CHAPTER12 Introduction to Asset Liability Management

1. CHAPTER12Introduction to Asset Liability Management What is in this Chapter? INTRODUCTION SOURCES OF INTEREST-RATE RISK Mortgage-backed Securities (MBS)

2. 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.

3. 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%.

4. 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

5. 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.

6. 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?

7. Duration of First National Bank's Assets and Liabilities Duration in year (or in %) 0.4 X (5/100)

8. Review: Duration Analysis for Bonds

9. 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)

10. 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

11. Example of Finance Company

13. 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%

14. 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

15. 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

16. 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

17. 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.

18. 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

19. 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.

20. 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

21. 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

22. 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

23. 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

24. 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.

25. 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

26. 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

27. 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)

28. 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.

29. 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

30. 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:

31. 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

32. 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

33. 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

34. 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

35. 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:

36. 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

37. 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

38. Mortgage-backed Securities (MBS) >Typical values for the parameters are given in the equation above >This function is shown in Figure 12-4

39. Mortgage-backed Securities (MBS)

40. 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

41. 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!!

42. 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

43. 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:

44. 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.