The term structure of interest rates: evidence of market segmentation in the long end of the...

ABSTRACT

One theory of the term structure of interest rates holds that markets are segmented by maturity, with each segment offering a yield resulting from the supply/demand equilibrium. Using data from United States Treasury constant maturity series, document significant bond market

reactions to Treasury announcements of reduced supplies of 30-year bonds coupled with Treasury's debt buyback program. The results support the market segmentation theory. Supply-demand imbalances pushed bond prices up (and yields down) while the yield curve segment comprising 3-month through 5-year maturities displayed its characteristic upward-sloping shape.

1. INTRODUCTION

The term structure of interest rates is a fundamental concept in finance. Multiple theories have been proposed, yet research to date has failed to definitively explain the shape of the yield curve in the context of one of these proposed theories.

The market segmentation theory describes the yield curve as a set of maturity segments comprising participants with a business need for specific maturities. The shape of the yield curve, consequently, arises from the supply-demand equilibrium within each maturity segment. Under the segmented markets theory, participants in one segment would be indifferent to supply-demand forces in adjacent maturity segments. A variant of the segmented markets theory, the preferred habitat theory, allows for segment participants to be induced to leave their preferred habitat when there are sufficient incentives; i.e., higher yields. Empirical evidence generally supports the market segmentation theory at the short end of the yield curve (Mustafa and Rahman, 1995, Park and Switzer, 1997, Simon, 1991, and Taylor, 1992), but research is scarce for longer dated debt.

In early 2000 the United States Treasury (Treasury), responding to continuing budget surpluses, embarked on a new strategy of buying back older debt and limiting the amount of new 30-year bonds it would offer for sale. These actions represented a significant change in the expected supply quantity of long-term bonds. If the market segmentation theory holds, there should have been a market reaction to the reduction in the supply of long-term Treasury bonds and increased competition for the available bonds, causing yields to decline.

Using data from Treasury's constant maturity databases, the empirical evidence supports the market segmentation theory. Market participants responded three times to news on changing supplies of long-dated Treasury debt coupled with Treasury's repurchases of longer maturity Treasury debt. Market reactions took place first in November of 1999 following announcement of a new Treasury debt buyback plan and again in January and February of 2000 when a reduced supply of 30-year Treasury debt became evident and Treasury simultaneously inaugurated its debt buyback program. Due to Treasury's participation on the buy side and absence on the sell side, yields on long-term debt continued to under perform their forecast rates for a period of weeks in both instances while the short-term end of the yield curve continued to display its characteristic upward slope, thereby producing a dome-shaped yield curve.

2. UNITED STATES TREASURY AUCTIONS

The United States Treasury, as of 1998, had been a consistent net borrower for over thirty years. During this time interval, the U.S. federal budget had been continuously in a deficit situation. Beginning with the 1998 fiscal year (FY), however, the U.S. government began a series of annual budget surpluses. The 1998 FY surplus was $69 billion and rose to $123 billion in 1999. The expectation of continuing surpluses prompted a number of Treasury actions.

On August 4, 1999 Treasury announced a permanent reduction in its schedule of 30-year bond offerings. Instead of three times a year, Treasury kept the February and August offerings but eliminated November's offering. Treasury's recent experience had been to offer $10 billion of 30-year debt in each offering month. Also on August 4, Treasury indicated the opening of a sixty-day comment period regarding Treasury's proposed rule to allow it to buy back outstanding bonds.

Treasury's regularly scheduled debt refunding meeting took place on November 3, 1999. At that meeting, Treasury announced it was offering $25 billion of new debt to replace $29.3 billion that was coming due, but comprised of only 5-year and 10-year notes. Treasury further noted that in fiscal 1999 a net $88 billion of debt reduction took place and stated its intent to go forward with its debt buyback rule, although officials did not say whether or not buybacks would take place.

Any uncertainty surrounding Treasury's actual buyback rule implementation was eliminated January 13, 2000. That day Treasury Secretary Summers announced the beginning of its buyback program with a repurchase of as much as $30 billion in calendar 2000. Summers specified the targeted Treasury bonds for repurchase as "... debt that has substantial remaining maturity."

