Hedging Performance of GNMA Futures Under Rising and

Falling Interest Rates Joanne Hill Joseph Liro

Thomas Schneeweis

his study is concerned with the effectiveness of GNMA futures as a hedge for T mortgage bankers and other issuers and- holders of mortgage-backed securi- ties. Since the effectiveness of minimum-risk hedge ratios may differ under various financial market conditions, the optimum size of futures positions is analyzed for (1) periods of rising versus falling interest rates, and (2) the effect of the Federal Re- serve's policy change in October 1979 toward greater use of monetary aggregates as targets. The results show that minimum-risk hedge ratios differ significantly under rising and falling rate conditions, as well as for pre- and post-October 1979 periods.

The GNMA market consists of mortgage-backed certificates guaranteed by the Government National Mortgage Association, These certificates represent market- able shares in pools of Federal Housing Administration and Veterans Administra- tion mortgage loans. The GNMA futures contract traded at the Chicago Board of Trade has a principal amount of $100,000, a stated interest rate of 8%, and an as- sumed 12-year maturity of deliverable GNMAs. A futures hedge is usually initiated by buying (selling) futures contracts and terminated by closing out the position when the spot market transaction occurs. The position is usually closed by selling (buying) the contract in the futures market rather than taking delivery.

Mortgage bankers may reduce part of their interest-rate risk exposure between the time of loan commitments and the marketing date of the GNMA or conventional mortgage pool by selling GNMA futures.' Pension funds, insurance companies,

'Usually the GNMA yield at issue L 50 basis pointr above that of mortgages in the pool For intermediation the banker keep 44 of these p i n & GNMA 6. The object of hedging is to protect this intermediation revenue.

Joanne Hill is an Associate Professor at the University of Massachusetts, Amherst.

Joseph Liro is an Assistant Professor at the University of Massachusetts, Amherst.

Thomas Schneeweis is an Associate Professor at the University of ilfmsachusetts, Amherst.

The Journal o l Futures Markets. Vol. 3. So. 4,403413 (1983) .S I983 by John Wile! & Sons. Inc. CCC 02iO-73 lli8310403- I 1502.10

and banking institutions that hold mortgage portfolios can offset short-term losses in principal value by selling GNMA futures contracts. These same institutions may also wish to buy futures now because they anticipate a future purchase of mortgages under interest-rate conditions that may be less favorable than those currently pre- vailing. Risk is reduced to the extent that the gain in the futures position offsets the losses in the vdue of the mortgage portfolio.

In the first part of the analysis hedging effectiveness and minimum-risk hedge ratios for GNMA futures are determined using weekly GNMA spot prices and GNMA futures prices. Minimum-risk hedge ratios and their effectiveness are then analyzed with respect to three dimensions. First, separate minimum-risk hedge ra- tios measures are determined for periods of rising and falling interest rates. Sec- ond, the measures are examined across two subperiods, separated by a major Fed- eral Reserve Board policy change. Third, the risk-reduction measures are examined across futures contracts with different numbers of weeks remaining to delivery.

I. DETERJILTATION AND STABILITY OF

The effectiveness of a hedged cash position is dependent on the size of the futires position and the degree of correlation between changes in the vaiue of cash posi- tions and changes in futures prices over the hedging period. In a particular hedg- ing period the comovement between GNMA future and GNMA spot positions may not be perfect for several reasons. First, the GNMA portfolio being hedged may not consist of the particular GNMA securities that are the cheapest to deliver to fulfill the futures contract at the same time as the hedge? Second, each GSJU pool of se- curities or portfolio of GNMA pools has its own maturity characteristics that influ- ence changes in value over time. Third, the futures price is influenced by factors that do not necessarily affect the spot GNMA price? These factors include fmanc- ing costs, changes in the cheapest deliverable GNMA pool, the opportunity costs of posting variation margin, and expected changes in the supply and demand for GNMA securities between now and delivery of the futures. Fourth, random and in- dependent price changes may occur in each market over time.

