CHAPTER 12 Introduction to Asset Liability Management What is in this Chapter? INTRODUCTION DURATION...

CHAPTER 12Introduction 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) 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 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%.

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 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 rate-

sensitive and the mortgage (one kind of banks’ assets) is rate-insensitive

The interest rate risks will rise when the RSL (rate-sensitive 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

9

Duration Gap 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

= $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

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

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


Figure 12-1a illustrates a possible scenario

Figure 12-1b shows the net interest income (NII), i.e., interest income minus interest costs


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. 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


What are the differences between the risk of the structural interest-rate position and the market risk of the trading room? 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.


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.


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 bondsThe tranches can also be split as to whether they are entitled to the interest payments only (IO) or principal payments only (PO)


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.


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


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:

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



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


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


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


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:


>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


The prepayment rate as a percentage of the PSA can be modeled as follows:

100% PSA: in each year, 6% of the remaining borrowers are expected to prepay

r is the market-refinancing rate

>if r decrease, then prepayment rate?

a, b, c and d are constant


>Typical values for the parameters are given in the equation above

>This function is shown in Figure 12-4



Constant prepayment rate: 6% in each year

The non-constant prepayment rate and the prepayment rate is negatively relative with interest rate

Figure 12-5 shows the effect of rate changes on the NPV of principal-only (PO) payments.

>The sudden drop in value occurs in the region where prepayment rates drop and the average time for the cash flows increases dramatically


>As the rate begins to increase from 6% to 8%, the value drops because of the greater discounting

>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

Once the prepayment rate stabilizes at a new low level, the discounting effect again begins to dominate

Hint: the interest rate has two effects: (1) the discounting effect (2) prepayment effect!!

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


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 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.

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CHAPTER 12 Introduction to Asset Liability Management What is in this Chapter? INTRODUCTION DURATION...

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