February 2, 2000, at its quarterly refunding meeting, Treasury announced it was again reducing its 30-year bond offerings and added that 10-year maturity offerings would be reduced as well. New 30-year bonds would only be offered in February, with smaller August re-openings of the February series. The proposed sale of 30-year maturity debt in 2000 would be reduced to half the 1999 FY level. 10-year maturity Treasury debt would only be offered in February and August with smaller re-openings in May and November of each year.

The consecutive annual budget surpluses, which prompted a change in Treasury Department refunding actions, presents an opportunity to test the market segmentation theory at the long end of the maturity structure. November 3, 1999, Treasury actually omitted, for the first time in recent experience, an offering of 30-year bonds. Given this change in supply, a potential market reaction could have occurred as reflected in the yield on the 30-year constant maturity Treasury (CMT) reported for the week ending November 5, 1999. Specifically, a reduction in the supply of 30-year Treasury bonds should have caused bond prices to increase and yields to decline. Furthermore, the announcement that Treasury would go forward with its proposed buyback program indicated to bond investors the potential for increased competition for long-term Treasury debt, making a market reaction more likely. A market reaction characterized by increasing prices and declining yields on 30-year CMTs would be consistent with the segmented markets theory of a supply/demand equilibrium existing within a given maturity segment.

A second significant market event should have been anticipated as a consequence of Treasury's announcement January 13, 2000 that it was proceeding with its debt buyback program with an emphasis on higher yield, longer maturity issues. If market segmentation exists in the long-term segment of the yield curve, yields on the 30-year CMT reported for the week ended January 14 should have declined relative to other maturities in anticipation of Treasury repurchasing long-dated debt in competition with other long-term maturity segment participants.

The third bond market reaction should have taken place three weeks later when Treasury announced on February 2, 2000 it was reducing the supply of both 10-year and 30-year bond offerings while simultaneously entering the financial markets as a purchaser of long-dated Treasury bonds, thereby affecting both supply and demand levels. The decline in the yield on the 30-year CMT reported for the week ending February 4, 2000 should be more pronounced during this event due to the simultaneous decrease in supply and increase in demand.

3. DATA AND METHODOLOGY

Using actively traded instruments of all maturities, Treasury weekly estimates a yield curve and publishes a series commonly referred to as Constant Maturity Treasury (CMT) yields. The CMT data series are used to test for market segmentation. There are a number of advantages to using Treasury bond data to examine market segmentation.

Government issued bonds have little asset-specific information that would affect prices, variables typically affecting government bond prices relate to aggregate economic information, and the release of that information is on a known time schedule (Elton, 1999). Furthermore, economic news is rapidly incorporated into government bond prices (Balduzzi, Elton and Green, 2001). Balduzzi et al detect a significant news impact on bond prices with maturities ranging from three months to 30 years; however, they also report the market adjusts to the news in a fairly efficient manner with bid-ask spreads returning to normal levels within 15 minutes.

According to the preferred habitat version of the market segmentation theory, market participants have a preferred maturity but can be induced to depart from that maturity. In the context of the preferred habitat theory, therefore, the shape of the yield curve should remain fairly stable absent any shocks that would significantly alter the supply-demand equilibrium in any one of the segments. Accordingly, the yield on a long-term bond can be approximated as the yield on a short-term instrument plus a series of risk premiums between adjacent maturity segments. The yield curve for 30-year Treasury bond maturities is approximated as:

(1) [k.sub.L] = [B.sub.o] + [B.sub.1][k.sub.3mos] + ([B.sub.i])(mr[p.sub.i])

where [k.sub.L] is the long-term yield (i.e., 30-year CMT bonds) while [B.sub.o] is a regression-determined constant and [B.sub.1] represents the coefficient associated with [k.sub.3mos], the constant maturity 3-month Treasury. The term ([B.sub.i]) represents a vector of coefficients associated with (mr[p.sub.i]), the vector of maturity risk premiums corresponding to contiguous maturity segments of the term structure.