Ederington (1979) was among the first to analyze the hedging effectiveness of GNMA futures. In his study of the US. Treasury bill and GNhiA futures markets, Ederington concluded that it was possible to eliminate, on average, approximately 75% of the risk of price changes accompanying cash.positions in GNhLb or T bills

HEDGLiG EFFECTIVEMSS

'The Chicago Board of Trade has compikd a set of factors that adjust the principal amount olGNMAs required for delivery to compensate those who deliver GSJUs with coupon rates other than 8%. For example, an 11 7% CNMA certificate has a factor of 0.817439 or requires 581,713.90 principal amount for deliver?.. In eschaage the deliverer receives the settlement price. If the deliverer cannot buy 11 % CNMAs at a price of a t least the (setdement pricelad- justed principal amount) there will be P loss on delivery. Therefore, at any point in time the cheapest GNMA to deliver would be the certificate for which the following difference is the smallest (or most negative)

current futures price

(factor x S100,ooO) for x% coupon

Current GNYA price for xo/. coupon -

The d u e of GSJI.4 futures would then be most influenced by supply-and-demand conditions in the market for this particular Gi'ihIA coupon.

3Futures prices retlect levels and changes in financing costa of the underlying instrument because futures are in effect an alternative to purchasing the instrument today and carrying it until the deliver?. date and thereby incurring the financing chaiges.

404 / HILL LIRO. .OD SCHSEEU'EIS

with the nearby GNMA or T-bill futures contract over a Cweek hedging period. Us- ing a similar methodological approach, Hill and Schneeweis (1980,1982) examined the value of GNMA futures as hedges for corporate bond portfolios. Roughly 60- 75% of the monthly price change variance of highquality corporate bond indices was shown to have been e l i a t e d via GNMA futures held at the minimum-risk hedge ratio.

Drawing on the work in the area of commodity hedging by Johnson (1960) and Stein (1%1), Ederington showed that this minimum-risk hedge ratio and hedging effectiveness are related to the covariance or correlation between spot and futures price changes and the variance of futures price changes over the period of the hedge. This hedge ratio can be interpreted as the weight of the futures position in a portfolio consisting of both spot and futures positions or the proportion of the pre- determined spot position that is hedged.

The function below, which describes the variance of the hedged portfolio, can be minimized with respect to X, to find the size of the futures position ha t provides the least amount of risk exposure.

(1)

where CH, is the change in the value during period t of the hedged spot position, C,,, C, are the value changes during period t of the spot position and futures contracts, respectively, Xfis the proportion of the portfolio held in future contracts; X; would equal the optimal hedge ratio (HR*) with Xf < 0 representing a short posi- tion and X, > 0 a long position in futures.

(2)

(3) The optimum hedge ratio is, therefore, equivalent to the negative of the slope coef- ficient of a regression of spbt price changes on futures price changes.

The use of absolute price changes instead of the percentage change in value (returns) is warranted because of the unique circumstances associated with the hedging decision in the portfolio model. The fvst circumstance relates to the objec- tive of a futures hedging strategy. This objective is to minimize potential losses from a predetermined,frxed position of GNMA security pools. The futures position should not be viewed as a substitute for a GNMA cash position. Rather, futures are combined with the cash position to minimixe losses in value of this cash position. Therefore, effective hedging depends on the amount of covariance between value changes of the cash securitp and the futures?

A second basis for the reliance on price change versus returns is that the futures positions have no initial or investment value and thus do not provide returns on in- vestment in the normal sense. The only costs associated with futures hedges are transaction costs, opportunic costs in funds provided as margin before gains on the cash position are realized, and costs associated with basis risk? As a result of

min Var(C&) = Var(C,,) + X,?Var(C,) + zy/Cov(C,,, C&

svar(c,,ysx, = 2X/Var( Cf) + 2 cov (C3, C/) = 0, X' = Cov(C,, C/)Nar(C/) = HR*.

?his implies that according to the pordolio approach to the hedging decision a S1 change in the value of the cash position brings the investor the same change in utility regardlesa of the size of this position. The focus is the futures snategp that bat offsets this $1 loss. For further dseusaion of the problems in using percentage changes see Grauer. F., and Rentzler. J. (1980): "Are Futures Contracb Risky," Proceedings ofthe First Annual Sponsors Conference, Center for the Study of Futures Jfarkeu. Columbia University.

'Basis risk refers to the fact that in a world of imperfect foresight gains and losses on cash and futures positions may not offset each other esactly in evey period.

