Post on 30-Dec-2015
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–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)
n
1tt
t
YTM) (1
CF PriceMarket
Bank Discount Rate (DR)
Maturity toDays #
360*
FV
Price Purchase- FV DR
Where: FV equals Face Value
Yield to Maturity
Maturity toDays #
365*
Price Purchase
Price Purchase- 100 YTM
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
Assets Earnings Total
ExpensesInterest - IncomeInterest NIM
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 SizeBank
Gap ISDollar
Interest Sensitivity
Ratio sLiabilitie SensitiveInterest
Assets SensitiveInterest
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
• Asset-Sensitive Bank– Interest Rates Rise• NIM Rises
– Interest Rates Fall• NIM Falls
• Liability-Sensitive Bank– Interest Rates Rise• NIM Falls
– Interest Rates Fall• NIM Rises
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
n
1tt
t
n
1tt
t
YTM) (1CFYTM) (1CF *t
D
Price Sensitivity of a Security
27
r
rD
P
P
10
0
r
Ddr
r
dr
r
CFr
tCF
P
dP
r
dr
r
nCF
r
CF
r
CF
r
CF
PP
dP
drr
nCF
r
CF
r
CF
r
CFdP
r
CF
r
CF
r
CF
r
CFP
tt
t
ttt
nn
nn
nn
111
1
111
3
1
2
1
1
11
3
1
2
1
1111
n
1
n
1
0
0
33
22
11
00
0
143
32
21
0
33
221
0
Modified Duration
r
DDm
1
rDP
Ptherefore m
0
0,
ConvexityThe 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
n
1 iAiA i
D *w D
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
n
1iLiL i
D * w D
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
TA
TL * D - D DG LA
r
rD
A
LD
A
NW
Lr
rDA
r
rDNW
r
rD
L
Lr
rD
A
A
LA
LA
L
A
1
11
1
1
Impact of Changing Interest Rates on a Bank’s Net Worth
PositiveGap
Interest Rate Rise
NW Decrease
Interest Rate Fall NW Increase
NegativeGap
Interest Rate Rise
NW Increase
Interest Rate Fall NW Decrease
ZeroGap
Interest Rate Rise
No Change
Interest Rate Fall 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