# Futures versus swaps: some considerations for the thrift industry.

Futures Versus Swaps: Some Considerations for the Thrift Industry

Introduction

Studies have shown that financial managers often lack an understanding of the mechanics of hedging, lack the expertise to construct and manage hedges, or simply fail to appreciate the benefits of hedging [2,3,11]. Thrift managers are not an exception, and historically, thrifts have been reluctant to hedge. The experiences of the industry over the last decade, however, have forced thrifts to re-examine their risk management practices, and many are now struggling to understand hedging concepts and hedging tools.(1)

Prior to the introduction of swaps, the principal instruments for hedging interest rate risk were interest rate futures contracts. Thrifts were never big users of futures. The studies noted above have shown that managers mistakenly regard futures as "speculative" in nature or only suitable for hedging short term risk exposures. Swaps, on the other hand, have been widely embraced during the last few years as an effective long term risk management tool.

In this article, the source of a thrift's long term interest rate risk are examined, and swaps and futures hedging strategies for the management of this risk are compared. The argument is that while swaps hedges can be very effective, they are not necessarily superior to futures hedges when cost is considered.

Thrifts and Interest Rate Risk:

The Problem

Consider the case of a thrift institution which acquires, either by origination or assignment, conventional fixed rate mortgages using funds obtained from the sale of three month certificates of deposit (CDs). To make the example concrete, suppose the thrift purchases $25 million of newly originated 20 year mortgage debt having a coupon of ten percent and yielding ten percent - thus the mortgages are priced at par. The mortgagors will make payments to the thrift on a quarterly basis.(2) The thrift funds the mortgages by selling $25 million of three month (90 day) CDs. The plan is to refund the mortgage assets every three months by selling replacement CDs. This process would be continued until the mortgages mature. At the time of the initial CD sale, the three month CD rate is eight percent.

The example is complicated a bit by the amortizing nature of mortgage debt. At each refunding, fewer CDs need to be sold to carry the mortgage assets. Consider the first three and the last three payments in the amortization schedule. These are depicted in Table 1 on page 16.(3) Notice that, after the first CD cycle matures, the thrift only needs to raise $24.90 million from the sale of replacement CDs. After the 78th cycle matures, the thrift will only need to raise $1.40 million from the sale of replacement CDs.

Table : Table 1

Amortization of Mortgage Debt

In a stable interest rate environment, the thrift would simply carry the mortgages unhedged and enjoy a rate spread of two percent, which is the differences between the ten percent the thrift receives on its mortgage assets and the eight percent the thrift pays on its CD liabilities. The first set of cash flows is illustrated in Figure 1 on page 17. The exhibit depicts the initial exchange of principals between the thrift and the mortgagors on the one hand and the thrift and the third party lenders (CD purchasers) on the other.

The CDs mature at the time the first mortgage payment is made, and the thrift must refund its mortgage assets with the sale of replacement CDs. The thrift will receive a payment of $725.65 thousand from the mortgagors, will pay $25.50 million to the third party lenders to retire its matured CDs, and will receive $24.90 million from the sale of new CDs to third party lenders. The cash flows between the thrift and the mortgagors and the thrift and the third party lenders are depicted in Figure 2 on page 17.

These cash flows provide the thrift with a net inflow of $125 thousand, which is, of course, one quarter's rate spread on $25 million: 0.25 x (10% - 8%) x $25 million. Barring any premature repayment of principal by the mortgagors, the cash flows depicted in Figure 2 are known with certainly since the pay/receive rates were locked in at the time the mortgages were funded. However, it cannot be known at the time of the initial mortgage funding what the three month CD rate will be at the time of the first refunding; nor can it be known at the time of the initial mortgage funding what the refunding rate will be for any of the subsequent 78 refundings. It is evident that the liability side of the thrift's mortgage business involves a floating rate of interest (reset once every three months) while the asset side involves a fixed rate of interest (ten percent). This floating/fixed rate mismatch is the source of the thrift's interest rate risk.

If three month CD rates do not change from their eight percent level and no mortgagors prepay, the second cash flow stream will produce net revenues of $124.49 thousand. The thrift will receive $725.65 thousand from the mortgagors, will pay $25.40 million to the third party lenders to retire the second CD financing, and will receive $24.80 million from third party lenders on the sale of replacement CDs. Of course, there is no guarantee that the three month CD rate will not change. Nevertheless, the expected present value of the mortgage lending as a function of the expected rate spread can be calculated as follows:

[Mathematical Expression Omitted]

where E[D(t)] denotes the expected rate spread at time t, PR(t) denotes the principal remaining at time t(i.e., the portion of the principal which has not yet amortized), and k denotes the thrift's discount rate - presumably its risk adjusted cost of funds. Assuming that D(t) = 2 percent for all t, that k is ten percent (the current mortgage rate), and that there are no mortgage principal prepayments, then the expected present value of the mortgages to the thrift is $3.43 million.

If the CD rate rises, the refunding becomes more expensive and the thrift's revenue declines accordingly. The rise in the CD rate reduces the rate spread D(t) and thus reduces the present value of the mortgage assets.

The Swap Hedge

The thrift described in the preceding section can hedge its interest rate risk by becoming a counterparty to a fixed-for-floating interest rate swap. In such a swap, the thrift would agree to make quarterly fixed rate payments on $25 million of amortizing debt to a swap dealer in exchange for the swap dealer's quarterly floating rate payments to the thrift. The floating rate side of a fixed-for-floating rate swap is usually tied to LIBOR but can just as easily be tied to some other rate, such as the T-bill rate or a commercial paper rate. In this case, it would be tied to the three month CD rate.