HEDGING PERFORMANCE OF GNMk /do5

the problems in determining an appropriate investment base, Black (1976) and McEnally and Rice (1979) advocate the use of price changes instead of a return formulation.

The measure of hedging effectiveness (E') for the minimum-risk hedge is de- fined as the proportional reduction in the variance of changes in the value of the cash position that comes from maintaining the hedge ratio determined above rather than holding an unhedged position (XI = 0). E' is the coefficient of determination for the regression of spot price changes on futures' price changes used to estimate HR*.

To the extentthat the variances and covariance are stable, historical data can, therefore, be used appropriately to help solve for the minimum-risk hedge ratio and to estimate its potential effectivness in reducing the variability in spot price changes. Hedge ratios and hedging effectiveness, however, may shift over time, due to changes in market conditions and in market participants. Ratios and effec- tiveness may also vary for contracts with different times to delivery.

The correlation structure of price changes could shift over time as a function of the direction of interest-rate movements and their impact on various participants in the futures market. Those with long positions in mortgages would tend to in- crease their hedging activity when they anticipate increases in interest rates above those anticipated by the market. The opposite behavior would be expected of those with short positions. The relative amount of hedging participation and the extent of cash futures arbitrage in the rising and falling interest-rate market could impact hedge ratios. In addition, as GNMA yields change direction, the cheapest deliver- able instrument may change and thereby alter hedging effectiveness.

If significant differences in hedging effectiveness and hedge ratios are shown to occur in rising versus falling rate environments, both passive and selective hedgers of mortgage rate risk would want to incorporate these differences in their hedging strategies. A passive hedger is one that maintains a continuous futures hedge be- cause of the desire to eliminate all exposure to fluctuations in mortgage rates. Cer- tain segments of the real estate and construction industries on both the buy and sell sides would be examples of such hedgers. If hedging effectiveness and ratios shift over the economic cycle, appropriate changes would need to be made in the size of their futures position over time.

Selective hedging would be done by economic units that are using the futures market as an alternative to liquidating or investing in a cash position in mortgage instruments based on some interest-rate forecast. These hedgers, primarily finan- cial institutions, would be interested in the hedge ratio that is most relevant to the interest-rate sc.knario that they envision occurring. It is true that the mere exis- tence of different optimal hedging strategies in rising versus falling rate markets does not assure selective or passive hedgers that they will be able to capitalize on these differences in the futures. Such differences need to be stable, and hedgers need to be able to identify the general direction in which rates will move over the hedging period. Selective hedgers, being involved directly in fEed-income security

406 / HILL URO. AND SCHSEEWEIS

markets, may be most skilled at predicting mortgage-rate directions and thus find the results of this analysis particularly useful.

Minimum-risk hedge ratios and hedging effectiveness may also change over time due to structural changes in the ked-income markets which affect the volatility of spot price change. One such change occurred in October 1979 when the Federal Reserve announced that monetary policy would be based primarily upon monetary aggregate targets and that monetary policy would not be used to influence general interest-rate levels to the extent it had in the past. The effect of this policy change was to create much greater volatility of short-term rates. Increased volatility in spot GNMA prices and short-term rates should affect the volatility of prices of futures contracts. Increased volatility of daily interest rates, due m part to the Federal Re- serve's new policy targets, is transmitted to futures prices through the implied ex- pected financing costs of spot GNMA positions. An increase in interest-rate volatil- ity, whatever the source, should increase the incentive to use futures hedges and, thus, should increase participation in the relevant futures market.

In addition to a changing economic environment, the term to delivery of the fu- tures contract may be associated with different levels of hedge ratios and hedging performance. At any point in time, several GNMA futures contracts are available calling for delivery at %month intervals. The contract closest to delivery typically has the largest trading volume. This is true until the contract gets very close to de- livery, at which time participants who do not wish to execute delivery have closed or are closing out their positions. For this reason futures price movements of con- tracts close to delivery are affected by supply-and-demand factors unique to the nearby contract6

II. DESCRIPTION OF DATA AND HEDGING RESULTS

Data Set and Statistical Methodology

The data set of futures price changes includes weekend to weekend contract value differences beginning with the first Friday of January 1977 and ending with the closing price of the last Friday in 1980.' Price changes for each contract are grouped according to the number of weeks remaining to delivery (e.g., the June 1977 contract last trades on the third Wednesday of June, the prior Friday's settle- ment price is reflected as the price with one week remaining to delivery).

