Managing Bank Asset Liability Exposure

Townsend Walker, a senior vice president at Bank of America, explains alternatives for managing interest rate risk.

For most companies, interest rate risk is something to be managed while they go about their main business of making cars, computers or soap. For banks, interest rate risk is central to the business; managing it successfully is how banks make money.

Let's take a look at the two ways in which rate indices create an exposure and the possible solutions. The exposures are created when the rate on the asset and the rate on the liability are different, for example, prime and LIBOR; and when the rates were the same, but the maturity of the assets was longer than the maturity of the liabilities.

Different rates

Prime loans are funded by Eurodollar deposits, federal funds and bank CDs. The spreads between the asset index and the liability indices widen and narrow. This leads to volatile lending spreads and volatile income. A solution to this exposure is a basis swap, in which the bank pays out prime and receives LIBOR (or federal funds or T-bill rates). Both legs of the swap are floating rate indices, and the swap fixes the spread between them. To see how the spread is maintained after the basis swap hedge is in place, we'll look at two different rate scenarios in Table 1. The spread in the swap is 250 basis points.

Table 1: Prime/Libor Swap

Flows	Prime is 9% LIBOR is 6%	Prime is 11% LIBOR is 10%
Loan interest (prime)	9.00%	11.00%
Funding cost (LIBOR)	(6.00)	(10.00)
Swap outflow (prime-250)	(6.50)	(8.50)
Swap inflow (LIBOR)	6.00	10.00
Net lending spread	2.50	2.50

In the scenario above, you would pay your counterparty 0.50 percent on the notional amount on settlement day; in the second scenario, your counterparty would pay you 1.50 percent on the notional amount on the settlement day.

The details of a prime/LIBOR basis swap look like this:

Notional Amount: $150,000,000
Transaction Date: September 6, 1996
Effective Date: September 8, 1996
Maturity Date: September 8, 1999
LIBOR Rate Payer Payment Dates: December 8, March 8, June 8, September 8
LIBOR Rate Payer: Swap dealer
LIBOR Rate Reference: 3-month LIBOR, Reuters page LIBOR, September 8
LIBOR Rate Reset Dates: March 6, June 6, September 6, Dec. 6
LIBOR Rate Day Count: Actual/360
Prime Rate Payer: Bank
Prime Rate Reference: Federal Reserve Report H-15
Prime Rate Payment Dates: December 8, March 8, June 8, September 8
Spread: Minus 2.50 percent
Prime Rate Day Count: Actual/360
Method of Averaging: Weighted
Business Day Convention: Modified following business day

The portion of the prime loan portfolio funded by federal funds can be hedged by a prime/federal funds basis swap. The principles are the same as the prime/LIBOR basis swap. The indices are two floating rates with a fixed spread established between them.

Other alternatives for hedging the prime loan portfolio depend on your taking a view on the direction of rates. Because there are many alternatives to choose from, especially with two interest rates that can be hedged, you need a way to filter through them. One way of making sure that you have considered all the alternatives and their consequences is to go through the following procedure:

1. Classify the hedges as to whether they fix rates or provide insurance, and whether they are symetric or asymetric.

2. Consider how the premium on the insurance will be paid.Will it be by paying the full premium or earning premium through another transaction?

3. Look at what happens if interest rates go up and if interest rates go down.

4. Think about the consequences if just one leg of the exposure were hedged and the other were left unhedged.

5.Consider the consequences if both legs are hedged.

Table 2 is an example of this process.

Table2: Alternatives for Hedging a prime Loan Portfolio Funded with Eurodollar Deposits

Hedging Alternatives	Fix a Rate	Insurance	Insurance Payment
Prime	Swap to receive fixed and pay prime	Buy a floor on prime	Sell a cap on prime
Rates up	Narrow	?	Narrow
Rates down	Widen	Widen	Widen
LIBOR	Swap to pay fixed and receive LIBOR	Buy a cap on LIBOR	Sell a floor on LIBOR
Rates up	Widen	Widen	Widen
Rates down	Narrow	?	Narrow
Both Prime and LIBOR	Equiavalent to a prime/LIBOR basis swap	Buy a floor on prime and buy a cap on LIBOR	A collar on prime and a collar on LIBOR
Rates up	Stable	Widen	?
Rates down	Stable	Widen	?