Swap dealers routinely price the fixed rate side of an interest rate swap as a spread over United States Treasuries of a similar average life. <4> In this particular case, the mortgage debt has an average life of 13.22 years. Thus, the swap dealer would take the T-bond with a maturity closest to 13.22 years and add a premium. The size of the premium will depend on whether the swap dealer is paying or receiving fixed rate. Suppose, for purposes of this example, that the swap dealer is currently offering to pay the 13.22 year T-bond yield plus 38 basis points and is offering to receive fixed rate for the 13.22 year T-bond yield plus 54 basis points. Both rates are quoted against the three month CD rate. Suppose further that the 13.22 year T-bond yield is currently 8.40 percent. <5>

In this case, the thrift is looking to convert its floating rate liabilities to fixed rate liabilities. Thus, the thrift is the fixed rate payer (floating rate receiver) and will pay a quarterly rate of 8.94 percent (8.40 % + 0.54 %). The cash flows between the thrift and the swap dealer are depicted in Figure 3 on page 18.

Now, by combining the cash flows between the thrift and the mortgagors and the thrift and the third party lenders (Figure 1) with the cash flows between the thrift and the swap dealer (Figure 3), the completely hedged set of cash flows depicted in Figure 4 on page 44 is obtained. Notice that there is no longer any interest rate uncertainly in the thrift's position. The thrift is now both paying and receiving the three month CD rate, so they fully offset one another. The thrift is receiving ten percent from the mortgagors and paying 8.94 percent to the swap dealer. The end result is a fixed rate spread of 1.06 percent for the life of the mortgages.

This example illustrates the standard hedge using interest rate swaps, and it is the precise type of situation for which swap dealers market their services. The swap hedge is very effective, but notice that the swap hedge is not costless. The two percent rate spread which the mortgage-assets/CD-liabilities were expected to generate has been reduced to 1.06 percent. The reduction in the rate spread represents the cost of the hedge [7]. An equivalent, but alternative, way to appreciate this cost is to look at the change in the present value of the rate spread. In this case, the present value of the rate spread declines from $3.43 million to $1.82 million. The difference of $1.61 million is the cost of the hedge.

The Future Hedge

The futures alternative to the swap hedge is a little more complicated than a simple short hedge. The thrift is concerned that interest rates might rise. A rise in rates would result in an increase in the thrift's cost of CD funding for its mortgage assets. The appropriate strategy is to sell a sufficient number of interest rate futures, using either T-bond futures or mortgage futures. The Chicago Board of Trade (CBOT) discontinued its GNMA futures contract, but new mortgage-based futures are being introduced. For simplicity, suppose that a futures contract on 30 year mortgages exists. This is the "contract" that will be used to illustrate the futures hedge. The goal is to determine the appropriate number of futures to sell short so as to precisely offset any change in rates and preserve the present value of the asset/liability rate spread.

There are a number of difficulties in determining the appropriate number of mortgage futures to sell. First, if changes in the CD rate are not perfectly correlated with changes in the mortgage rate, hedging will be inexact at best. Second, the hedge ratio is not stable over time - as the mortgages age, the hedge ratio will need to be recalculated. The latter problem is addressed first.

The hedge ratio can be estimated using any of the various hedge ratio models - depending on the analyst's preferences. The most versatile approach is the dollar value basis point (DVBP) model. The "dollar value of a basis point" is defined as the change in the market value of $100 of face value debt for a one basis point change in the instrument's yield. To begin, the DVBP of the debt instrument to be hedged is divided by the DVBP of the instrument underlying the futures, regarded as the futures DVBP. This ratio is then multiplied by the yield beta ([...sub.y]). The yield beta is the ratio of the change in the yield of the instrument to be hedged and the change in the yield of the hedging instrument. This yield beta is found by simple linear regression [8, Chapter 12]. The product of the DVBP ratio and the yield beta is then the hedge ratio. The dollar size of the hedge is: [Mathematical Expression Omitted] The dollar size of the hedge is then translated into a specific number of futures contracts by dividing by the face value of a single futures contract: [FV.sub.hedge] =[FV.sub.cash] x DVBP(cash)/DVBP(futures) x [Beta.sub.y.sup.*]

(2)

To continue with the example, the DVBP of the mortgages held in the mortgage portfolio is calculated, which, as it happens, is $0.068. Next, the DVBP of the futures is calculated. Suppose the futures DVBP is $0.085. Next, the yield beta between the 20 year mortgage rate (the mortgages held by the thrift) and the rate on the mortgages underlying the futures is estimated. Suppose now that the beta is 1.06, that is, for each one basis point change in the yield of the thrift's mortgages is expected. in the yield of the thrift's mortgages is expected. The initial hedge for the thrift's position is then:

At the time of the first refunding, the thrift would recalculate the size of the hedge based on its new level of mortgage principal, the new values of the DVBPs, and the yield beta for 19.75 year mortgages, as opposed to the earlier 20 year mortgages. This process would be repeated every three months and the size of the futures hedge adjusted accordingly.

The hedge is very effective, provided that all yield changes in the CD rate are matched by identical changes in the mortgage yield. That is, if three month CD yields rise by one basis point, the 20 year mortgage yield must also rise by one basis point. Later, after the first refunding, a one basis point change in CD yields must be matched by a one basis point change in 19.75 year mortgage yields. Although this is not a realistic scenario, consider the outcome as if it were and suppose that immediately after the mortgages were acquired (while the mortgages still have a 20 year life), rates rise by one basis point. The next CD refunding is then expected to cost 8.01 percent (up from eight percent). The present value of the mortgage/CD rate spread declines by $17.10 thousand. This is completely offset, however, by $17.10 thousand profit on the futures hedge.

