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### Chapter Seven

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
- 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

Bank Discount Rate (DR)

Where: FV equals Face Value

Market Interest Rates

Function of:

- Risk-Free Real Rate of Interest
- Various Risk Premiums
- Default Risk
- Inflation Risk
- Liquidity Risk
- Call Risk
- Maturity 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

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

Interest-Sensitive Assets – Interest Sensitive Liabilities

Dollar Interest-Sensitive Gap

=

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

Interest Rates Rise

NIM Rises

Interest Rates Fall

NIM Falls

Liability-Sensitive Bank

Interest Rates Rise

NIM Falls

Interest Rates Fall

NIM Rises

Gap Positions and the Effect of Interest Rate Changes on the BankZero 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 Assets and Liabilities
- Changes in the Volume of Interest-Sensitive 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

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

The Concept of Duration

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

Convexity

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

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

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

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