In the previous chapters, we discussed the measurement and management of market risks for trading operations. Here, we discuss the market and liquidity risks associated with the rest of the bank’s balance sheet, including commercial loans, mortgages, and customer deposits. The management of this part of the balance sheet is called asset liability management (ALM). There are two primary risks associated with ALM: interest-rate and liquidity risk. The interest-rate risk arises from the possibility that profits will change if interest rates change. The liquidity risk arises from the possibility of losses due to the bank having insufficient cash on hand to pay customers. Both risks are due to the difference between the bank’s assets and liabilities.
Asset liability management deals with the management of the market risks that arise from a bank’s structural position. The structural position is primarily created by the bank’s intermediation between depositors and borrowers. The deposits are checking accounts, savings accounts, and fixed deposits. The loans to borrowers are commercial loans, personal loans, car loans, credit-card debt, home-improvement loans, and mortgages. Asset liability management is most important for universal or retail banks and less important for trading or investment banks.
Asset liability management is distinct from the management of market risk in trading operations because ALM positions are relatively illiquid. After origination, the assets and liabilities are typically held by the bank until they mature, although it is becoming increasingly common to bundle banking products such as loans into securities and sell or trade them with other banks. This is especially true of mortgage-backed securities (MBS). Mortgage-backed securities fall in the gray area between trading and ALM, and depending on the bank, they may be held either in the trading book or the ALM book. The rule of thumb is that positions that are commonly liquidated within a month are treated as traded instruments with the risk measured in the trading-VaR framework. Positions that cannot be quickly liquidated, and any associated hedge instruments, are treated in the ALM framework.
It is not crucially important whether an instrument is measured in the trading-VaR or ALM frameworks, so long as the risks are well monitored somewhere. Whereas trading VaR has a one-day horizon, ALM risks are typically managed on a monthly basis with a large amount of consideration being given to long-term trends and customer behavior.
The best illustration of ALM risks is given by the U.S. savings and loan (S&L) crisis. Savings and loan banks are local banks that are mandated to take in retail deposits and make retail loans. For many years, the Federal Reserve kept interest rates stable, and the S&Ls had a stable business. They took in deposits for which they paid around 4%, and they lent 30-year mortgages paying about 8% at fixed rates. This gave a 4% profit before noninterest expenses. 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 new higher rates. The S&Ls were then locked into receiving 8% from the longterm, fixed-rate mortgages and paying 16% to the short-term, floating-rate deposits. This caused many S&Ls to go bankrupt. The crisis could have been avoided if the S&Ls had practiced better asset liability management and not exposed themselves so badly to this risk.
In addition to interest-rate risks, asset liability management also includes the management of the funding 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 collapses. This panic can be self-fulfilling, and if the bank does not have enough liquid assets available, it may not be able to meet the demand for cash, even though the total value of assets may be much higher than the value of liabilities. In most developed countries, this risk is greatly reduced by deposit insurance backed by the government. For example, 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. This reduces the incentive to panic.
A liquidity crunch can also occur if the bank has had a heavy reliance on short-term, interbank loans and the lending banks lose confidence in their creditworthiness. This was the situation faced by many of the Asian banks and companies in the crisis of 1997.
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 they lend funds to each other. This helps the bank to minimize the risk within each unit and measure its profitability. This aspect of ALM is called funds transfer pricing.
With this basic understanding of interest-rate and liquidity risk, the ALM chapters are organized as follows:
• A discussion of the sources of interest-rate risks
• A discussion of the risk characteristics of ALM instruments, such as mortgages and checking accounts
• Measurement of ALM interest-rate risk at the bank level
• Measurement of ALM funding-liquidity risk at the bank level
• Allocation of ALM risks to business units through transfer pricing
• Organization of ALM risk management
The remainder of this chapter discusses the sources of interest-rate risk and the characteristics of ALM instruments.
Asset liability management oversees the management of the long-term, structural interest-rate position. All other market risks are typically managed by the trading room. However some banks also have large, structural foreign-exchange positions that cannot be quickly changed. For example, many banks in emerging-market countries have a large portion of their balance sheets in the form of loans denominated in U.S. dollars. In such cases, both the structural interest rate and the structural FX positions are managed in the ALM framework. The discussion below will focus on interest rates. FX positions can be treated using a combination of the techniques discussed in this chapter and the VaR chapter.