There is, however, an inconsistency in the assumptions. It was assumed that, on average, the yield on a 20 year mortgage changes by more than the yield on 30 year mortgage futures (yield beta was 1.06). Yet, parallel shifts were assumed in three month CD and 20 year mortgage yields and every mortgage maturity less than 20 years. The reality, of course, is that short term rates and long term rates are not equally volatile. The size of the hedge must be adjusted to account for this difference in volatilities.

The first step in the adjustment is to calculate what will be called an "adjustment beta." The adjustment beta ([Beta.sub.a]) is the ratio of the change in the three month CD rate to the change in the 20 year mortgage rate. This is estimated in the same manner as the yield beta. To continue, suppose that the adjustment beta is found to be 1.35. This suggests that for each basis point change in the 20 year mortgage rate, the CD rate can be expected to change by 1.35 basis points, typical of the greater volatility of short term rates.

The final step is to adjust the size of the hedge to reflect the difference in yield volatilities. This is accomplished by multiplying the face value of the hedge obtained with the DVBP model by the adjustment beta. The full hedge model is:

Thus, the thrift can hedge by selling 288 mortgage futures at the time the mortgages are acquired. The full set of cash flows (excluding principal flows) associated with this strategy is depicted in Figure 5 on page 44.

At the time of each refunding, the thrift would recalculate all five of the variables which enter into the determination of the optimal hedge: [FV.sub.cash], DVBP(cash), DVBP(futures), [Beta.sub.y], and [Beta.sub.a]. All other things being equal, [FV.sub.cash], DVBP(cash), and [Beta.sub.a] will decline with the passage of time; [Beta.sub.y] will rise; and DVBP(futures) will not change. The combined effect is such that the size of the hedge decreases with each refunding. Of course, the futures used in the hedge are of limited term, so the thrift will need to periodically roll forward into later delivery futures. The strategy requires a balancing of the frequency of rollover against the liquidity of the instrument. The near delivery futures will typically be more liquid and thus involve less liquidity cost, but, at the same time, necessitate more frequent rollover and thus involve greater transaction costs.

The hedge strategy presented here is neither perfectly effective nor costless. Like most futures hedging, there will be some basis risk as the various yields involved in the hedging model fluctuate in a less than perfectly predictable manner. The futures hedge is therefore less effective than the nearly perfectly effective swap hedge. Nevertheless, the futures hedge may still be preferable. The swap hedge is quite costly - resulting in a considerable forfeiture of present value. The futures hedge may be less costly [8, Chapter 12]. If so, the trade-off is one of efficacy against cost. The comparative efficacies and costs of the swap hedge and the futures hedge are empirical issues. No effort is made to address these issues here, but this is clearly an area ripe for study.

Considerations for

the Optimal Hedge

There are two other considerations in the choice of the hedging instrument. The first involves intermediate cash flows engendered by the hedge. The second involves mortgage prepayments.

Daily marking-to-market of futures will necessitate the regular transfer of variation margin to and from the margin account of the thrift. There are no comparable intermediate transfers of funds with a swap hedge. This would seem to suggest a preference for the swap hedge. This conclusion, however, is premature. Assuming the futures hedge behaves perfectly, the precise amount of the margin transfer out (in) of the thrift's account will be matched by an increase (decrease) in the present value of its rate spread. Suppose, for example, that interest rates decline. Margin will be transferred from the thrift's margin account, since it is short futures. At the same time, the decline in the cost of the thrift's CD liabilities will result in an increase in the value of the rate spread. Thus, as long as the thrift has sufficient liquidity to meet its margin requirements, these intermediate cash flows should not be an overriding consideration.

The second, and far more significant, consideration is mortgage prepayment by mortgagors. Conventional mortgage indentures typically allow the mortgagor to prepay the mortgage principal without penalty after some initial period. Mortgages are prepaid for a variety of reasons.[6] The more unpredictable the prepayment rate, the greater the advantage of futures hedging over swap hedging.

Suppose that immediately after acquiring the mortgages and entering into a swap with a swap dealer, interest rates decline and $2 million of mortgage debt is prepaid. The thrift can easily adjust its liabilities by simply refunding $2 million less in the next sale of CDs. The swap hedge, however, is not so easily adjusted. In fact, unless very special provisions have been included in the swap agreement to allow the thrift to amortize the swap more quickly, the thrift will, quite likely, be locked into the swap.

In such a situation, the portion of the swap no longer covering actual mortgages becomes a speculation and exposes the thrift to precisely the kind of interest rate risk the thrift entered the swap to avoid. One solution is to negotiate a cancellation of a portion of the swap principal with the swap dealer. As a general rule, the swap dealer will oblige but only if adequately compensated. Alternatively, the thrift could default on the swap. A default would bring the swap default provisions into play. These provisions require the thrift to indemnify the swap dealer for the cost of securing a replacement swap [9, Chapter 4]. A default will, of course, damage the reputation of the thrift and make subsequent hedging more difficult.

A swap can be written with a provision granting the thrift the option to accelerate the amortization of the swap principal. This option has value, however, and the swap dealer will not grant it without compensation - which in turn further reduces the profitability of holding a mortgage portfolio.

The prepayment problem is minimized with the futures hedge. The thrift can simply lift a sufficient portion of its futures hedge to offset the portion of the mortgages which have been prepaid. However, since the greatest number of prepayments is likely to occur when interest rates decline and the mortgagors can prepay without penalty, the mortgage principal received may not be sufficient to cover the loss on the futures hedge. Nevertheless, the ability to easily offset the futures hedge, in whole or in part, allows the thrift to minimize this source of uncertainty. To protect against a decline in rates and accelerated prepayments, the thrift might couple the futures hedge with an appropriate position in interest rate options. Several forms of interest rate options could be used for this purpose, including call options on interest rate futures, call options on a debt instrument, and over-the-counter interest rate floors[6].

