1
Bank Asset/Liability Management
Oleg Deev
2
Contents
1. ALM gaps
2. Interest rate gap and earnings sensitivity analysis
3. Duration gap and economic value of equity analysis
4. Management of interest rate risk
Example
€ 100 million 5-year fixed-rate loans at 8% = € 8 million interest
€ 90 million 30-day time deposits at 4% = € 3.6 million interest
€10 million equity
Calculate Net interest income and Net interest margin (NIM).
Assume that interest rates rise 2% (deposit costs will rise in next year
but not loan interest). How it affects NII and NIM?
3
Example - solution
€ 100 million 5-year fixed-rate loans at 8% = € 8 million interest
€ 90 million 30-day time deposits at 4% = € 3.6 million interest
€10 million equity
Net interest income = € 4.4 million
Net interest margin (NIM) = (€ 8 - € 3.6)/ € 100 = 4.4%
If interest rates rise 2%, deposit costs will rise in next year but not loan
interest. Now, NIM = (€ 8 - € 5.4)/ € 100 = 2.6%.
Thus, NIM depends on interest rates, the amount of funds, and the
earning mix (rate x amount).
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Asset liability gaps
3Y,1Y-Floater
3Y-Fixed-rate
Bond
Capital
Maturity 3Y 3Y
Interest Rate
Maturity 1Y 3Y
1. Maturities
2. Risk:= Maturity mismatches/ gaps
Liquidity Risk
3Y-Loan,
fixed-rate
rate (3Y IR)
Yes No
Interest
Rate Risk
Yes
No
1Y-deposit,
fixed-rate rate
(1Y IR)
3Y-Loan,
fixed-rate
rate (3Y IR)
3Y-deposit,
1Y-floating
(1Y IR)
3Y-Loan,
1Y-floating
(1Y IR)
1Y-deposit,
fixed-rate
rate (1Y IR)
3Y-Loan,
fixed-rate
rate (3Y IR)
3Y-deposit,
fixed-rate
rate (3Y IR)
Liquidity-risk (gap):
Mismatch in
capital-maturity
Interest rate-risk (gap):
Mismatch in
interest rate maturity
1 2
3 4
2 dimensions
=> 4 possible mismatch
cases between Assets
and Liabilities
5
Liquidity risk/ mismatch
Interest rate risk/ mismatch Interest rate risk/ mismatch
No No Yes Yes
No Yes No Yes
Asset liability gaps
Liquidity risk/ mismatch
No Yes
3Y 3YLoan capital maturity
3Y 1YFunding capital mat’y
0.75% 0.75%Loan, Ly premium
0.75% 0.25%Funding, Ly premium
0 0.50%Liquidity return
Interest rate risk/ mismatch Interest rate risk/ mismatch
No Yes No Yes
Loan IR maturity 3Y 3Y 1Y 3Y
Funding IR mat’y 3Y 1Y 1Y 1Y
Loan, risk-free IR 1.50% 1.50% 0.50% 1.50%
Funding, risk-free IR 1.50% 0.50% 0.50% 0.50%
IR return 0 1.00% 0 1.00%
Liquidity return
IR return 0 1.00% 0 1.00%
0 0 0.50% 0.50%
Conclusion:
Risk <=>
Return
6
Managing Interest Rate Risk:
GAP and Earnings Sensitivity
Banks use two basic models to assess interest rate risk.
– Interest rate gap and earnings sensitivity analysis emphasizes income
statement effects by focusing on how changes in interest rates and the bank’s
balance sheet effect net interest income and net income.
– Duration gap and economic value of equity analysis emphasizes the market
value of stockholders’ equity by focusing on how these same changes affect the
market value of assets vs. the market value of liabilities.