For corresponding weeks, futures price changes are matched with GNMA cash price changes (8% coupon). Ordinary least-square (Ow regressions of GNMA spot price changes on contemporaneous GNMA futures price changes provide esti- mates of hedging effectiveness (R2) and minimum-risk hedge ratios (regressionco- efficient on spot price). To determine if estimated hedge parameters differed with respect to time to delivery, separate regressions are run for price changes on con- tracts with 5-8,9-13,14-17,18-21, and 22-26 weeks remaining to delivery.6

6The CNMA certiiicate delivery futures trade for the laat time 5 businesa dap before the delivery day, the busi- nesr day closest to the 16th of tbe conbact month.

'The source of the tuturer price data was the daily Coturer price tapes made available by the Chicago Board of Trade. The source of the GNMA 8% coupon spot prices waa the Chicago Board of Trade Statistical Annual (1977-1980).

BRiee changes for contracts with 4 or less m e h remaining to delivery were dropped from the dataset It was felt there observations were too dose to delivery to be useful in assessing hedging potential.

HEDGINC PERFORMANCE OF C N W /407

The data set is also divided into observations before and after October 1979. In October 1979 the Federal Reserve Board announced the policy change of targeting monetary aggregates instead of interest rates. Observations are also segmented by the sign of the GNMA price change. This divides the data set into observations from weeks in which yields were rising (prices falling) and from weeks in which yields were falling (prices rising). Of the 315 possible futures price changes in the data set, 181 occurred in weeks in which GNMA yields rose, 118 occurred in weeks in which GNMA yields fell, and 16 occurred in weeks in which there was no change.9

Two types of statistical analysis are used to compare estimated levels of hedge ratios and effectiveness across subsets of the sample. First, separate OLS regres- sions are estimated.for each subset of the sample to determine minimum-risk hedge ratios and effectiveness measures. Neter and Wasserman (1972) provide a proce- dure for estimating a confidence region for coefficients of determination (Rz). This procedure is used to analyze the significance and the stability of the hedging effec- tiveness measures.10

The second test permits statistical comparison of hedge ratios over different market conditions.l' Two sets of slope a d intercept terms, along with an interac- tion term, are added to the regression model to compare the several subsets of data under analysis. This procedure was first suggested by Gujarati (1970) and facilitates the testing of the hypotheses that hedge ratios are equal under rising versus falling GNMA rates and before and after October 1979. The full model estimated becomes

c, = a0 + a1 D(I ) + azD(T) - 013 ~ ( O W 9 + P I c, + 8 2 D ( W f + P 3 D(T)Cf + P 4 W) ~ ( T ) C f ,

where

C,, Cf = change. in GNMA spot and futures prices, D(Z) = 1 if C, < 0 (GNMA rates rose)

= 0 if C, > 0 (GNMA rates fell), D ( T ) = 1 if observation is after October 1979

= 0 if observation is before October 1979.

If the coefficient & or P3 is significant, a shift in the hedge ratio is indicated after Oc- tober 1979 (&) or in periods of increasing GNMA yields 92). The coefficient p4 represents the interaction between the post-October 1979 period effect and the ris- ing GNMA yield effect.

?here are more observations (315) than weeks in the period (208) because in several instances two CNMA fu- tures contracts qualied for inclusion in the sample during a particular week, e.g., when the March contract has 5 weeks remainiig to delivery. the June contract has 18.

'('l'wo levels of hedging effectiveness are said to differ if their confidence regions do not overlap. This test re- quires a transformation of the sample correlation coefficient (r) as follows:

Z' = (V2) lo& ( I + r/ l - r), G(Z) = ( Ih) - 3

to produce a confidence region around the mean of the distribution of (2')M [Z' - Z(1 - a/2).(Z')]2 5 p2 s [Z' + Z(1 - a/2)IJ(Z~)]2.

(The confidence limits are squared to determine limits for the coefficient of determination.) "Yo ex post hedging tests on the post-October 1979 period were conducted because of insufficient data at

the time this study was completed. Other expost tests of hedging effectivenesa for CNMA futures using holdout periods (Hill and Schneeweis, 1980, 1982) show a high correspondence between expected and realized hedging performance.