An alternative solution to the prepayment problem is to use a mixed hedge - part swap and part futures. The swap portion can be used to cover that amount of mortgage debt not likely to be prepaid and the futures hedge can cover the rest.

Endnotes

(1) Thrifts are also candidates for asset/ liability management strategies on which much has been written. Examples include McNulty [10], Kaufman [5], Toevs [13], and Gardner and Mills [4]. For an extensive bibliography on gap analysis through 1983, see Sinkey [12]. For a discussion of the relationship between gap analysis and futures hedging, see Belongia and Santoni [1]. Nevertheless, the nature of the thrift's core business renders asset/liability management solutions inadequate at best.

(2) In most cases, residential mortgage debt of the type held by thrifts will involve monthly rather than quarterly payments. However, little is lost by the quarterly payments. The cash flow diagrams and analysis are simplified a bit by this assumption without any fundamental damage to the realism of the example.

(3) The amortization schedule was generated using A-Pack: An Analytical Package for Business from MicroApplications. This IBM-based software package encompasses a great many analytical techniques frequently employed in the various business disciplines. It has many applications in the design of hedging strategies. Interested parties can call MicroApplications directly at (516) 821-9355.

(4) Average life is used by swap dealers to equate the maturities of nonamortizing Treasury debt and amortizing mortgage debt. For a discussion of the measurement and use of average life in pricing the fixed rate side of swaps, see Marshall and Kapner [9].

(5) The T-bond rate is a semi-annual rate while this particular example involves quarterly payments and thus a quarterly compounded rate. This necessitates a conversion from semi-annual rate to its quarterly compounded equivalent. For purposes of this example, the adjustment is not made. The adjustment process is discussed in Marshall and Kapner [9], Chapter 3.

(6) The prepayment rate is the percentage of the mortgages on which the mortgagors elect to prepay the principal during some defined period of time. Some of the factors which cause prepayment are highly predictable. These include such things as the death of the home owner, the sale of the home, and foreclosure. The most important of the less predictable factors is the general level of interest rates. A decline in rates will lead to some refinancings; thus, the greater the decline in interest rates the higher the prepayment rate.

References

[1.] Belongia, M.T. and G.J. Santoni. "Hedging Interest Rate Risk with Financial Futures: Some Basic Principles." Review, Federal Reserve Bank of St. Louis, October 1984. Reprinted in Wilcox, J.A., ed. Current Reading on Money, Banking, and Financial Markets. Boston: Little Brown, 1987.

[2.] Block, S.B. and T.J. Gallagher. "The Use of Interest Rate Futures and Options by Corporate Financial Managers." Financial Management, Autumn 1986.

[3.] Booth, J.R., R.L. Smith, and R.W. Stolz. "The Use of Interest Futures by Financial Institutions." Journal of Bank Research, Spring 1984.

[4.] Gardner, M.J. and D.L. Mills. "Asset/ Liability Management: Current Perspectives for Small Banks." The Journal of Commercial Bank Lending, December 1981.

[5.] Kaufman, G. "Measuring and Managing Interest Rate Risk: A Primer." Economic Perspectives, Federal Reserve Bank of Chicago, January/ February 1984.

[6.] Kapner, K.R. and J.F. Marshall. Swaps Handbook: Swaps and Related Risk Management Instruments. New York: The New York Institute of Finance, 1990.

[7.] Loeys, J.G. "Interest Rate Swaps: A New Tool for Managing Risk: Review of Business, Federal Reserve Bank of Philadelphia, May/June 1985. Reprinted in Wilcox, J.A., ed. Current Reading on Money, Banking, and Financial Markets. Boston: Little Brown, 1987.

[8.] Marshall, J.F. Futures and Option Contracting: Theory and Practice. Cincinnati: SouthWestern, 1989.

[9.] _____ and K.R. Kapner. Understanding Swap Finance. Cincinnati: South-Western, 1990.

[10.] McNulty, J.E., "Measuring Interest Rate Risk: What Do We Really Know?" Journal of Retail Banking, Spring/Summer 1986. Reprinted in Wilcox, J.A., ed. Current Reading on Money, Banking, and Financial Markets. Boston: Little Brown, 1987.

[11.] Quinn, L.R. "How Corporate America Views Financial Risk Management." Futures, January 1989.

[12.] Sinkey, J. Commercial Bank Financial Management. New York: Macmillan, 1983.

[13.] Toevs, A. "Gap Management: Managing Interest Rate Risk in Banks and Thrifts." Economic Review, Federal Reserve Bank of San Francisco, Spring 1983.

PHOTO : Figure 1 Initial Exchange of Principals and Documents

PHOTO : Figure 2 Cash Flows at Time of First Mortgage Payment

PHOTO : Figure 3 Interest Rate Swap with Swap Dealer

John F. Marshall is Associate Professor of Finance at St. John's University in Jamaica, New York and a risk management consultant for several leading financial institutions.