Yields on 30-year maturities are estimated using weekly data for the thirty weeks ending April 9, 1999 through October 29, 1999, a period of generally rising yields punctuated by twenty-five basis point increases in the Fed Funds rate on June 30 and August 24. The forecast yield on the 30-year bond is then compared to Treasury's CMT yield by subtracting the forecast yield from the actual yield. Significant departures of the actual yields from the forecast yields are assessed using a cumulative probability distribution function.

4. EMPIRICAL RESULTS

Yields on 30-year Treasury bonds were approximated using the yield on the 3-month CMT and a series of maturity risk premiums corresponding to the yield curve segments of 3 to 6 months, 6 months to 1 year, 1 to 2 years, 2 to 3 years, and 3 to 5 years, plus a constant. Risk premiums for time intervals beyond the five-year CMT are not used because it is anticipated that 10-year bond yields might reflect changes in supply-demand equilibriums at the same time the 30-year bond adjusts to the reduced supply. The regression determined coefficients are displayed in Table 1.

The regression results in Table 1 show that the yields on the 30-year CMTs can be almost entirely explained as a function of the three-month Treasury bill yield plus a series of maturity risk premiums. The regression constant for the 30-year CMT reflects the maturity risk premium for the five-year to thirty-year maturity interval.

Table 2 reports the regression model forecast errors for the 17 weeks beginning November 5, 1999 and ending February 25, 2000. Over the 30-week estimation period the difference in yields (actual CMT yield minus forecast yield) for the 30-year CMT had a mean value of 0.003667% with a standard deviation of .02619%. Based on this mean and standard deviation, Table 2 contains the probability that a random value smaller (i.e., more negative) than the 'Difference' value could occur. As indicated in Table 2, there was a significant market reaction the week ended November 5, 1999. This reaction coincided with Treasury's announcement on November 3 that it was not offering any 30-year maturity bonds as part of its refunding operations and that it planned to proceed with its debt buyback program. During the subsequent two weeks the rates on 30-year CMTs significantly under performed their forecast rates.

Treasury's announcement January 13, 2000 of its intentions to go ahead with its buyback program was greeted with a significant reaction in the 30-year maturity segment of the bond market, as indicated in Table 2 where the forecast yield was .05% above the actual yield. The probability of a random value of that magnitude or smaller (i.e., a larger negative value) is only two percent. Bond market participants clearly perceived Treasury's actions as first affecting bond supplies in the longest maturity segment of the market even though Treasury did not indicate a date when it would commence its buyback program.

As noted previously, Treasury's November 3 announcement produced a statistically significant bond market reaction that persisted for the subsequent two weeks. In the absence of further Treasury announcements, the bond market reaction to the January 13 announcements might have been similarly short-lived. Treasury's February 2, 2000 announcement of further reductions in the sale of new 30-year Treasury debt coupled with the announcement of immediate implementation of Treasury's debt buyback program, however, produced a significant change in the supply-demand equilibrium. Table 2 shows the forecast yield on 30-year Treasury bonds was a full 40 basis points higher than the actual yield reported for the week ending February 4, 2000.

The empirical results reported in Table 2 support the segmented markets hypothesis. The news of Treasury implementing a debt buyback plan and simultaneous reduction in the current and future sale of new 30-year Treasury bonds altered the relative supply of and demand for bonds in the longest maturity segment of the yield curve.

