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CHAPTER12 Introduction to Asset Liability Management. What is in this Chapter? INTRODUCTION SOURCES OF INTEREST-RATE RISK Mortgage-backed Securities (MBS). INTRODUCTION. Asset liability management (ALM)

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## CHAPTER12 Introduction to Asset Liability Management

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**CHAPTER12Introduction to Asset Liability Management**What is in this Chapter? INTRODUCTION SOURCES OF INTEREST-RATE 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) • Question: How to evaluate the size to rate sensitivity?**Duration of First National Bank's Assets and Liabilities**Duration in year (or in %) 0.4 X (5/100)**Review: Duration Analysis for Bonds**• Duration in year (or %)=duration in dollars (or $)/V (the initial value) • (Duration in dollars) x (change in interest rate)= the change of V in dollars ($) • (Duration in year) x (change in interest rate)=the change of V in percentage (%) • The change of V in dollars=(the chance of V in %) x the initial value (V)**Duration Gap Analysis**%VDURr 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/ADURl] = 2.7 [(95/100) 1.03] = 1.72 %NW = DURgapr = 1.72 .05 = .086 = 8.6% NW = .086 $100m = $8.6m**Duration Analysis**If r 5% Duration Gap Analysis DURgap = DURa [L/ADURl] = 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**INTRODUCTION**• liquidity risks • This is the challenge of ensuring that the bank has sufficient liquid assets available to meet all its required payments, including the possibility of a "run on the bank." • A run on the bank occurs when deposit customers lose confidence in a bank's creditworthiness and rush to the bank to take out their savings before the bank collapse**In most developed countries, this risk is greatly reduced by**deposit insurance backed by the government. • In the United States the Federal Deposit Insurance Company (FDIC) guarantees that retail depositors will be compensated up to $100,000 if their bank fails**INTRODUCTION**• By modeling and understanding ALM risks: • banks seek to minimize the risks and know how much to charge customers to cover the capital consumed by the risks. • Another important aspect of ALM is determining the fair, risk-minimizing interest rates that should be charged internally between the bank's business units when the lend funds to each other.**SOURCES OF INTEREST-RATE RISK**• Many banks in emerging-market countries have a large portion of their balance sheets in the form of loans denominated in U.S. dollars • Both the structural interest rate and the structural FX positions are managed in the ALM framework**The primary cause of structural interest-rate risk is:**• customers want both long-term loans and quick access to any deposits • This leaves banks in a position in which they are receiving long-term, fixed-rate interest payments from borrowers and paying short-term, floating-rate interest to depositor.**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**SOURCES OF INTEREST-RATE 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**SOURCES OF INTEREST-RATE RISK**• 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. • With options, the expectation is that every option will be exercised to maximize the advantage to the holder**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.**MAIN PRODUCT CLASSES HELD IN ALM PORTFOLIOS**• The main classes of products for asset liability management are the following: • Assets • Retail personal loans • Retail mortgages • Credit-card receivables • Commercial loans • Long-term investments • Traded bonds • Derivatives**MAIN PRODUCT CLASSES HELD IN ALM PORTFOLIOS**• Liabilities • Retail checking accounts • Retail savings accounts • Retail fixed-deposits accounts • Deposits from commercial customers • Bonds issued by the bank**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 >if r decrease, then prepayment rate? 100% PSA: in each year, 6% of the remaining borrowers are expected to prepay**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)**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 sudden drop in value occurs in the region where prepayment rates drop and the average time for the cash flows increases dramatically The non-constant prepayment rate and the prepayment rate is negatively relative with interest rate**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 >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 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**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)**• 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. • The response to changes in interest rates can have significant negative convexity; i.e., the value can rise as rates rise.

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