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ALM
Interest rate risk Liquidity risk
• Plot volumes
with their
interest rate
maturity
• Plot volumes
with their
liquidity
maturity
• Plot net
position
(= uncovered
position)
• Plots cash
flows
(= Δ-view of
volume
ladder/
previous plot)
• Plots IRsensitivity
in
each bucket
• Plots funding
needs
(=uncovered/
unfunded
assets)
Liquidity gaps
Cumulative gap
IR-gaps
Loan, 6.00%
3Y, 0.5Y
Loan, 7.00%
10Y, 10Y
Funding, 6.00%
0.5Y, 0.5Y
Funding, 6.50%
4Y, 4Y
400
200
300
300
Assets Liabilities
8
ALM
Assets Liabilities
Bond, 6.00%
3Y, 0.5Y
Loan, 7.00%
10Y, 10Y
Funding, 6.00%
0.5Y, 0.5Y
Funding, 6.50%
4Y, 4Y
400
200
300
300
• Plot volumes
with their
interest rate
maturity
• Bond enters
with its
“liquidation
horizon”, not
with its legal
maturity
• Plot net
position
(= uncovered
position)
• Partially
counter-
balances/
nets outflow of
6M-funding
(-400, 6M)
• Plots IRsensitivity
in
each bucket
• Open/
uncovered
funding
position is
reduced
• Replacing the loan by a bond that can be sold
within 6M => Ly maturity: 6M.
• IR-profile: unchanged, Ly risk: reduced.
Interest rate risk Liquidity risk
Liquidity gaps
Cumulative gap
IR-gaps
9
Interest rate gap
10
The IR-gap directly translates into a change in Net Interest Income:
IR-Gap = Air – Lir (Volume of interest rate-sensitive assets and liabilities)
ΔNII = Gapcum * Δr = (Air – Lir ) * Δr (Δr : interest rate reelvant for valuation)
Loan, 6.00%
3Y, 0.5Y
Loan, 7.00%
10Y, 10Y
Funding, 6.00%
0.5Y, 0.5Y
Funding, 6.50%
4Y, 4Y
400
200
300
300
Assets Liabilities
• Positively gapped
• NII increases in rising interest rates because new
funding at roll-over dates (100 at t=0.5, 300 at
t=4) becomes more expensive.
• NII grows in decreasing rate environment
Traditional interest rate gap analysis
Steps in IR-gap Analysis:
1. Develop an interest rate forecast.
2. Select a series of sequential time intervals for determining what
amounts of assets and liabilities are rate sensitive within each
time interval.
3. Group assets and liabilities into these time intervals or
“buckets” according to time to first repricing.
4. Calculate IR-gap.
5. Forecast net interest income given the assumed interest rate
environment and repricing characteristics of the underlying
instruments.
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Interest rate gap analysis
12
0.5 0.5 1 3 ∞
Total [ON, 6M] (6M, 12M] (1Y, 2Y] (2Y, 5] (5Y, ∞]
Assets Mortgages, fixed rate 125.00 10.00 10.00 25.00 40.00 40.00
Mortgages, floating rate 100.00 50.00 50.00
Interbank demand deposits 75.00 75.00
Sovereign bonds 60.00 30.00 0.00 30.00
Cash 20.00 20.00
Non-earnings assets 20.00 20.00
Total assets 400.00 135.00 60.00 55.00 40.00 110.00
Liabilities Term deposits -200.00 -50.00 -100.00 -50.00
Retail Demand deposits -125.00 -125.00
Interbank demand deposits -25.00 -25.00
Non-interest bearing liabilities -10.00 -10.00
Capital -40.00 -40.00
Total Liabilities -400.00 -200.00 -100.00 -50.00 0.00 -50.00
Swap Receive [fix] 200.00 100.00 100.00
Pay [floating] -200.00 -200.00
Periodic gap -265.00 -40.00 105.00 140.00 60.00
Cumulative gap -265.00 -305.00 -200.00 -60.00 0.00
Δ r 1.00%
Δ NII per bucket -1.33 -1.53 -2.00 -1.80
Δ NII per bucket p.a. -2.65 -3.05 -2.00 -0.60