Introduction

Studies have shown that financial managers often lack an understanding of the mechanics of hedging, lack the expertise to construct and manage hedges, or simply fail to appreciate the benefits of hedging [2,3,11]. Thrift managers are not an exception, and historically, thrifts have been reluctant to hedge. The experiences of the industry over the last decade, however, have forced thrifts to re-examine their risk management practices, and many are now struggling to understand hedging concepts and hedging tools.(1)

Prior to the introduction of swaps, the principal instruments for hedging interest rate risk were interest rate futures contracts. Thrifts were never big users of futures. The studies noted above have shown that managers mistakenly regard futures as "speculative" in nature or only suitable for hedging short term risk exposures. Swaps, on the other hand, have been widely embraced during the last few years as an effective long term risk management tool.

In this article, the source of a thrift's long term interest rate risk are examined, and swaps and futures hedging strategies for the management of this risk are compared. The argument is that while swaps hedges can be very effective, they are not necessarily superior to futures hedges when cost is considered.

Thrifts and Interest Rate Risk:

The Problem

Consider the case of a thrift institution which acquires, either by origination or assignment, conventional fixed rate mortgages using funds obtained from the sale of three month certificates of deposit (CDs). To make the example concrete, suppose the thrift purchases $25 million of newly originated 20 year mortgage debt having a coupon of ten percent and yielding ten percent - thus the mortgages are priced at par. The mortgagors will make payments to the thrift on a quarterly basis.(2) The thrift funds the mortgages by selling $25 million of three month (90 day) CDs. The plan is to refund the mortgage assets every three months by selling replacement CDs. This process would be continued until the mortgages mature. At the time of the initial CD sale, the three month CD rate is eight percent.

The example is complicated a bit by the amortizing nature of mortgage debt. At each refunding, fewer CDs need to be sold to carry the mortgage assets. Consider the first three and the last three payments in the amortization schedule. These are depicted in Table 1 on page 16.(3) Notice that, after the first CD cycle matures, the thrift only needs to raise $24.90 million from the sale of replacement CDs. After the 78th cycle matures, the thrift will only need to raise $1.40 million from the sale of replacement CDs.

Table : Table 1

Amortization of Mortgage Debt

Principal Remaining Payment Payment Component Book Value Number (thous $) (thous $) (mil $) 1 725.65 100.65 24.90 2 725.65 103.17 24.80 3 725.65 105.75 24.69 78 725.65 673.84 1.40 79 725.65 690.68 0.71 80 725.73 708.03 0.00

In a stable interest rate environment, the thrift would simply carry the mortgages unhedged and enjoy a rate spread of two percent, which is the differences between the ten percent the thrift receives on its mortgage assets and the eight percent the thrift pays on its CD liabilities. The first set of cash flows is illustrated in Figure 1 on page 17. The exhibit depicts the initial exchange of principals between the thrift and the mortgagors on the one hand and the thrift and the third party lenders (CD purchasers) on the other.

The CDs mature at the time the first mortgage payment is made, and the thrift must refund its mortgage assets with the sale of replacement CDs. The thrift will receive a payment of $725.65 thousand from the mortgagors, will pay $25.50 million to the third party lenders to retire its matured CDs, and will receive $24.90 million from the sale of new CDs to third party lenders. The cash flows between the thrift and the mortgagors and the thrift and the third party lenders are depicted in Figure 2 on page 17.

These cash flows provide the thrift with a net inflow of $125 thousand, which is, of course, one quarter's rate spread on $25 million: 0.25 x (10% - 8%) x $25 million. Barring any premature repayment of principal by the mortgagors, the cash flows depicted in Figure 2 are known with certainly since the pay/receive rates were locked in at the time the mortgages were funded. However, it cannot be known at the time of the initial mortgage funding what the three month CD rate will be at the time of the first refunding; nor can it be known at the time of the initial mortgage funding what the refunding rate will be for any of the subsequent 78 refundings. It is evident that the liability side of the thrift's mortgage business involves a floating rate of interest (reset once every three months) while the asset side involves a fixed rate of interest (ten percent). This floating/fixed rate mismatch is the source of the thrift's interest rate risk.

If three month CD rates do not change from their eight percent level and no mortgagors prepay, the second cash flow stream will produce net revenues of $124.49 thousand. The thrift will receive $725.65 thousand from the mortgagors, will pay $25.40 million to the third party lenders to retire the second CD financing, and will receive $24.80 million from third party lenders on the sale of replacement CDs. Of course, there is no guarantee that the three month CD rate will not change. Nevertheless, the expected present value of the mortgage lending as a function of the expected rate spread can be calculated as follows:

[Mathematical Expression Omitted]

where E[D(t)] denotes the expected rate spread at time t, PR(t) denotes the principal remaining at time t(i.e., the portion of the principal which has not yet amortized), and k denotes the thrift's discount rate - presumably its risk adjusted cost of funds. Assuming that D(t) = 2 percent for all t, that k is ten percent (the current mortgage rate), and that there are no mortgage principal prepayments, then the expected present value of the mortgages to the thrift is $3.43 million.

If the CD rate rises, the refunding becomes more expensive and the thrift's revenue declines accordingly. The rise in the CD rate reduces the rate spread D(t) and thus reduces the present value of the mortgage assets.

The Swap Hedge

The thrift described in the preceding section can hedge its interest rate risk by becoming a counterparty to a fixed-for-floating interest rate swap. In such a swap, the thrift would agree to make quarterly fixed rate payments on $25 million of amortizing debt to a swap dealer in exchange for the swap dealer's quarterly floating rate payments to the thrift. The floating rate side of a fixed-for-floating rate swap is usually tied to LIBOR but can just as easily be tied to some other rate, such as the T-bill rate or a commercial paper rate. In this case, it would be tied to the three month CD rate.

