CHAPTER 12
Introduction to Asset Liability Management
What is in this Chapter?
INTRODUCTION
DURATION GAP
SOURCES OF INTEREST-RATE
RISK
ALM RISK versus MARKET RISK
Mortgage-backed Securities (MBS)
INTRODUCTION
Asset liability management (ALM)
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interest rate risk: The interest-rate risk arises from the
possibility that profits will change if interest rates
change.
liquidity risk: The liquidity risk arises from the
possibility of losses due in the bank having insufficient
cash on hand to pay customers.
Both risks are due to the difference between the bank's
assets and liabilities.
INTRODUCTION
The best illustration of ALM : U.S. savings and
loan (S&L) crisis
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Savings and loan banks: retail banks, receive retail
deposits and make retail loans
For many years, interest rates stable. Deposits for
around 4% (floating rate), and they lent 30-year
mortgages paying about 8% at fixed rates.
Then in the 1980s, the Federal Reserve allowed interest
rates to float. Short-term interest rates rose to 16%.
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Many deposit customers withdrew their funds or
demanded the higher rates
The rate of mortgages is fixed with 8%, however the
rate of deposits is floating and the banks have to pay
16% to deposit customers
This causes the banks a lot of loss and go to bankrupt
INTRODUCTION
Several keys of the above example
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The rate of deposit is floating and the rate of mortgage
is fixed
The deposit (loan) is more (less) sensitive to interest
rate
Or, the deposits (one kind of banks’ liabilities) is ratesensitive and the mortgage (one kind of banks’ assets)
is rate-insensitive
The interest rate risks will rise when the RSL (ratesensitive liabilities) is not equal to RSA (rate-sensitive
assets)
Duration of
First National
Bank's
Assets and
Liabilities
Duration in year
(or in %)
0.4 X (5/100)
Review: Duration Analysis
%V  DUR  r
r  5%, from 10% to 15% 
Asset Value
= %P  Assets
= 2.7  .05  $100m
= $13.5m
Liability Value = %P  Liabilities
= 1.03  .05  $95m
Duration Gap
Analysis
= $4.9m
NW = $13.5m  ($4.9m) = $8.6m
DURgap = DURa  [L/A  DURl]
= 2.7  [(95/100)  1.03]
= 1.72
%NW = DURgap  r
= 1.72  .05
= .086 = 8.6%
NW = .086  $100m
= $8.6m
9
Example of Finance Company
Duration Analysis
If r  5%
Duration Gap Analysis
DURgap =
DURa  [L/A  DURl]
=
1.16  [90/100  2.77] = 1.33 years
% NW =
DURgap X r
=
(1.33)  .05
=
.0665 = 6.5%
Managing Interest-Rate Risk
Strategies for Managing Interest-Rate Risk

In example above, shorten duration of bank assets or
lengthen duration of bank liabilities
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To completely immunize net worth from interest-rate
risk, set DURgap = 0
Reduce DURa = 0.98  DURgap = 0.98  [(95/100)  1.03] = 0
Raise DURl = 2.80  DURgap = 2.7  [(95/100)  2.80] = 0
SOURCES OF INTEREST-RATE RISK
Figure 12-1a illustrates a
possible scenario
Figure 12-1b shows the net interest
income (NII), i.e., interest income
minus interest costs
SOURCES OF INTEREST-RATE RISK
Figure 12-1c:
noninterest expenses
are partially floating
Figure 12-1d : the result is the
net earnings for the bank
ALM Risk vs. Market Risk
The measurement of ALM risks is made more
difficult than the management of a simple bond
portfolio.
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because of the indeterminate maturities of assets and
liabilities.
The indeterminate maturity describes the uncertainty as
to when customers will make or ask for payments
We will discuss the above behaviors in detail in the
following discussion
Uncertain prepayment and withdraw behaviors
ALM Risk vs. Market Risk
What are the differences between the risk of the
structural interest-rate position and the market risk
of the trading room?
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In the trading room, all transactions are clearly
structured. With bonds, the maturity is known, and the
term is fixed by the contract underlying the security.
ALM Risk vs. Market Risk
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In contrast, ALM products such as mortgages and
deposits have many implicit or embedded options that
make the values dependent not only on market rates,
but also on customer behavior.
For example, customers have the option to withdraw
their deposit accounts whenever they wish, or to prepay
a mortgage early if they find a cheaper mortgage
elsewhere.
Mortgage-backed Securities (MBS)
In the United States, there is a large market of
traded mortgage-backed securities (MBS)不動產
抵押貸款債券
In an MBS, the payments from many mortgages
are pooled together.