(1) Fixed rate volumes, Receive 465.00 405.00 250.00 110.00 0.00
(2) Fixed rate volumes, Pay -200.00 -100.00 -50.00 -50.00 0.00
(1) + (2) = CumGap 265.00 305.00 200.00 60.00 0.00
Δ NII per bucket -1.33 -1.53 -2.00 -1.80
Δ NII per bucket p.a. -2.65 -3.05 -2.00 -0.60
=(400-135)+(200-0) =465-60-0 =250-40-100
*(-1)
Interest rate gap analysis
13
0.5 0.5 1 3 ∞
Total [ON, 6M] (6M, 12M] (1Y, 2Y] (2Y, 5] (5Y, ∞]
Assets Mortgages, fixed rate 125.00 10.00 10.00 25.00 40.00 40.00
Mortgages, floating rate 100.00 50.00 50.00
Interbank demand deposits 75.00 75.00
Sovereign bonds 60.00 30.00 0.00 30.00
Cash 20.00 20.00
Non-earnings assets 20.00 20.00
Total assets 400.00 135.00 60.00 55.00 40.00 110.00
Liabilities Term deposits -200.00 -50.00 -100.00 -50.00
Retail Demand deposits -125.00 -125.00
Interbank demand deposits -25.00 -25.00
Non-interest bearing liabilities -10.00 -10.00
Capital -40.00 -40.00
Total Liabilities -400.00 -200.00 -100.00 -50.00 0.00 -50.00
Swap Receive [fix] 200.00 100.00 100.00
Pay [floating] -200.00 -200.00
Periodic gap -265.00 -40.00 105.00 140.00 60.00
Cumulative gap -265.00 -305.00 -200.00 -60.00 0.00
Δ r 1.00%
Δ NII per bucket -1.33 -1.53 -2.00 -1.80
Δ NII per bucket p.a. -2.65 -3.05 -2.00 -0.60
(1) Fixed rate volumes, Receive 465.00 405.00 250.00 110.00 0.00
(2) Fixed rate volumes, Pay -200.00 -100.00 -50.00 -50.00 0.00
(1) + (2) = CumGap 265.00 305.00 200.00 60.00 0.00
Δ NII per bucket -1.33 -1.53 -2.00 -1.80
Δ NII per bucket p.a. -2.65 -3.05 -2.00 -0.60
Retail Demand deposits -125.00 -125.00
Interbank demand deposits -25.00 -25.00
Non-interest bearing liabilities -10.00 -10.00
Capital -40.00 -40.00
Total Liabilities -400.00 -200.00 -100.00 -50.00 0.00 -50.00
Swap Receive [fix] 200.00 100.00 100.00
Pay [floating] -200.00 -200.00
Periodic gap -265.00 -40.00 105.00 140.00 60.00
Cumulative gap -265.00 -305.00 -200.00 -60.00 0.00
Δ r 1.00%
Δ NII per bucket -1.33 -1.53 -2.00 -1.80
Δ NII per bucket p.a. -2.65 -3.05 -2.00 -0.60
(1) Fixed rate volumes, Receive 465.00 405.00 250.00 110.00 0.00
(2) Fixed rate volumes, Pay -200.00 -100.00 -50.00 -50.00 0.00
(1) + (2) = CumGap 265.00 305.00 200.00 60.00 0.00
Δ NII per bucket -1.33 -1.53 -2.00 -1.80
Δ NII per bucket p.a. -2.65 -3.05 -2.00 -0.60
Change in Income in
[0,1Y]
-3.00% 8.55
-2.00% 5.70
-1.00% 2.85
0.00% 0.00
1.00% -2.85
2.00% -5.70
3.00% -8.55
1%
Interest rate gap analysis
14
oday's volume: Elasticity parameter
125 -10% Mortgages, fixed rate
75 -5% Interbank demand deposits
Assets Δ r Position Total [ON, 6M] (6M, 12M] (1Y, 2Y] (2Y, 5] (5Y, ∞]
-2.00% Mortgages, fixed rate 140.75 11.26 11.26 28.15 45.04 45.04
-2.00% Interbank demand deposits 82.50 82.50 0.00 0.00 0.00 0.00
-1.00% Mortgages, fixed rate 137.50 11.00 11.00 27.50 44.00 44.00
-1.00% Interbank demand deposits 80.95 80.95 0.00 0.00 0.00 0.00
1.00% Mortgages, fixed rate 112.50 9.00 9.00 22.50 36.00 36.00
1.00% Interbank demand deposits 69.05 69.05 0.00 0.00 0.00 0.00
2.00% Mortgages, fixed rate 109.25 8.74 8.74 21.85 34.96 34.96
2.00% Interbank demand deposits 67.50 67.50 0.00 0.00 0.00 0.00
All other assets 225.00 10.00 10.00 55.00 40.00 110.00
-25 Interbank demand deposits
-125 15% Retail Demand deposits
Liabilities Δ r Position Total [ON, 6M] (6M, 12M] (1Y, 2Y] (2Y, 5] (5Y, ∞]