Swap dealers routinely price the fixed rate side of an interest rate swap as a spread over United States Treasuries of a similar average life. <4> In this particular case, the mortgage debt has an average life of 13.22 years. Thus, the swap dealer would take the T-bond with a maturity closest to 13.22 years and add a premium. The size of the premium will depend on whether the swap dealer is paying or receiving fixed rate. Suppose, for purposes of this example, that the swap dealer is currently offering to pay the 13.22 year T-bond yield plus 38 basis points and is offering to receive fixed rate for the 13.22 year T-bond yield plus 54 basis points. Both rates are quoted against the three month CD rate. Suppose further that the 13.22 year T-bond yield is currently 8.40 percent. <5>

In this case, the thrift is looking to convert its floating rate liabilities to fixed rate liabilities. Thus, the thrift is the fixed rate payer (floating rate receiver) and will pay a quarterly rate of 8.94 percent (8.40 % + 0.54 %). The cash flows between the thrift and the swap dealer are depicted in Figure 3 on page 18.

Now, by combining the cash flows between the thrift and the mortgagors and the thrift and the third party lenders (Figure 1) with the cash flows between the thrift and the swap dealer (Figure 3), the completely hedged set of cash flows depicted in Figure 4 on page 44 is obtained. Notice that there is no longer any interest rate uncertainly in the thrift's position. The thrift is now both paying and receiving the three month CD rate, so they fully offset one another. The thrift is receiving ten percent from the mortgagors and paying 8.94 percent to the swap dealer. The end result is a fixed rate spread of 1.06 percent for the life of the mortgages.

This example illustrates the standard hedge using interest rate swaps, and it is the precise type of situation for which swap dealers market their services. The swap hedge is very effective, but notice that the swap hedge is not costless. The two percent rate spread which the mortgage-assets/CD-liabilities were expected to generate has been reduced to 1.06 percent. The reduction in the rate spread represents the cost of the hedge [7]. An equivalent, but alternative, way to appreciate this cost is to look at the change in the present value of the rate spread. In this case, the present value of the rate spread declines from $3.43 million to $1.82 million. The difference of $1.61 million is the cost of the hedge.

The Future Hedge

The futures alternative to the swap hedge is a little more complicated than a simple short hedge. The thrift is concerned that interest rates might rise. A rise in rates would result in an increase in the thrift's cost of CD funding for its mortgage assets. The appropriate strategy is to sell a sufficient number of interest rate futures, using either T-bond futures or mortgage futures. The Chicago Board of Trade (CBOT) discontinued its GNMA futures contract, but new mortgage-based futures are being introduced. For simplicity, suppose that a futures contract on 30 year mortgages exists. This is the "contract" that will be used to illustrate the futures hedge. The goal is to determine the appropriate number of futures to sell short so as to precisely offset any change in rates and preserve the present value of the asset/liability rate spread.

There are a number of difficulties in determining the appropriate number of mortgage futures to sell. First, if changes in the CD rate are not perfectly correlated with changes in the mortgage rate, hedging will be inexact at best. Second, the hedge ratio is not stable over time - as the mortgages age, the hedge ratio will need to be recalculated. The latter problem is addressed first.

The hedge ratio can be estimated using any of the various hedge ratio models - depending on the analyst's preferences. The most versatile approach is the dollar value basis point (DVBP) model. The "dollar value of a basis point" is defined as the change in the market value of $100 of face value debt for a one basis point change in the instrument's yield. To begin, the DVBP of the debt instrument to be hedged is divided by the DVBP of the instrument underlying the futures, regarded as the futures DVBP. This ratio is then multiplied by the yield beta ([...sub.y]). The yield beta is the ratio of the change in the yield of the instrument to be hedged and the change in the yield of the hedging instrument. This yield beta is found by simple linear regression [8, Chapter 12]. The product of the DVBP ratio and the yield beta is then the hedge ratio. The dollar size of the hedge is: [Mathematical Expression Omitted] The dollar size of the hedge is then translated into a specific number of futures contracts by dividing by the face value of a single futures contract: [FV.sub.hedge] =[FV.sub.cash] x DVBP(cash)/DVBP(futures) x [Beta.sub.y.sup.*]

(2)

To continue with the example, the DVBP of the mortgages held in the mortgage portfolio is calculated, which, as it happens, is $0.068. Next, the DVBP of the futures is calculated. Suppose the futures DVBP is $0.085. Next, the yield beta between the 20 year mortgage rate (the mortgages held by the thrift) and the rate on the mortgages underlying the futures is estimated. Suppose now that the beta is 1.06, that is, for each one basis point change in the yield of the thrift's mortgages is expected. in the yield of the thrift's mortgages is expected. The initial hedge for the thrift's position is then:

[FV.sub.hedge] = $25 million x $0.068/$0.085 x 1.06 (4) = $21.35 million = 214 futures.

At the time of the first refunding, the thrift would recalculate the size of the hedge based on its new level of mortgage principal, the new values of the DVBPs, and the yield beta for 19.75 year mortgages, as opposed to the earlier 20 year mortgages. This process would be repeated every three months and the size of the futures hedge adjusted accordingly.

The hedge is very effective, provided that all yield changes in the CD rate are matched by identical changes in the mortgage yield. That is, if three month CD yields rise by one basis point, the 20 year mortgage yield must also rise by one basis point. Later, after the first refunding, a one basis point change in CD yields must be matched by a one basis point change in 19.75 year mortgage yields. Although this is not a realistic scenario, consider the outcome as if it were and suppose that immediately after the mortgages were acquired (while the mortgages still have a 20 year life), rates rise by one basis point. The next CD refunding is then expected to cost 8.01 percent (up from eight percent). The present value of the mortgage/CD rate spread declines by $17.10 thousand. This is completely offset, however, by $17.10 thousand profit on the futures hedge.