In the first column, rates are fixed with swaps. In the second column insurance is provided by a floor on prime and a cap on LIBOR. In the third column the floor and cap premiums are offset by selling a cap on prime and selling a floor on LIBOR. You are concerned with what happens to your lending spread after the hedge. Will it be stable, will it widen, will it narrow, or will you be able to predict what will happen as rates move up or down?

The upper left-hand corner of the table shows what happens if you enter into a swap to receive a fixed rate and pay prime. The LIBOR rate is unhedged. If interest rates go up, the rate you receive on the loan is fixed, so a rising LIBOR rate will narrow the margin between the fixed rate and LIBOR. If interest rates go down, the rate you receive on the loan asset is fixed so a falling liability rate will widen the margin on the loan portfolio.

The middle of the second column shows what happens if you buy a cap on LIBOR and leave the prime rate unhedged. If rates go up, earnings on the loan portfolio will rise as prime rises, and LIBOR is capped. If rates go down, the hedge has no effect; so the effect of the rate movement on your lending spread is not predictable.

The lower right hand corner of the table shows what happens if you buy a floor on prime and, to reduce the premium, sell a cap. At the same time you buy a cap on LIBOR and to reduce the premium, sell a floor. The lending spread is not predictable, but it will fall inside the shaded band shown in Illustration 1.

Illustration 1: Collars on Prime and LIBOR

This analysis gives you the framework for a decision. You are able to test your interest rate forecasts against the cost of the hedges and the prospects for your lending spreads.

The derivatives presented for offsetting the insurance premiums are fairly conservative. They were chosen on the principle that you were willing to trade off some benefit of higher rates on prime and lower rates on LIBOR to reduce the premiums, but not assume additional risk. So these collars have the benefit of defining the risks you take.

Other derivatives will reduce the premiums, but introduce additional risk if you are wrong in your rate forecast. For example, if you think that rates will rise, one alternative is to buy a cap on LIBOR and offset the premium by selling a floor on prime. If rates do rise the loan spread widens. If rates fall, however, you could end up losing money. And as prime falls below the floor level, you make a net payment on the floor you sold. This causes the net earnings on the loan portfolio to fall faster than LIBOR falls. (See the shaded portion in Illustration 2.)

Illustration 2: Purchase a Cap on LIBOR and Sell a Floor on Prime

Different Maturities

Funding six-month loans with one-month deposits can create a high level of volatility in lending spreads. The solutions to this exposure are short-term swaps and futures. With short-term swaps the fixed leg may be as short as three months, while the floating leg of the swap is one month. The principles and conventions of these swaps are the same as those where the fixed leg is five years and the floating leg is six months.

The exposure can also be hedged with a strip of futures contracts. There is a futures contract where the underlying instrument is one-month Eurodollar deposits. It is called the LIBOR futures contract. The discussion of the pros and cons of using Eurodollar futures contracts also applies to the LIBOR contracts. However, because the contracts are on one-month deposits rather than three-month deposits, the timing risks are moderated considerably.

Investment Portfolio

The portion of the investment portfolio classified as held-to-maturity is difficult to adjust to changing market conditions. In a period of rising rates a bank may find that the duration of its bond portfolio is longer than desired. Rather than buying shorter-dated securities to reduce the duration of the portfolio, it can use a swap to accomplish the same results. To see how this works let's first look at the duration of a swap and how it affects the duration of a bond portfolio.