The primary cause of structural interest-rate risk is that customers want both longterm loans and quick access to any deposits that they have made. Furthermore customers like to have certainty in the interest payments that they will be required to make and therefore ask for fixed-rate loans. 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 depositors. A simple model for this situation is that the bank is long a series of long-term, fixed-rate bonds and short a series of floating-rate bonds. Figure 12-1a illustrates a possible scenario. The upper arrows represent the fixed-rate payments into the bank, and the lower arrows represent the floating-rate payments made by the bank. Figure 12-1b shows the net interest income (NII), i.e., interest income minus interest costs. From this net income, we can also deduct noninterest expenses (NIE or NIX), such as staff costs. Noninterest expenses are partially floating (Figure 12-1c). The result is the net earnings for the bank (Figure 12-1d) and shows that risk arises from the mismatch between the interest-rate characteristics of the assets and liabilities.
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. Therefore, the risk of the structural interest-rate position is generally more difficult to measure than 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.
FIGURE 12-1a Illustration of Payment Volatility
FIGURE 12-1b Illustration of Volatility in Net Interest Income
FIGURE 12-1c Illustration of Volatility in Noninterest Expenses
FIGURE 12-1d Illustration of Volatility in Net Earnings
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.
Another feature of retail products is that customers pay rates that are not tightly linked to market rates. Retail customers typically have interest payments that are a fixed percentage above or below prime. Prime is the rate that the bank advertises for its retail customers, and is not directly determined by the market. Therefore, it is called an administered rate. Prime is typically held constant for several months and is only changed when there has been a significant change in the market rates. Optimally hedging a portfolio of prime-paying assets is one of the great challenges of ALM, as there will always be a difference between the yield from prime-based assets and the yield on market-based assets. This difference is called basis risk. It is the risk that arises from having assets and liabilities that reprice on a different basis.
In this section, we review the characteristics of the main product classes that make up the portfolio to be managed by the asset liability manager. This facilitates the later discussion of risk measurement for these products. Retail transactions, such as deposits and mortgages, have many implicit or explicit options, such as the option for customers to prepay the principal before it is finally due, or the option for deposit customers to withdraw their money at any time. This introduces customer behavior into the modeling of the risks. The behavior depends on the structure and purpose of the product. 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
Liabilities
• Retail checking accounts
• Retail savings accounts
• Retail fixed-deposits accounts
• Deposits from commercial customers
• Bonds issued by the bank
Below, each asset and liability will be examined in greater depth, beginning with the assets.
Retail personal loans may be either fixed or floating rate. If they are floating, they are priced off the prime rate. Fixed-rate loans are generally paid off in equal installments. The installments include both interest payments and a partial repayment of the outstanding principal. The amount of each installment (I) depends on the initial amount lent (L), the periodic interest rate (r), and the number of periods over which the payments will be made (T). The NPV of the installments must equal the initial amount lent:
This equation can be rearranged to give the installment amount as a function of L, r, and T:
For example, if the annual rate is 8%, a $100, 6-year loan would have annual installments of $21.63.
Retail loan agreements generally allow the customer to pay the loan amount back to the bank earlier than originally required. Customers might do this if they had an unexpected windfall, or if rates had fallen and they were able to get a replacement loan elsewhere at a lower rate. This prepayment risk is not significant for loans of one or two years, but is significant for mortgages. Banks often discourage prepayment by requiring the customer to pay a fee called a prepayment penalty.
If the loan has a floating rate, there is less incentive to prepay because whenever rates fall, the required payment falls. However, floating-rate loans often have a cap on the maximum amount of interest that can be charged or the maximum increase per year. This effectively gives the customer a put option to force the bank to accept a liability paying the full rate in exchange for the capped rate.
Most mortgages in the United States are fixed rate and have a maturity of many decades. In the emerging markets, mortgages tend to be for a shorter term and only fixed for the initial years. This reduces the interest-rate risk for the bank, but increases the probability of the customer being unable to pay if interest rates rise. From an ALM perspective, long-term, fixed-rate mortgages could be considered to be simple bonds if it was not for the prepayment option.
To see the importance of the prepayment option, consider a $100, 10-year bond paying 10% anually. If the current 10-year rate was 10%, the bond would be worth $100. If the rates dropped to 5% the bond would be worth $159, and the holder would have gained $59:
Now consider a similar bond, but structured as a mortgage with a prepayment option. If rates dropped to 5%, the borrower would be sensible to pay back the $100 and get a new mortgage at 5%. In this case, the bank issuing the mortgage simply receives $100 from the customer and does not gain the $59.
