Chapter Twelve Asset-Liability Management: Determining and Measuring Interest Rates and Controlling Interest-Sensitive and Duration Gaps

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

Historical View of Asset-Liability Management Asset Management Strategy Liability Management Strategy Funds Management Strategy

Interest Rate Risk Price Risk Reinvestment 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

Yield to Maturity (YTM)

Bank Discount Rate (DR) Where: FV equals Face Value

Yield to Maturity

Market Interest Rates Function of: Risk-Free Real Rate of Interest Various Risk Premiums Default Risk Inflation Risk Maturity Risk Liquidity Risk Call Risk

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

The Maturity Gap and the Yield Curve Maturity Gap between the Average Maturity of Assets and the Average Maturity of Liabilities Positive Maturity Gap and Upward-Sloping Yield Curve Lead to a Positive Net Interest Margin

Net Interest Margin

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

Interest-Sensitive Gap Measurements Dollar Interest-Sensitive Gap Interest-Sensitive Assets – Interest Sensitive Liabilities = Relative Interest-Sensitive Gap Interest Sensitivity Ratio

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

Interest-Sensitive Liabilities Borrowings from Money Markets Short-Term Savings Accounts Money-Market Deposits Variable-Rate Deposits

Asset-Sensitive Bank Has: Positive Dollar Interest-Sensitive Gap Positive Relative Interest-Sensitive Gap Interest Sensitivity Ratio Greater Than One

Liability Sensitive Bank Has: Negative Dollar Interest-Sensitive Gap Negative Relative Interest-Sensitive Gap Interest Sensitivity Ratio Less Than One

Gap Positions and the Effect of Interest Rate Changes on the Bank Liability-Sensitive Bank Interest Rates Rise NIM Falls Interest Rates Fall NIM Rises Asset-Sensitive Bank Interest Rates Rise NIM Rises Interest Rates Fall NIM Falls

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

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

NIM Influenced By: Changes in Interest Rates Up or Down Changes in the Spread Between Asset Yields and Liability Costs (Shape of Yield Curve) Changes in the Volume of Interest-Bearing Assets and Liabilities Changes in the Mix of Assets and Liabilities

Cumulative Gap The Total Difference in Dollars Between Those Bank Assets and Liabilities Which Can be Repriced over a Designated Time Period Changes in NIM=Overall Change in Interest Rate * Size of the Cumulative Gap

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

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 and the Choice of Planning Periods is Highly Arbitrary Interest-Sensitive Gap Does Not Consider the Impact of Changing Interest Rates on Equity Position

The Concept of Duration Duration is the Weighted Average Maturity of a Promised Stream of Future Cash Flows

To Calculate Duration

Price Sensitivity of a Security

Modified Duration

Convexity The Rate of Change in an Asset’s Price or Value Varies with the Level of Interest Rates or Yields r p

Factors Influencing Convexity Duration ( Maturity) Coupon Rate Asset Values Change Differently According to Their Duration, Coupon Rates and Market Interest Rates

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

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

Duration Gap

Impact of Changing Interest Rates on a Bank’s Net Worth Positive Gap Interest Rate Rise NW Decrease Interest Rate Fall NW Increase Negative Zero No Change

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