408 / HILL LIRO. AYD SCHSEEWEIS

Empirical Resuits and Analysis

A comparison between hedge ratio and hedge effectiveness estimates based on the full data set and selected subsets of the data is presented in Table 1. Results are re- ported for observations segmented by weeks remaining to delivery as well as for the full data set. Examination of these results leads to several points that are worthy of further discussion.

Table I EEDGE RATIOS AND EFFECTIYENFSS ESTIMATES

(WEEKLY GNMA SPOT AhD FUTURES PRICE CHANGES)

~

Full data set (1977-1980)

5-8 9-13

14-17 18-21 22-26

All

1977-September 1979 5-8 9-13

14-17 18-21 22-26

All

November 1979-1980 5-8 9-13

14-17 18-2 1 22-26

All

GNMA rates rising

GNMA rates falling

5-8 9-13

14-17 18-21 22-26

,411

5-8 9-13

14-17 18-2 1 22-26

A1

0.90 0.75 0.68 0.83 0.88 0.81

0.82 0.80 0.74 0.81 1.10 0.90

0.91 0.74 0.66 0.84 0.79 0.78

0.74 0.48 0.44 0.63 0.70 0.58

0.85 0.97 0.63 0.73 0.93 0.82

0.86 58 0.56 73 0.7 1 58 0.66 60 0.64 65 0.66 315

0.72 44 0.70 53 0.70 41 0.73 44 0.73 44 0.71 226

0.90 14 0.55 20 0.72 17 0.65 16 0.61 20 0.65 88

0.54 35 0.38 46 0.47 25 0.47 35 0.46 39 0.43 181

0.92 21 0.62 23 0.58 30 0.59 22 0.67 22 0.66 118

HEDCINC PERFORMANCE OF G S M ~ / 409

Based on all available data, hedges of GNMA positions using the minimum-risk hedge ratio provided an average reduction in variability of from 56 to 86%. In the month prior to the delivery month the effectiveness of the hedging strategy was sig- nificantly higher (86%) than during other subsets of time to delivery for the GNMA futures contract. In addition, the estimate of the hedge ratio tends to be higher in the month prior to delivery than in preceding months. These larger hedge ratios and levels of effectiveness for the nearest weeks to delivery occur because the fu- tures contract becomes more simiiar to the deliverable GNMA security as the GNMA futures contract nears delivery. Therefore, near-delivery GNMA futures re- flect more closely the price movements of the GNMA security.

In addition to time-to-delivery effects, changing market conditions can alter min- imum-risk hedge ratios and hedging effectiveness measures. Table I1 presents re- sults concerning the effectiveness of pursuing a minimum-risk hedging strategy when the Federal Reserve’s October 1979 policy initiatives and GNMA rising and falling market conditions are both taken into account. The difference in the perfor- mance of a hedging strategy, as measured by the coefficient of determination, in rising and falling rate environments is statistically significant. Prior to October 1979 there was no statistical difference in hedging effectiveness measured over weeks when rates fell (45%) versus the effectiveness during weeks when rates rose (60%). After the policy change at the Federal Reserve Board, a marked decrease occurred in the effectiveness of hedging during periods of rising rates (60-23%). Concurrently, the hedging effectiveness of a long futures position, a position that reduces losses on falling GNMA rates, improved from 45% during the pre-October

Table I1 COMPARISON OF HEDGING EFFECTIYENESS

*&: No Difference in Hedging Effectiveness

Hedging Effectiveness Levels u = 5% u = 10%

Pre-October 1979 versus Post-October 1979

Rising versus falling GNMA rates 0.71 0.65 Accept

0.43 0.66 Reject

Pre-October 1979 Period Rising versus falling GNMA rates 0.60 0.45 Accept

Rising versus falling GNMA rates 0.23 0.61 Accept

Pre-October versus post-October 1979 0.60 023 Reject

Pre-October versus post-October 1979 0.45 0.6 1 Accept

Post-October 1979

Ruing GNMA rates

Falling GIVMA rates

Accept

Reject

Accept

Reject

Reject

Accept

410 / HILL, LIRO. AYD SCHSEEWEIS

1979 period to 61 % during the post-October 1979 period; however, this difference is not large enough to be statistically significant.