In the United States, there is a large market of traded mortgage-backed securities (MBS). 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 most secure bonds are paid first, and once they have been paid the next tranche is entitled to payment, and so forth. The 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 of 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 the payment streams therefore depends heavily on customer behavior.
The Public Securities Association (PSA) has published a standard for the expected conditional prepayment rate (CPR). 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 the CPR is the SMM (single monthly mortality rate). This is the percentage of the remaining pool that prepays each month. The CPR and SMM are simply related:
(1 - CPR) = (1 - SMM)12
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 prepayment. Figure 12-3 shows the same mortgage but with prepayments at 100% PSA. With prepayments, the stream of interest payments is reduced, and the principal payments are early.
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. Prepayments increase as the gap between the old and new mortgage rates widens. 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. Prepayment also requires that customers be sufficiently financially sophisticated to realize that they can refinance more cheaply. Customers also exercise their prepayment option suboptimally whenever they sell their homes.
A typical prepayment function can be approximated as a logistic function. The form of the logistic function is as follows:
This function equals one when x equals negative infinity and equals zero when x equals positive infinity. The function has the shape of an S curve between one and zero. The prepayment rate as a percentage of the PSA can be modeled as follows:
FIGURE 12-2 Mortgage Amortization with No Prepayments
FIGURE 12-3 Mortgage Amortization with Prepayments at 100% PSA
Here, r is the market-refinancing rate. a, b, c, and d are constants. a determines the maximum %PSA, b determines the sharpness of the customer response, c determines the rate at which the refinancing is equal to 100% PSA. d is the residual amount of refinancing that will always take place, however adverse the market, because of people moving to new homes. Typical values for the parameters are given in the equation below:
This function is shown in Figure 12-4.
TABLE 12-1 Effect of Prepayment Speed on NPV
FIGURE 12-4 Rate of Prepayment as a Function of Prevailing Market Rates
Knowing how changes in interest rates cause changes in the prepayment rate, we can estimate the effect of rate changes on the value of a mortgage-backed security.
Changes in market rates affect both the discount rate and the timing of the cash flows from the MBS. 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.
Figure 12-6 shows the effect of rate changes on the NPV of interest-only (IO) payments. This shape is very interesting. 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. Such regions in which value increases as rates increase are referred to as having negative convexity. Once the prepayment rate stabilizes at a new low level, the discounting effect again begins to dominate, and positive convexity returns above 10%. By slicing the payment streams, securities can be formed with many interest-rate characteristics.
FIGURE 12-5 The Effect of Rate Changes on the NPV of Principal-Only Repayments
FIGURE 12-6 The Effect of Rate Changes on the NPV of Interest-Only Payments
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.
In the example above, the security holders are entitled to all of the principle or interest cash flows. We could have sliced each of those cash flows into multiple tranches in which the most-secure tranches are always paid first, and the least-secure tranches get the residual payments. In this case, the most-secure tranches behave like normal bonds unless there is a very severe drop in rates, and the least-secure tranches have an even stronger response to changes in rates because they are effectively leveraged.
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.
• The response to changes in interest rates can have significant negative convexity; i.e., the value can rise as rates rise.
Many banks have a large portion of their assets in the form of credit-card receivables, either from credit cards that they have originated, or from asset-backed securities (ABS) that are backed by credit-card receivables. Interest payments are usually a fixed percentage above the prime rate, often with caps on the maximum that can be charged.
The value of credit-card receivables depends on two main factors: the default rate, and the difference between market rates and the rate charged on the cards. The most important factor is the default rate, which can be on the order of 10% to 20%. The default rate is generally measured as a credit risk, but it is also possible to model it as an ALM risk in a similar way to the modeling of prepayments for mortgages.
Large commercial loans are priced relative to the prevailing market rates, and can therefore be considered to have the characteristics of bonds, possibly with prepayment options that will be exercised as efficiently as if they were traded instruments.
The ALM book often also includes such balance-sheet items as “strategic investments,” which were bought by the senior management as a way of investing the bank’s excess funds. The ALM book may also include real estate that is used by the bank or owned by the bank as an investment. Long-term investments such as these have values that are sensitive to interest-rate movements, and therefore should be included in the analysis of the bank’s structural interest-rate position. It is difficult to model the interest-rate sensitivity of illiquid equities or real estate, but a reasonable proxy is to use the interest-rate sensitivity of market indices or to build cash-flow models for company income and realestate rental rates.
The ALM book can also include liquidly traded instruments, such as bonds, swaps, and options. Identical instruments could also be held in the trading book, but the instruments in the ALM book are held either to modify the interest-rate position of the book, or as a temporary place to invest the bank’s funds before they are used for customer transactions.