The duration of a swap is equal to the duration of the fixed-rate leg minus the duration of the floating rate leg. The duration of the fixed leg of a five year swap with a 6 percent coupon is the same as the duration of a five-year note with a 6 percent coupon. The calculation of the duration of a five year 6 percent swap with a floating leg tied to six-month LIBOR is:

Fixed leg 4.48 years Floating leg (0.50) years

Duration of swap 3.98 years

When you add shorter-term bonds to a portfolio, the resulting portfolio duration is the average of the longer bonds and the shorter bonds. On the other hand, adding a swap results in a direct reduction of the portfolio's duration. Let's look at the case of a single 10-year 6 percent bond with a duration of 7.83 years. If you buy a five-year 6 percent bond in the same amount, the duration of the portfolio is now 6.16 years, the average of 7.83 and 4.48 years. If you enter into a five-year swap to pay a fixed rate of 6 percent with a notional amount equal to the 10-year bond, the duration of the portfolio is now 3.81 years, 7.83 years minus 3.98 years. The swap is a more effective way to reduce the duration of the portfolio and its sensitivity to rising rates.

The swap can also be used to extend the duration and interest rate sensitivity of a portfolio. To extend duration, you would enter into a swap where you receive the fixed rate and pay the floating rate.

Embedded Options

The problem with embedded options is that customers pay off high-rate mortgages when rates go down and refinance at lower rates. The bank is usually not able to shift the rate down on its liabilities at the same pace. The result is that the bank's income falls.

Defining the exposure

To structure a hedge for the mortgage portfolio, the first step is to divide the portfolio into different segments. Mortgage portfolios are not homogeneous, the mortgages carry different rates and are often tied to different interest rate indices. Prepayment will depend on the current rate structure of each bank's portfolio, the behavior of the customer base and the mortgage products the competition is offering. Historical experience will help you model the prepayment characteristics of each segment of the portfolio. Prepayment is generally triggered as market interest rates fall below the rate prevailing in each segment of the mortgage portfolio. For hedging purposes it makes sense to structure a hedge for each rate and index segment of the portfolio. As a note of caution, even after the portfolio is modeled and segmented, you should not expect the hedges to be perfect since customer behavior is not predictable. It is, however, worthwhile to implement a hedging program to protect income. An imperfect hedge that does not generate additional risk is better than none.

Hedging alternatives for the mortgage portfolio

Three alternatives that have been used to hedge the exposure of mortgage portfolios are floors, digital floors and index-accreting swaps. An index-accreting swap is one in which the notional amount of the swap increases as a specified interest rate index goes down. The accretion schedule is specified in the terms of the transaction. An accretion schedule may look like this:

Change in the Index	Accretion of Notional Amount
- 1 %	110%
- 2%	125%
- 3%	140%

index-accreting swaps generally start out at a lower rate than traditional swaps in order to pay for the options that are embedded in them. These options effectively layer in additional swaps as rates decline.

To hedge a mortgage portfolio segment, you would either buy a floor, buy a digital floor, or receive a fixed rate on the index-accreting swap. There will be cost savings in the hedging program if some of the derivatives are arranged to start in the future rather than today. This would be the case in the situation where mortgage rates are at 7 percent, you have a mortgage portfolio segment priced at 5 percent, and rates are not expected to decline precipitously.

Illustration 3 (next page) shows how the various alternatives behave with changes in future rates. It is assumed that all of the alternatives are structured to protect at the same rate level, denoted as R. When the floor level is reached you will be compensated for the difference between the index rate and market rates, so that a given rate level will be protected. In terms of protecting the income of a mortgage portfolio, a floor protects the income level for a given notional amount but does not compensate you if you lose mortage balances in the refinancing process. The digital floor can be structured to provide additional payoff when the floor level is reached. Thereafter the return from the digital floor declines with market rates. A digital floor generates additional income once rates fall to a given level. In that respect, if mortgage payoffs are triggered at certain rate levels you will receive a one-time compensation for the loss of income. At lower rate levels it is not particularly effective. The index-accreting swap will return a lower rate than a traditional swap before it begins to accrete, but then effectively increase the return to the original amount of the swap as the accretion begins. The index-accreting swap mirrors most closely the rate and balance problems when mortgages are refinanced. It effectively adds balances back at the same rate at which they were lost. This is offset to some extent by the low return when rates remain above the level at which accretion begins.