5. METHODOLOGICAL ISSUES

One potential explanation for the significant results would be a lack of estimation model stability. To test for stability problems, the model estimated over the April 9 to October 29, 1999 period was used to predict the rate on the 30-year CMT for the preceding twenty weeks; i.e., the weeks ending November 20, 1988 through April 2, 1999. Over that test period, the error terms averaged -0.006% with a standard deviation of 0.0092%. Levene's Test for equality of variances produced an F statistic of 3.465 with an accompanying significance level of .069; i.e., the hypothesis of equivalence of variances for the two samples cannot be rejected. The two-tailed t-statistic of -1.016 (for assumed equal variances) has an accompanying significance level of .315. Taken together, these statistics indicate that the 30-year CMT estimation model reliably estimated the yield on the 30-year CMT for the twenty weeks preceding the estimation period. This result does not, necessarily, imply that the estimation model was stable going forward in time. It does, however, support Elton's (1999) conjecture that government bonds are useful assets for obtaining estimates of expected returns from realized returns.

A second test of model validity was conducted by revising the estimation period. Estimation periods from thirty to sixty weeks prior to the week ended November 5, 1999 were used to re-estimate the relationship given in equation 1. Each estimation model produced a statistically significant deviation (at the .05 level or better) for the week ended November 5, 1999 thereby confirming a market reaction to Treasury's announcement.

A second potential explanation for the observed decline in long-term bond yields would be a reduction in yields as a consequence of a changed central bank policy. Fuhrer's (1996) empirical results indicate monetary policy factors must be considered as they affect the term structure. Given the potential for monetary policy effects, yields should have risen in anticipation of the Federal Reserve continuing the rate hike pattern it initiated in 1999. On February 2, 2000 the Federal Reserve added 25 basis points to both the Fed funds rate (from 5.5% to 5.75%) and the discount rate (from 5.00% to 5.25%), thereby signaling a continuation of its existing monetary policy. The fact that the 30-year CMT yield declined while the Fed was raising rates tends to confirm, rather than reject, market segmentation theory since higher, short-term yields did not induce market participants to move from the longer term market segments to shorter-term segments.

The third potential contributor to the forecast yield being higher than the actual yield for 30-year bonds would be a period of time characterized by an inverted yield curve. An inverted yield curve would show a violation of the condition

(2) [k.sub.5 years] > [k.sub.3 years] > [k.sub.2 years] > [k.sub.1 year] > [k.sub.6 months] >[k.sub.3 months]

where k is the CMT yield corresponding to the subscripted maturity. During the period November 5, 1999 through February 25, 2000, the condition given in (2) above is never violated. The results confirm the lack of an inverted yield curve condition that might have caused an over-estimation of the 30-year CMT yields.

6. CONCLUSIONS

The term structure of interest rates is one of the fundamental concepts taught in many finance courses. Multiple theories have been proposed to explain the shape of the term structure, but research to date has not definitively explained which of the theories provides the best explanation for the term structure shape. One of the major theories, the market segmentation theory, suggests that the term structure is actually comprised of multiple time intervals, each with its own supply-demand relationship. The shape of the yield curve, consequently, is derived from the supply and demand equilibriums in the various maturity segments.

Using yields provided by the U.S. Treasury on its constant maturity debt instruments, market segmentation theory was demonstrated to be a viable theory for explaining the term structure of interest rates. Due to continuing budget surpluses throughout most of the 1990s, Treasury began to reduce its offering of 30-year maturity debt late in 1999. On three separate occasions Treasury announced actions that were construed by bond market participants as reducing the supply of long-term debt. These actions included two decreases in the issuance of 30-year Treasury debt during its quarterly refunding operations and the announcement of a debt buyback program that would focus on higher-yield, longer-term issues. The bond market reaction on each occasion was upward pressure on prices with the concomitant reduction in yields.

The evidence of market segmentation is even more compelling when one examines the behavior of the remaining segments of the maturity schedule. During the time period November 5, 1999 to February 25, 2000, yields on Treasury debt with maturities ranging from 3 months through five years continued to display the characteristic upward-sloping yield curve shape. During the latter part of this time period, from January 21 to February 25, yields on Treasury's 30-year constant maturity bonds were declining. Central bank monetary policy changes can be ruled out as explaining the shape of the yield curve since the Federal Reserve continued it rate increase pattern with an additional 25 basis points on February 2, 2000.