This concludes the discussion of assets, let us now turn to liabilities.
Checking and savings accounts are also known as demand deposit accounts (DDA). Demand deposits such as checking and savings accounts have a contractual maturity of zero because they must be repaid to the customers as soon as they are demanded. Checking and savings accounts receive interest payments that are equal to or close to zero. Customers have DDAs for convenience and cash management. From a bank’s point of view, the profitability of a checking account is the income the bank can make from investing the funds, plus any fees charged to the customer, minus all the administrative costs. Although checking accounts are demand deposits and can be withdrawn at any time, in practice the total balance for the sum of all checking accounts in a bank is typically relatively stable.1 The net effect is that the banks can rely on having most of this money for many months or years. However, when interest rates rise, the total balance of checking accounts tends to fall as customers become more careful in sweeping their checking accounts into high-yielding savings accounts, money market accounts, or mutual funds.
In general, the value of a liability is the NPV of the cash flows from the liability. In the case of a noninterest-bearing checking account, the cash flows arise from changes in the net balance.
As an illustration, consider a simplified model for checking accounts. On the day the bank opens, a million customers come in, and they deposit $500 each. If the market remains stable, the net balance is expected to fluctuate between $400 million and $600 million. The bank can therefore consider $400 million to be “core” long-term deposits and the remaining as short-term funds. If the bank assumes that it will be in the checking-account business for at least 5 years, it can value the NPV of its liabilities as being $100 million owed immediately and $400 million to be paid in 4 years’ time. Assuming an interest rate of 5%, this liability is worth $413 million (not including the administrative costs of servicing):
If interest rates suddenly move to 10%, and the payments remain stable at $100 and $400, the value of the liability would fall to $348:
However, if the customers withdraw half of the $400 million to invest elsewhere, the liability becomes worth $424:
This demonstrates negative convexity. In this example, the change in value is strongly dependent on how the balance changes when rates change. A simple model for the changes in balance would be to say that there is an expected growth, a response to changes in rates, and a random element. This could be modeled by the equation below:
Bt = Bt-1(γ - ρ(rt - rt-1) + 
t)
Here, Bt is the balance at time t, Bt-1 is the balance at the previous time step, φ determines the extent to which depositors withdraw their funds when rates increase, and t is a random term. Such a model can be constructed by carrying out a regression between historical changes in balances and changes in rates. The model can then be used to estimate the value of the liability under different assumptions for rate changes.
Deposit accounts such as money market accounts may also pay a small amount of floating-rate interest. This makes their value more like the value of a floating rate bond paying the overnight rate. The NPV of a bond paying the overnight rate is always 100%. Therefore, the NPV of money market accounts is less sensitive to changes in market rates, as it is a less significant loss if customers withdraw early.
Fixed deposits (FDs) are offered in increments of months or years. Fixed deposits are also known as certificates of deposit (CDs). In FDs, customers guarantee not to withdraw the funds for a given period, and they are rewarded by receiving a relatively high fixed-interest payment. If the customers withdraw their funds early, they forfeit the interest income. If at the end of the deposit period, customers choose to redeposit (or “roll over”) the funds, the new rate is based on the prevailing market rates. Fixed deposits therefore have interest-rate characteristics that are similar to short-term bonds or floating-rate bonds. The main difference between fixed deposits and bonds is that the interest rate is not tied directly to the market rate, but is more commonly tied to the prime rate minus a few percent. The prime rate is the rate posted by the bank to its retail customers. It is only changed when there is a significant change in market rates, and typically changes every one to six months. It is often modeled as a lagged response to changes in the three-month rate. The prime rate is changed by banks as a response to both the market rates and the competitive situation; the value of fixed deposits is therefore a complex function of the market behavior, customer behavior, and bank behavior.
Large deposits from commercial customers are generally priced very close to the prevailing interbank rate, and are therefore well approximated as bonds.
The ALM book also contains bonds issued by the bank. These bonds are occasionally issued by banks to adjust their interest-rate position, raise funds, or modify the capital structure. They are a useful benchmark in determining the bank’s true cost of debt.
In this chapter, we introduced the two risks associated with ALM, namely, interest-rate and liquidity risk. We also detailed the sources of these risks and the characteristics of ALM instruments. Next, we discuss the measurement of interest-rate risk for ALM.
1 Although the total amount in retail checking accounts increases sharply on payday at the end of each month, the net balance from one month’s end to the next is stable.