Illustration 3: Alternatives for Hedging a Mortgage Portfolio

Lack of Loan Demand

Banks are reluctant to chase away depositors when loan demand is slack because deposits are the entree for selling other bank services. But, depositing these excess funds in the federal funds market results in thinner margins. Buying securities creates interest rate and liquidity risks, especially if the money is needed before the maturity of the securities. Banks have employed a number of derivatives to address this situation: swaps to receive a fixed rate, index-amortizing swaps and structured notes.

Swaps

A swap to receive a fixed rate moves you out the yield curve and generates a higher return. At the same time, cash is available in the event that loan demand picks up unexpectedly. The likelihood of this swap producing undesirable results is low since you do not have to undo the swap when loan demand picks up.

When loan demand is slack the earnings and costs are:

Earnings on short-term deposit of cash	LIBOR
Pay the floating rate on the swap	(LIBOR)
Receive the fixed rate on the swap	Treasury plus swap spread
Net return	Treasury plus swap spread

When loan demand picks up the earnings and costs are:

Earnings on the loan	LIBOR, or prime plus loan spread
Pay the floating rate on the swap	(LIBOR)
Receive the fixed rate on the swap	Treasury plus swap spread
Net return	Treasury plus loan spread plus swap spread

You will incur an opportunity cost if short-term rates rise above the fixed rate on the swap. This likelihood can be mitigated by keeping the maturity of the swap on the short side.

Index-amortizing swap

The attraction of an index-amortizing swap is that it offers the receiver an above-market fixed rate. The additional earnings can be from 50 to 100 basis points. An index-amortizing swap is one in which the notional amount of the swap amortizes as short-term rates decline. A typical structure is:

Notional amount: $100,000,000, when the notional amount amortizes to 15 percent of the notional amount the swap terminates
Stated Maturity: 3 years
Lock-out period (notional amount does not change): 1 year
Amortization frequency: Quarterly
Rate reset frequency: Quarterly
Fixed rate: 5.75 percent
Floating rate: 4 percent

Amortization: On each quarterly reset following the lockout period, the notional amount of the swap amortizes based on the change in rates from the current three-month LIBOR.

Change in LIBOR	Amortization
+ 4%	10%
+3	15
+2	25
+1	50
0	60
-1	75
-2	100

The index-amortizing swap behaves like a mortgage portfolio since the notional amount of the swap declines as rates fall. With the swap, however, the amount falls on a predictable schedule. Many banks have viewed this swap as a means of generating incremental return when loan demand is low and interest rates are expected to fall.

To see the attraction and risks of this swap it is useful to compare the fixed rate on the index-amortizing swap with comparable fixed rates on a standard one-year swap (lock-out period) and a standard three-year swap (final maturity).

One-year standard swap = 5.00%
Three-year standard swap = 6.50%
index-amortizing swap = 5.75%

The index-amortizing swap is attractive if rates are stable or are expected to fall. You will earn a premium above shorter-term market rates. If rates rise, however, the swap does not amortize very rapidly and you earn less than you could have from a standard swap. These swaps were attractive to banks from 1991 through 1993 when rates were falling. They were unattractive in 1994 when short-term interest rates rose rapidly. A number of well-known financial institutions took write-offs to reflect the decline in the value of these instruments.

Index-amortizing swaps and index-accreting swaps are structured by combining a standard swap with swaptions. With the index-amortizing swap you are selling options to the derivatives dealer to cancel portions of the swap as rates fall. With the index-accreting swap, you are buying options to enter into swaps in additional amounts as rates fall. The unique part of both structures is that the rates that trigger the options are short-term interest rates, not longer-term fixed rates.