TABLE 1. REGRESSION RESULTS FOR 30-YEAR TREASURY BOND YIELDS

This table summarizes the regression results using 30-year constant
maturity Treasury (CMT) bond yields (in percentage terms) as dependent
variables. Independent variables are the yield on 3-month CMT bills
and maturity risk premiums (mrp) representing the yield difference
between the 3- and 6-month CMTs, etc. Yield differences are obtained
by subtracting the shorter-maturity yield from the longer maturity
yield. In parenthesis are the significance levels for the coefficient
t-tests, except for the adjusted r-square value, which is the ANOVA
F-statistic significance level.

                     Regression Coefficients

                     3-month    mrp      mrp        mrp
Bond      Constant   Treasury   6-3mos   1yr-6mos   2yrs-1yr

30-year    1.708       .760      .682      .928       .534
           (.000)     (.000)    (.000)    (.000)     (.000)

          Regression Coefficients

          mrp      mrp      Adjusted
Bond      3-2yrs   5-3yrs   R-square

30-year    .781    1.251      .983
          (.141)   (.000)    (.000)

TABLE 2. PERFORMANCE OF 30-YEAR CMT BOND

This table shows the probability that a random value smaller
(i.e., more negative) than the 'Difference' value will occur.
The difference variable represents the actual yield on the
30-year CMT bond less the yield forecast for the 30-year CMT
using the regression model specified in Table 1. The probability
value is based on the distribution of the 'Difference' value
over the 30-week estimation period.

                   Actual    Forecast                Probability of a
Week               30-year   30-year                  more negative
Ending               CMT       CMT      Difference     difference'

November 5, 1999    6.12       6.20          -0.08         .00
November 12         6.06       6.14          -0.08         .00
November 19         6.11       6.18          -0.07         .00
November 26         6.22       6.24          -0.02         .18
December 3          6.30       6.32          -0.02         .18
December 10         6.22       6.24          -0.02         .18
December 17         6.32       6.33          -0.01         .30
December 24         6.46       6.45           0.01         .60
December 31         6.46       6.50          -0.04         .05
January 7, 2000     6.58       6.60          -0.02         .18
January 14          6.66       6.71          -0.05         .02
January 21          6.73       6.77          -0.04         .05
January 28          6.57       6.76          -0.19         .00
February 4          6.33       6.73          -0.40         .00
February 11         6.30       6.75          -0.45         .00
February 18         6.23       6.76          -0.53         .00
February 25         6.13       6.66          -0.54         .00

REFERENCES

Balduzzi, P., Elton, E.J., and Green, T.C., "Economic News and Bond Prices: Evidence from the U.S. Treasury Market", Journal of Financial and Quantitative Analysis, Vol. XXXVI (4), 2001, 523-543.

Elton, E.J., "Expected Return, Realized Return, and Asset Pricing Tests", The Journal of Finance, Vol. LIV (4), 1999, 1199-1220.

Fuhrer, J.C., "Monetary Policy Shifts and Long-Term Interest Rates", The Quarterly Journal of Economics, Vol. CXI (4), 1996, 1183-1209.

Mustafa, M. and Rahman, M., "Cointegration between US Short-Term and Long-Term Interest Rates (both nominal and real)", Applied Financial Economics, Vol. V, 1995, 323-327.

Park, T.H. and Switzer, L.N., "Forecasting Interest Rates and Yield Spreads: The Informational Content of Implied Futures Yields and Best-fitting Forward Rate Models", Journal of Forecasting, Vol. XVI (4), 1997, 209-224.

Simon, D.P., "Segmentation in the Treasury Bill Market: Evidence from Cash Management Bills", Journal of Financial and Quantitative Analysis, Vol. XXVI (1), 1991, 97-108.

Taylor, M.P., "Modeling the Yield Curve", The Economic Journal, Vol. CII, 1992, 524-537.

Dr. Aaron L. Phillips earned his D.B.A. in Finance at Southern Illinois University, Carbondale in 1986. He is currently an Associate Professor of Finance at California State University, Bakersfield and a Certified Cash Manager (CCM).