There is, however, an inconsistency in the assumptions. It was assumed that, on average, the yield on a 20 year mortgage changes by more than the yield on 30 year mortgage futures (yield beta was 1.06). Yet, parallel shifts were assumed in three month CD and 20 year mortgage yields and every mortgage maturity less than 20 years. The reality, of course, is that short term rates and long term rates are not equally volatile. The size of the hedge must be adjusted to account for this difference in volatilities.

The first step in the adjustment is to calculate what will be called an "adjustment beta." The adjustment beta ([Beta.sub.a]) is the ratio of the change in the three month CD rate to the change in the 20 year mortgage rate. This is estimated in the same manner as the yield beta. To continue, suppose that the adjustment beta is found to be 1.35. This suggests that for each basis point change in the 20 year mortgage rate, the CD rate can be expected to change by 1.35 basis points, typical of the greater volatility of short term rates.

The final step is to adjust the size of the hedge to reflect the difference in yield volatilities. This is accomplished by multiplying the face value of the hedge obtained with the DVBP model by the adjustment beta. The full hedge model is:

[FV.sub.hedge] = [FV.sub.cash] x DVBP(cash)/DVBP(futures) x [Beta.sub.y] x [Beta .sub.a] (5) = $21.35 million * 1.35 = $28.82 million = 288 futures.

Thus, the thrift can hedge by selling 288 mortgage futures at the time the mortgages are acquired. The full set of cash flows (excluding principal flows) associated with this strategy is depicted in Figure 5 on page 44.

At the time of each refunding, the thrift would recalculate all five of the variables which enter into the determination of the optimal hedge: [FV.sub.cash], DVBP(cash), DVBP(futures), [Beta.sub.y], and [Beta.sub.a]. All other things being equal, [FV.sub.cash], DVBP(cash), and [Beta.sub.a] will decline with the passage of time; [Beta.sub.y] will rise; and DVBP(futures) will not change. The combined effect is such that the size of the hedge decreases with each refunding. Of course, the futures used in the hedge are of limited term, so the thrift will need to periodically roll forward into later delivery futures. The strategy requires a balancing of the frequency of rollover against the liquidity of the instrument. The near delivery futures will typically be more liquid and thus involve less liquidity cost, but, at the same time, necessitate more frequent rollover and thus involve greater transaction costs.

The hedge strategy presented here is neither perfectly effective nor costless. Like most futures hedging, there will be some basis risk as the various yields involved in the hedging model fluctuate in a less than perfectly predictable manner. The futures hedge is therefore less effective than the nearly perfectly effective swap hedge. Nevertheless, the futures hedge may still be preferable. The swap hedge is quite costly - resulting in a considerable forfeiture of present value. The futures hedge may be less costly [8, Chapter 12]. If so, the trade-off is one of efficacy against cost. The comparative efficacies and costs of the swap hedge and the futures hedge are empirical issues. No effort is made to address these issues here, but this is clearly an area ripe for study.

Considerations for

the Optimal Hedge

There are two other considerations in the choice of the hedging instrument. The first involves intermediate cash flows engendered by the hedge. The second involves mortgage prepayments.

Daily marking-to-market of futures will necessitate the regular transfer of variation margin to and from the margin account of the thrift. There are no comparable intermediate transfers of funds with a swap hedge. This would seem to suggest a preference for the swap hedge. This conclusion, however, is premature. Assuming the futures hedge behaves perfectly, the precise amount of the margin transfer out (in) of the thrift's account will be matched by an increase (decrease) in the present value of its rate spread. Suppose, for example, that interest rates decline. Margin will be transferred from the thrift's margin account, since it is short futures. At the same time, the decline in the cost of the thrift's CD liabilities will result in an increase in the value of the rate spread. Thus, as long as the thrift has sufficient liquidity to meet its margin requirements, these intermediate cash flows should not be an overriding consideration.

The second, and far more significant, consideration is mortgage prepayment by mortgagors. Conventional mortgage indentures typically allow the mortgagor to prepay the mortgage principal without penalty after some initial period. Mortgages are prepaid for a variety of reasons.[6] The more unpredictable the prepayment rate, the greater the advantage of futures hedging over swap hedging.

Suppose that immediately after acquiring the mortgages and entering into a swap with a swap dealer, interest rates decline and $2 million of mortgage debt is prepaid. The thrift can easily adjust its liabilities by simply refunding $2 million less in the next sale of CDs. The swap hedge, however, is not so easily adjusted. In fact, unless very special provisions have been included in the swap agreement to allow the thrift to amortize the swap more quickly, the thrift will, quite likely, be locked into the swap.

In such a situation, the portion of the swap no longer covering actual mortgages becomes a speculation and exposes the thrift to precisely the kind of interest rate risk the thrift entered the swap to avoid. One solution is to negotiate a cancellation of a portion of the swap principal with the swap dealer. As a general rule, the swap dealer will oblige but only if adequately compensated. Alternatively, the thrift could default on the swap. A default would bring the swap default provisions into play. These provisions require the thrift to indemnify the swap dealer for the cost of securing a replacement swap [9, Chapter 4]. A default will, of course, damage the reputation of the thrift and make subsequent hedging more difficult.

A swap can be written with a provision granting the thrift the option to accelerate the amortization of the swap principal. This option has value, however, and the swap dealer will not grant it without compensation - which in turn further reduces the profitability of holding a mortgage portfolio.