-2.00% Retail Demand deposits -106.97 -106.97 0.00 0.00 0.00 0.00
-2.00% Interbank demand deposits -66.28 -66.28 0.00 0.00 0.00 0.00
-1.00% Retail Demand deposits -110.69 -110.69 0.00 0.00 0.00 0.00
-1.00% Interbank demand deposits -57.76 -57.76 0.00 0.00 0.00 0.00
1.00% Retail Demand deposits -139.31 -139.31 0.00 0.00 0.00 0.00
1.00% Interbank demand deposits 7.76 7.76 0.00 0.00 0.00 0.00
2.00% Retail Demand deposits -143.03 -143.03 0.00 0.00 0.00 0.00
2.00% Interbank demand deposits 16.28 16.28 0.00 0.00 0.00 0.00
All other liabilities -250.00 -50.00 -100.00 -50.00 0.00 -50.00
Swap Receive [fix] 200.00 0.00 0.00 100.00 100.00 0.00
Pay [floating] -200.00 -200.00 0.00 0.00 0.00 0.00
0.5 0.5 1 3 ∞
Δ r Position [ON, 6M] (6M, 12M] (1Y, 2Y] (2Y, 5] (5Y, ∞]
-2.00% Periodic gap -319.49 -78.74 133.15 185.04
-2.00% Cumulative gap -319.49 -398.23 -265.08 -80.04
-2.00% Δ NII per bucket 3.19 3.98 5.30 4.80
-1.00% Periodic gap -316.50 -79.00 132.50 184.00
-1.00% Cumulative gap -316.50 -79.00 132.50 184.00
-1.00% Δ NII per bucket 1.58 0.40 -1.33 -5.52
1.00% Periodic gap -293.50 -81.00 127.50 176.00
1.00% Cumulative gap -293.50 -81.00 127.50 176.00
1.00% Δ NII per bucket -1.47 -0.41 1.28 5.28
2.00% Periodic gap -290.51 -81.26 126.85 174.96
2.00% Cumulative gap -290.51 -81.26 126.85 174.96
2.00% Δ NII per bucket -2.91 -0.81 2.54 10.50
Interest rate gap analysis
15
With position changes
Without position
changes
-2.00% 7.18 5.7
-1.00% 1.98 2.85
1.00% 1.87- -2.85
2.00% 3.72- -5.7
Δ Income in next year
Interest rate sensitivity and
the interest rate (dollar) gap
Defensive versus aggressive asset/liability management:
– Defensively guard against changes in NII (e.g., near zero gap).
– Aggressively seek to increase NII in conjunction with interest rate
forecasts (e.g., positive or negative gaps).
– Many times some gaps are driven by market demands (e.g.,
borrowers want long-term loans and depositors want short-term
maturities).
Managing the Interest Rate Gap and
Earnings Sensitivity Risk
17
Simplified example
18
19
20
Strengths and Weaknesses
of Static Gap Analysis
¾ Strengths:
– Easy to understand.
– Indicates relevant amount and timing of interest rate risk.
– Suggests magnitudes of portfolio changes to alter risk.
¾ Weaknesses:
– Ex-post measurement errors.
– Ignores the time value of money.
– Ignores the cumulative impact of interest rate changes.
– Considers demand deposits to be non-rate sensitive.
– Ignores embedded options in assets and liabilities.
¾ IR-gap Divided by Earning Assets as a Measure of Risk:
– An alternative risk measure that relates the absolute value of a bank’s
gap to earning assets.
– The greater this ratio, the greater the interest rate risk.
– Banks may specify a target gap-to-earning-asset ratio in their ALCO
policy statements.
– A target allows management to position the bank to be either asset
sensitive or liability sensitive, depending on the outlook for interest
rates.
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Earnings Sensitivity Analysis
¾ Extends static gap analysis by making it dynamic.
– Model simulation or what-if analysis of all factors that affect net interest income
across a wide range of potential interest rate environments.
