, 7/e 7 -13 © 2008 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

Asset-Sensitive Bank Has: • Positive Dollar Interest-Sensitive Gap • Positive Relative Interest-Sensitive Gap • Interest Sensitivity Ratio Greater Than One Mc. Graw-Hill/Irwin Bank Management and Financial Services, 7/e 7 -14 © 2008 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

Liability Sensitive Bank Has: • Negative Dollar Interest-Sensitive Gap • Negative Relative Interest-Sensitive Gap • Interest Sensitivity Ratio Less Than One Mc. Graw-Hill/Irwin Bank Management and Financial Services, 7/e 7 -15 © 2008 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

Gap Positions and the Effect of Interest Rate Changes on the Bank • Liability-Sensitive Bank • Asset-Sensitive Bank – Interest Rates Rise • NIM Rises – Interest Rates Fall • NIM Falls Mc. Graw-Hill/Irwin Bank Management and Financial Services, 7/e – Interest Rates Rise • NIM Falls – Interest Rates Fall • NIM Rises 7 -16 © 2008 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

Zero Interest-Sensitive Gap • Dollar Interest-Sensitive Gap is Zero • Relative Interest-Sensitive Gap is Zero • Interest Sensitivity Ratio is One – When Interest Rates Change in Either Direction - NIM is Protected and Will Not Change Mc. Graw-Hill/Irwin Bank Management and Financial Services, 7/e 7 -17 © 2008 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

Important Decision Regarding IS Gap • Management Must Choose the Time Period Over Which NIM is to be Managed • Management Must Choose a Target NIM • To Increase NIM Management Must Either: – Develop Correct Interest Rate Forecast – Reallocate Assets and Liabilities to Increase Spread • Management Must Choose Volume of Interest-Sensitive Assets and Liabilities Mc. Graw-Hill/Irwin Bank Management and Financial Services, 7/e 7 -18 © 2008 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

NIM Influenced By: • Changes in Interest Rates Up or Down • Changes in the Spread Between Assets and Liabilities • Changes in the Volume of Interest. Sensitive Assets and Liabilities • Changes in the Mix of Assets and Liabilities Mc. Graw-Hill/Irwin Bank Management and Financial Services, 7/e 7 -19 © 2008 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

Cumulative Gap The Total Difference in Dollars Between Those Bank Assets and Liabilities Which Can be Repriced over a Designated Time Period Mc. Graw-Hill/Irwin Bank Management and Financial Services, 7/e 7 -20 © 2008 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

Aggressive Interest-Sensitive Gap Management Expected Change in Interest Rates Best Interest. Sensitive Gap Position Aggressive Management’s Likely Action Rising Market Interest Rates Positive IS Gap Increase in IS Assets Decrease in IS Liabilities Falling Market Interest Rates Negative IS Gap Decrease in IS Assets Increase in IS Liabilities Mc. Graw-Hill/Irwin Bank Management and Financial Services, 7/e 7 -21 © 2008 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

Problems with Interest-Sensitive Gap Management • Interest Paid on Liabilities Tend to Move Faster than Interest Rates Earned on Assets • Interest Rate Attached to Bank Assets and Liabilities Do Not Move at the Same Speed as Market Interest Rates • Point at Which Some Assets and Liabilities are Repriced is Not Easy to Identify • Interest-Sensitive Gap Does Not Consider the Impact of Changing Interest Rates on Equity Position Mc. Graw-Hill/Irwin Bank Management and Financial Services, 7/e 7 -22 © 2008 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

The Concept of Duration is the Weighted Average Maturity of a Promised Stream of Future Cash Flows Mc. Graw-Hill/Irwin Bank Management and Financial Services, 7/e 7 -23 © 2008 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

To Calculate Duration Mc. Graw-Hill/Irwin Bank Management and Financial Services, 7/e 7 -24 ©

Price Sensitivity of a Security Mc. Graw-Hill/Irwin Bank Management and Financial Services, 7/e 7

Convexity The Rate of Change in an Asset’s Price or Value Varies with the Level of Interest Rates or Yields Mc. Graw-Hill/Irwin Bank Management and Financial Services, 7/e 7 -26 © 2008 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

Duration of an Asset portfolio Where: wi = the dollar amount of the ith asset divided by total assets DAi = the duration of the ith asset in the portfolio Mc. Graw-Hill/Irwin Bank Management and Financial Services, 7/e 7 -27 © 2008 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

Duration of a Liability Portfolio Where: wi = the dollar amount of the ith liability divided by total liabilities DLi = the duration of the ith liability in the portfolio Mc. Graw-Hill/Irwin Bank Management and Financial Services, 7/e 7 -28 © 2008 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

Duration Gap Mc. Graw-Hill/Irwin Bank Management and Financial Services, 7/e 7 -29 © 2008

Change in the Value of a Bank’s Net Worth Mc. Graw-Hill/Irwin Bank Management and

Impact of Changing Interest Rates on a Bank’s Net Worth Positive Interest Rate Rise NW Decrease Gap Interest Rate Fall NW Increase Negative Interest Rate Rise NW Increase Gap Interest Rate Fall NW Decrease Zero Interest Rate Rise No Change Gap Interest Rate Fall No Change Mc. Graw-Hill/Irwin Bank Management and Financial Services, 7/e 7 -31 © 2008 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

Limitations of Duration Gap Management • Finding Assets and Liabilities of the Same Duration Can be Difficult • Some Assets and Liabilities May Have Patterns of Cash Flows that are Not Well Defined • Customer Prepayments May Distort the Expected Cash Flows in Duration • Customer Defaults May Distort the Expected Cash Flows in Duration • Convexity Can Cause Problems Mc. Graw-Hill/Irwin Bank Management and Financial Services, 7/e 7 -32 © 2008 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.