A Gujarati test was used to detect differences in the magnitude of the minimum- risk hedge ratios (HR*) before and after October 1979. Results of estimation of Eq. (6) are shown in Table 111. The model is estimated for the entire data set with dummy variables for both the pre- and post-October 1979 periods, D ( Q and for rising versus falling rate market conditions, D(1). In addition, the model with only the pre- and the post-October 1979 dummy vari-

ables is estimated on subsamples differentiated by the direction of GNMA yield movements. The coefficient of D(T)Cj is not significant when Eq. (6) is estimated for the overall sample +dicating that the size of the hedge ratio remains statisti- cally indistinguishable for pre- and post-October 1979 periods. It is clear, however, that the combination of rising rates and the post-October 1979 period does affect the size of the minimum-risk hedge position. This is demonstrated by the signifi- cantly negative coefficient of D(I)D(T)C' By adding the appropriate coefficients from column 1 of Table 111, an estimate of the minimum-risk hedge ratios can be determined under both rising and falling rates after October 1979. Under condi- tions of rising GNMA rates in the post-October 1979 period, the minimum-risk hedge ratio represents 34% of the value of the GNMA position. The 34% estimate for the weeks of rising interest rates is the summation of the coefficients associated with the variables C, D(Z)C' D(T)C' and D(I)D(T)Cf In weeks when rates are fall- ing, a minimum-risk futures hedge therefore would have required almost twice the number of contracts or (68 vs. 34%) in weeks when rates are falling than when rates are rising. The minimum-risk hedge ratio of 68% for weeks of falling GNMA yields is the summation of the coefficients of Cfand D(T)Cfonly.

Table 111 RESULTS OF HEDGE RATIO ESTIMATION WITH DURlMY VARIABLES

FOR RATE DIRECTION .4ND TIME PERIOD

Variables

OLS Regression Coefficients.

Rising GMIA Falling GNMA All Data Rate Data Rate Data

0.570 0.907 0.615 (4.07) (4.64)b (1 0.03)

D(I)Cf 0.336 (2.16)

D(T)Cf 0.114 - 0.565 0.137

Cf

(0.86) ( - 5.29) (0.84) DU)D(T)Cf - 0.680

(- 3.91) Multiple R2 0.765 0.545 0.689 DW statistic 2.27 1.91 1.88 So. of observationse 315 181 118

'Intercept coefficients are not shown. 'Numbers in parenthesis are I-statistics. The number of observations in for AU Data includes weeks in which CNM.4 rates did not change.

111. CONCLUSION The usefulness of futures hedging as a means of reducing the variability of income streams due to changes in mortgage interest rates is becoming increasingly clear to participants in the primary and secondary mortgage markets. Results of this study confirm the value of using GNMA futures to hedge. They also show that a hedging strategy and the associated hedging performance can be influenced by changing mortgage market conditions as well as by the time remaining to delivery of the GNMA futures contract. The analysis indicates that hedging effectiveness tends to increase as the delivery month of the futures contract approaches. An increase in the hedge ratio is also necessary as delivery approaches to provide the hedger with the maximum varability reduction. Hedging effectiveness tends to be relatively low during the period 14-17 weeks prior to contract delivery. These results may be at- tributed to replacement of the expiring future with the next deliverable future which has 14-17 weeks of life remaining.

The usefulness of determining hedging strategies based on simple historical price change correlations is questioned. Evidence is presented here of past instability in hedging performance and in the size of optimal hedge positions that can be associ- ated with periods in which GNMA rates are rising versus falling. Also, the post- Octcber 1979 environment, subsequent to’ the announced Federal Reserve policy of abandoning interest-rate stabilization, apparently contains some structural changes in fixed-income security markets that have reduced liedging effectiveness and optimal hedge ratios in periods of rising rates. Further analysis of post- October 1979 data is needed to reach conclusions regarding optimal GNMA fu- tures strategies for hedgers using these contracts.

The authors would like to thank their graduate research assistants Deborah Deskavich. Santosh Mo- han, and Barbara Whitney for their help in compilation of the empirical results. The authors would also like to thank the journal reviewers for their comments which have improved the presentation of this article.

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