¾ Steps to Earnings Sensitivity Analysis:
1. Forecast interest rates.
2. Forecast balance sheet size and composition given the assumed interest rate
environment.
3. Forecast when embedded options in assets and liabilities will be in money and
hence, exercised under the assumed interest rate environment.
4. Identify when specific assets and liabilities will reprice given the rate
environment.
5. Estimate net interest income and net income under the assumed rate
environment.
6. Repeat the process to compare forecasts of net interest income and net
income across different interest rate environments versus the base case.
The choice of base case is important because all estimated changes in earnings are
compared with the base case estimate.
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Duration gap analysis
How do changes in interest rates affect asset, liability, and
equity values?
In general, DV = -D x V x [Di/(1 + i)]
For assets: DA = -D x A x [Di/(1 + i)]
For liabilities: DL = -D x L x [Di/(1 + i)]
Change in equity value is: DE = DA - DL
DGAP (duration gap) = DA - W DL, where DA is the average duration of
assets, DL is the average duration of liabilities, and W is the ratio of total
liabilities to total assets.
DGAP can be positive, negative, or zero.
The change in net worth or equity value (or DE) here is different from the
market value of a bank’s stock (which is based on future expectations of
dividends). This new value is based on changes in the market values of
assets and liabilities on the bank’s balance sheet.
Duration gap analysis
EXAMPLE: Balance Sheet Duration
Assets € Duration (yrs) Liabilities € Duration (yrs)
Cash 100 0 CD, 1 year 600 1.0
Business loans 400 1.25 CD, 5 year 300 5.0
Total liabilities 900 2.33
Mortgage loans 500 7.0 Equity 100
€1,000 4.0 €1,000
DGAP = 4.0 - (.9)(2.33) = 1.90 years
Suppose interest rates increase from 11% to 12%. Now,
% DE = (-1.90)(0.01/1.11) = -1.7%.
€ DE = -1.7% x total assets = 1.7% x $1,000 = - €17.
Alternatively, the change in asset values = -4 x €1000 x 0.01/1.11 = - €36.04
and the change in the value of liabilities = -2.33 x €900 x 0.01/1.11 = - €18.89
such that DE = DA - DL = - €36.04 + €18.89 = - €17.14
Duration gap analysis
¾ Defensive and aggressive duration gap management:
– If you assume interest rates will decrease in the future, a positive
duration gap is desirable - as rates decline, asset values will
increase more than liability values increase (a positive equity effect).
– If you predict an increase in interest rates, a negative duration gap is
desirable -- as rates rise, asset values will decline less than the
decline in liability values (a positive equity effect).
– Of course, zero gap protects equity from the valuation effects of
interest rate changes -- defensive management.
– Aggressive management adjusts duration gap in anticipation of
interest rate movements.
Duration gap analysis
0: Given is the following balance sheet:
Rate
Markt
value Assets Liabilities
Markt
value Rate
100.0 Cash Term deposit, 1Y 620.0 5.00%
12.00% 700.0 Commercial loan, 3Y
Senior unsecured
corporate bond issue, 3Y 300.0 7.00%
8.00% 200.0 Treasury bond, 6Y Equity 80.0
1000 Σ Σ 1000
Position Coupon 0 1 2 3 4 5 6
Cash 100.0
3y-commercial loan 12% 700.0 84.0 84.0 784.0 0.0 0.0 0.0
Treasury bond, 6Y 8% 200.0 16.0 16.0 16.0 16.0 16.0 216.0
Term deposit, 1Y 5% 620.0 651.0
Senior unsecured corporate bond issue, 3Y7% 300.0 21.0 21.0 321.0
Cash flows x Time buckets
1: Compute the duration of the positions:
Position 0 1 2 3 4 5 6 yield NPV(yield)
Mod
Duration [y] PV
Cash -100.0 100.0 0.00 0.00 100.0
3y-commercial loan -700.0 75.0 67.0 558.0 0.0 0.0 0.0 12.00% 0.00 2.69 700.0
Treasury bond, 6Y -200.0 14.8 13.7 12.7 11.8 10.9 136.1 8.00% 0.00 4.99 200.0
Term deposit, 1Y -620.0 620.0 0.0 0.0 0.0 0.0 0.0 5.00% 0.00 1.00 620.0
Senior unsecured corporate bond issue, 3Y-300.0 19.6 18.3 262.0 0.0 0.0 0.0 7.00% 0.00 2.81 300.0
Present values x Time buckets
Note that all instruments
are at par.