The prepayment problem is minimized with the futures hedge. The thrift can simply lift a sufficient portion of its futures hedge to offset the portion of the mortgages which have been prepaid. However, since the greatest number of prepayments is likely to occur when interest rates decline and the mortgagors can prepay without penalty, the mortgage principal received may not be sufficient to cover the loss on the futures hedge. Nevertheless, the ability to easily offset the futures hedge, in whole or in part, allows the thrift to minimize this source of uncertainty. To protect against a decline in rates and accelerated prepayments, the thrift might couple the futures hedge with an appropriate position in interest rate options. Several forms of interest rate options could be used for this purpose, including call options on interest rate futures, call options on a debt instrument, and over-the-counter interest rate floors[6].

An alternative solution to the prepayment problem is to use a mixed hedge - part swap and part futures. The swap portion can be used to cover that amount of mortgage debt not likely to be prepaid and the futures hedge can cover the rest.

Endnotes

(1) Thrifts are also candidates for asset/ liability management strategies on which much has been written. Examples include McNulty [10], Kaufman [5], Toevs [13], and Gardner and Mills [4]. For an extensive bibliography on gap analysis through 1983, see Sinkey [12]. For a discussion of the relationship between gap analysis and futures hedging, see Belongia and Santoni [1]. Nevertheless, the nature of the thrift's core business renders asset/liability management solutions inadequate at best.

(2) In most cases, residential mortgage debt of the type held by thrifts will involve monthly rather than quarterly payments. However, little is lost by the quarterly payments. The cash flow diagrams and analysis are simplified a bit by this assumption without any fundamental damage to the realism of the example.

(3) The amortization schedule was generated using A-Pack: An Analytical Package for Business from MicroApplications. This IBM-based software package encompasses a great many analytical techniques frequently employed in the various business disciplines. It has many applications in the design of hedging strategies. Interested parties can call MicroApplications directly at (516) 821-9355.

(4) Average life is used by swap dealers to equate the maturities of nonamortizing Treasury debt and amortizing mortgage debt. For a discussion of the measurement and use of average life in pricing the fixed rate side of swaps, see Marshall and Kapner [9].

(5) The T-bond rate is a semi-annual rate while this particular example involves quarterly payments and thus a quarterly compounded rate. This necessitates a conversion from semi-annual rate to its quarterly compounded equivalent. For purposes of this example, the adjustment is not made. The adjustment process is discussed in Marshall and Kapner [9], Chapter 3.

(6) The prepayment rate is the percentage of the mortgages on which the mortgagors elect to prepay the principal during some defined period of time. Some of the factors which cause prepayment are highly predictable. These include such things as the death of the home owner, the sale of the home, and foreclosure. The most important of the less predictable factors is the general level of interest rates. A decline in rates will lead to some refinancings; thus, the greater the decline in interest rates the higher the prepayment rate.

References

[1.] Belongia, M.T. and G.J. Santoni. "Hedging Interest Rate Risk with Financial Futures: Some Basic Principles." Review, Federal Reserve Bank of St. Louis, October 1984. Reprinted in Wilcox, J.A., ed. Current Reading on Money, Banking, and Financial Markets. Boston: Little Brown, 1987.

[2.] Block, S.B. and T.J. Gallagher. "The Use of Interest Rate Futures and Options by Corporate Financial Managers." Financial Management, Autumn 1986.

[3.] Booth, J.R., R.L. Smith, and R.W. Stolz. "The Use of Interest Futures by Financial Institutions." Journal of Bank Research, Spring 1984.

[4.] Gardner, M.J. and D.L. Mills. "Asset/ Liability Management: Current Perspectives for Small Banks." The Journal of Commercial Bank Lending, December 1981.

[5.] Kaufman, G. "Measuring and Managing Interest Rate Risk: A Primer." Economic Perspectives, Federal Reserve Bank of Chicago, January/ February 1984.

[6.] Kapner, K.R. and J.F. Marshall. Swaps Handbook: Swaps and Related Risk Management Instruments. New York: The New York Institute of Finance, 1990.

[7.] Loeys, J.G. "Interest Rate Swaps: A New Tool for Managing Risk: Review of Business, Federal Reserve Bank of Philadelphia, May/June 1985. Reprinted in Wilcox, J.A., ed. Current Reading on Money, Banking, and Financial Markets. Boston: Little Brown, 1987.

[8.] Marshall, J.F. Futures and Option Contracting: Theory and Practice. Cincinnati: SouthWestern, 1989.

[9.] _____ and K.R. Kapner. Understanding Swap Finance. Cincinnati: South-Western, 1990.

[10.] McNulty, J.E., "Measuring Interest Rate Risk: What Do We Really Know?" Journal of Retail Banking, Spring/Summer 1986. Reprinted in Wilcox, J.A., ed. Current Reading on Money, Banking, and Financial Markets. Boston: Little Brown, 1987.

[11.] Quinn, L.R. "How Corporate America Views Financial Risk Management." Futures, January 1989.

[12.] Sinkey, J. Commercial Bank Financial Management. New York: Macmillan, 1983.

[13.] Toevs, A. "Gap Management: Managing Interest Rate Risk in Banks and Thrifts." Economic Review, Federal Reserve Bank of San Francisco, Spring 1983.

PHOTO : Figure 1 Initial Exchange of Principals and Documents

PHOTO : Figure 2 Cash Flows at Time of First Mortgage Payment

PHOTO : Figure 3 Interest Rate Swap with Swap Dealer

John F. Marshall is Associate Professor of Finance at St. John's University in Jamaica, New York and a risk management consultant for several leading financial institutions.

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Title Annotation: | hedging and financial managers |
---|---|

Author: | Marshall, John F. |

Publication: | Review of Business |

Date: | Dec 22, 1990 |

Words: | 4463 |

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