This pool of payments is then used to guarantee
payments on several tranches of bonds
The tranches can also be split as to whether they
are entitled to the interest payments only (IO) or
principal payments only (PO)
Mortgage-backed Securities (MBS)
The value of a tranche principal payments
increases when prepayments increase because the
cash flows happen sooner
Tranches entitled to interest payments drop
significantly in value when prepayments occur
because the interest-payment stream stops
The valuation of payment streams therefore
depends heavily on customer behavior.
Mortgage-backed Securities (MBS)
The Public Securities Association (PSA) has published a
standard for the expected conditional prepayment rate
(CPR)固定提前清償率
It says that 0% are expected to prepay in the first month,
rising linearly to 6% per annum at month 30
Thereafter, each year 6% of the remaining borrowers are
expected to prepay
An MBS with a prepayment rate matching this profile is
said to be at 100% PSA. An MBS with twice the
prepayment rate would be at 200% PSA
Mortgage-backed Securities (MBS)
A term related to CPR is the SMM (single
monthly mortality rate)
This is the percentage of the remaining poll that
prepays each month
The CPR and SMM are simply related:
Mortgage-backed Securities (MBS)
Figure 12-2 shows
the amount of
principal
outstanding on a
20-year, 8%
mortgage,
assuming that the
installments are
equal and there is
no prepaymen
Mortgage-backed Securities (MBS)
Figure 12-3 shows
the same
mortgage but with
prepayments at
100% PSA
>100% PSA: in
each year, 6% of
the remaining
borrowers are
expected to
prepay
With prepayment, the
stream of interest
payment is reduced
With prepayment, the principle payment
will increase first and drop in the last
Mortgage-backed Securities (MBS)
Table 12-1 shows
the NPV of the
principal and
interest payments
for different speeds
of prepayment
> Notice that as the
PSA increases, the
value of the
principal payments
increases, and the
value of the interest
payments decreases
Mortgage-backed Securities (MBS)
The PSA standard is a very simple model. The
main simplification is that in reality, the
prepayment rate is strongly affected by changes in
interest rates.
When market rates drop, new mortgages have
lower interest payments, and homeowners are
tempted to refinance their homes by taking out a
new mortgage and prepaying the old one
In other words, the prepayment is not a constant
and is related with interest rate
Mortgage-backed Securities (MBS)
The value of the option to prepay is the difference in
the NPV of the two alternative sets of interest
payments, minus the strike price
The strike price includes any prepayment penalties
and the plain hassle involved in refinancing
A typical prepayment function can be approximated
as a logistic function:
Mortgage-backed Securities (MBS)
>The value equals one when x equals negative
infinity and equal to zero when x equals positive
infinity
>the function has the shape of S curve between one
and zero
Mortgage-backed Securities (MBS)
The prepayment rate as a percentage of the PSA
can be modeled as follows:
a, b, c and d are
constant
r is the market-refinancing
rate
100% PSA: in each year, 6% of
the remaining borrowers are
expected to prepay
>if r decrease, then
prepayment rate?
Mortgage-backed Securities (MBS)
>Typical values for the parameters are given in the equation
above
>This function is shown in Figure 12-4
Mortgage-backed Securities (MBS)
Mortgage-backed Securities (MBS)
Constant prepayment rate: 6% in each year
Figure 12-5 shows the
effect of rate changes
on the NPV of
principal-only (PO)
payments.
The non-constant prepayment rate and the
prepayment rate is negatively relative with interest
rate
>The sudden drop in
value occurs in the
region where
prepayment rates drop
and the average time
for the cash flows
increases dramatically
Mortgage-backed Securities (MBS)
Once the prepayment rate stabilizes at a new low level, the
discounting effect again begins to dominate
>As the rate begins to
increase from 6% to 8%,
the value drops because of
the greater discounting
Hint: the interest rate has two effects: (1) the
discounting effect (2) prepayment effect!!
>From 8% to 10% as rates
increase, so does the value
of the security. This is
because there are
significantly fewer
prepayments of principal,
and therefore more interest
payments
MAIN PRODUCT CLASSES HELD IN
ALM PORTFOLlOS
The example above shows that the change in value
of an MBS can be a complex function of interest
rates
In reality, the value of an MBS is even more
complex because customer payments are also path
dependent
They are path dependent because the prepayment
rates depend not only on the current market rate,
but also on the previous rates
Mortgage-backed Securities (MBS)
If rates have previously been low, most of the
financially sophisticated borrowers will have
already prepaid, and a renewed drop in rates will
not cause a significant increase in prepayments
The accurate valuation of mortgage-backed
securities is highly complex and the subject of
many trading models, but the key points to be
aware of are as follows:
Mortgage-backed Securities (MBS)
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Mortgage-backed securities can be structured to have
values that are very complex functions of interest rates.
The value of an MBS is greatly dependent on the
prepayment rate.
The prepayment rate is a complex function of interest
rates.