Duration gap analysis
2: Compute the duration gap:
Weighted duration of assets: 2.88 years
Weighted duration of liabilities: 1.59 years
Duration gap (DGAP): 1.42 years
.
.
Liabs
Assets
Liab
Assets
D
MV
MV
DDGAP ×-=
ance sheet:
Rate
Markt
value Assets Liabilities
Markt
value Rate
100.0 Cash Term deposit, 1Y 620.0 5.00%
12.00% 700.0 Commercial loan, 3Y
Senior unsecured
corporate bond issue, 3Y 300.0 7.00%
8.00% 200.0 Treasury bond, 6Y Equity 80.0
1000 Σ Σ 1000
Duration gap analysis
3: Compute the change in EVE (i) analytically and (ii) approximated with DGAP:
(i) Analytically:
IR-shift: 1%
No Position Coupon 0 1 2 3 4 5 6 yield NPV(yield) New PV
Cash -100.0 100.0 100.0
3y-commercial loan 12% -700.0 74.3 65.8 543.4 0.0 0.0 0.0 12.00% -16.53 683.5
Treasury bond, 6Y 8% -200.0 14.7 13.5 12.4 11.3 10.4 128.8 8.00% -8.97 191.0
Term deposit, 1Y 5% -620.0 614.2 0.0 0.0 0.0 0.0 0.0 5.00% -5.85 614.2
Senior unsecured corporate bond issue, 3Y7% -300.0 19.4 18.0 254.8 0.0 0.0 0.0 7.00% -7.73 292.3
Economic Value of Equity (EVE)
Present values x Time buckets
(i) Analytically: Rate
Markt
value Assets Liabilities
Markt
value Rate
100.00 Cash Term deposit, 1Y 614.15 5.00%
12.00% 683.47 Commercial loan, 3Y
Senior unsecured
corporate bond issue, 3Y 292.27 7.00%
8.00% 191.03 Treasury bond, 6Y Equity 68.08
974.50 Σ Σ 974.50
Change in equity value: -11.92
(ii) Approximated with DGAP:
Duration gap: 1.419
Average yield on total assets: 10.00%
Yield shift: 1.00%
Change in equity value: -12.902 ≈ -11.92
Assets
Assets
MV
y
y
DGAPEVE
)1( +
D
×-@D
An Immunized Portfolio
Objective: Reduce Interest Rate Risk with DGAP > 0:
– Shorten asset durations by:
• Buying short-term securities and selling long-term securities.
• Making floating-rate loans and selling fixed-rate loans.
– Lengthen liability durations by:
• Issuing longer-term CDs.
• Obtaining more core transactions accounts from stable sources.
– Lengthen asset durations by:
• Buying long-term securities and selling short-term securities.
• Buying securities without call options.
• Making fixed rate loans and selling floating-rate loans.
– Shorten liability durations by:
• Issuing shorter-term CDs.
• Using short-term purchased liability funding from federal funds and
repurchase agreements.
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30
Strengths and Weaknesses:
DGAP and EVE Sensitivity Analysis
¾ Strengths:
– Duration analysis provides a comprehensive measure of interest rate risk for
the total portfolio.
– Duration measures are additive so that total assets may be matched with total
liabilities rather than matching of individual accounts.
– Duration analysis takes a longer-term view and provides managers with
greater flexibility in adjusting rate sensitivity because they can use a wide
range of instruments to balance value sensitivity.
¾ Weaknesses:
– It is difficult to compute duration accurately.
– “Correct” duration analysis requires that each future cash flow be discounted
by a distinct discount rate.
– A bank must continuously monitor and adjust the duration of its portfolio.
– It is difficult to estimate the duration on assets and liabilities that do not earn or
pay interest.
– Duration measures are highly subjective.
31
32
Literature
̶ CHOUDRY M. (2022). The Principles of Banking, 2nd ed. – Chapter 5.
̶ KOCH, T.W. and S.S. MacDONALD (2015). Bank Management.
Chapter 7-8.