Asset-Liability Management 1

1. Asset-Liability Management

The Purpose of Asset-Liability Management is to Control a Banks Sensitivity to Changes in Market Interest Rates and Limit its Losses in its Net Income or Equity

2. Yield to Maturity (YTM)

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

4. Conversion of DR into YTM

YTM equivalent yield =

(100 purchase price)/Purchase Price * (365/days to maturity)

Note that the DR ant the conversion to YTM equivalent yields are approximations that are popular with banks.

5. Example

Suppose that we purchase a money market security for $96. The security will mature in 90 days and its face value is $100.

What is the DR, the YTM equivalent yield, and the actual YTM?

6. Example

DR = (100 96)/100 * 360/90 = 0.16

Equivalent YTM = (100 96)/96 *365/90 = 0.1690

Actual YTM =

PV = -96, FV = 100, N = 90/365, I = ?

I = 18%

7. Interest Rate Risk : GAP & Earnings Sensitivity

When a banks assets and liabilities do not reprice at the same time, the result is a change in net interest income.

The change in the value of assets and the change in the value of liabilities will also differ, causing a change in the value of stockholders equity

8. Interest Rate Risk

Banks typically focus on either:

Net interest income or

The market value of stockholders' equity

GAP Analysis

A static measure of risk that is commonly associated with net interest income (margin) targeting

Earnings Sensitivity Analysis

Earnings sensitivity analysis extends GAP analysis by focusing on changes in bank earnings due to changes in interest rates and balance sheet composition

9. 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

10. Interest Rate Risk: Reinvestment Rate Risk

If interest rates change, the bank will have to reinvest the cash flows from assets or refinance rolled-over liabilities at a different interest rate in the future.

An increase in rates, ceteris paribus, increases a banks interest income but also increases the banks interest expense.

Static GAP Analysis considers the impact of changing rates on the banks net interest income.

11. Interest Rate Risk: Price Risk

If interest rates change, the market values of assets and liabilities also change.

The longer is duration, the larger is the change in value for a given change in interest rates.

Duration GAP considers the impact of changing rates on the market value of equity.

12. Measuring Interest Rate Risk with GAP

Traditional Static GAP Analysis GAP t = RSA t -RSL t

RSA t

Rate Sensitive Assets

Those assets that will mature or reprice in a given time period (t)

RSL t

Rate Sensitive Liabilities

Those liabilities that will mature or reprice in a given time period (t)

13. What Determines Rate Sensitivity?

An asset or liability is considered rate sensitivity if during the time interval:

It matures

It represents and interim, or partial, principal payment

It can be repriced

The interest rate applied to the outstanding principal changes contractually during the interval

The outstanding principal can be repriced when some base rate of index changes and management expects the base rate / index to change during the interval

14. 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

15. Interest-Sensitive Liabilities

Borrowings from Money Markets

Short-Term Savings Accounts

Money-Market Deposits

Variable-Rate Deposits

16. Example

A bank makes a $10,000 four-year car loan to a customer at fixed rate of 8.5%. The bank initially funds the car loan with a one-year $10,000 CD at a cost of 4.5%. The banks initial spread is 4%.

What is the banks one year gap?

17. Example

Traditional Static GAP Analysis

What is the banks 1-year GAP with the auto loan?

RSA 1yr = $0

RSL 1yr = $10,000

GAP 1yr = $0 - $10,000 = -$10,000

The banks one year funding GAP is -10,000

If interest rates rise (fall) in 1 year, the banks margin will fall (rise)

18. Measuring Interest Rate Risk with GAP

Traditional Static GAP Analysis

Funding GAP

Focuses on managing net interest income in the short-run

Assumes a parallel shift in the yield curve, or that all rates change at the same time, in the same direction and by the same amount.

19. Other Gap Measurements Relative Interest-Sensitive Gap Interest Sensitivity Ratio

20. Asset-Sensitive Bank Has:

Positive Dollar Interest-Sensitive Gap

Positive Relative Interest-Sensitive Gap

Interest Sensitivity Ratio Greater Than One

21. Liability Sensitive Bank Has:

Negative Dollar Interest-Sensitive Gap

Negative Relative Interest-Sensitive Gap

Interest Sensitivity Ratio Less Than One

22. Net Interest Margin

23. Factors Affecting Net Interest Income

Changes in the level of interest rates

Changes in the composition of assets and liabilities

Changes in the volume of earning assets and interest-bearing liabilities outstanding

Changes in the relationship between the yields on earning assets and rates paid on interest-bearing liabilities

24. Example

Consider the following balance sheet:

25. Examine the impact of the following changes

A 1% increase in the level of all short-term rates?

A 1% decrease in the spread between assets yields and interest costs such that the rate on RSAs increases to 8.5% and the rate on RSLs increase to 5.5%?

Changes in the relationship between short-term asset yields and liability costs

A proportionate doubling in size of the bank?

26. 1% increase in short-term rates With a negative GAP, more liabilities than assets reprice higher; hence NII and NIM fall

27. 1% decrease in the spread NII and NIM fall (rise) with a decrease (increase) in the spread. Why the larger change?

28. Changes in the Slope of the Yield Curve

If liabilities are short-term and assets are long-term, the spread will

widen as the yield curve increases in slope

narrow when the yield curve decreases in slope and/or inverts

29. Proportionate doubling in size NII and GAP double, but NIM stays the same. What has happened to risk?

30. Changes in the Volume of Earning Assets and Interest-Bearing Liabilities

Net interest income varies directly with changes in the volume of earning assets and interest-bearing liabilities, regardless of the level of interest rates

31. RSAs increase to $540 while fixed-rate assets decrease to $310 and RSLs decrease to $560 while fixed-rate liabilities increase to $260 Although the banks GAP (and hence risk) is lower, NII is also lower.

32. Changes in Portfolio Composition and Risk

To reduce risk, a bank with a negative GAP would try to increase RSAs (variable rate loans or shorter maturities on loans and investments) and decrease RSLs (issue relatively more longer-term CDs and fewer fed funds purchased)

Changes in portfolio composition also raise or lower interest income and expense based on the type of change

33. Changes in Net Interest Income are directly proportional to the size of the GAP

If there is a parallel shift in the yield curve:

It is rare, however, when the yield curve shifts parallel

If rates do not change by the same amount and at the same time, then net interest income may change by more or less.

34. Summary of GAP and the Change in NII

Asset-Liability Management 1

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