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.