The effectiveness of interest-rate futures contracts for hedging Japanese bonds of different credit quality and duration

International Review of Financial Analysis

13 (2004) 13–25

The effectiveness of interest-rate futures contracts

for hedging Japanese bonds of different credit

quality and duration

Martin Younga,1, Warren Hoganb,2, Jonathan Battenc,*

aDepartment of Finance, Banking and Property, College of Business, Massey University,

Private Bag 11222, Palmerston North, New ZealandbSchool of Finance and Economics, University of Technology, Sydney 2002, New South Wales, Australia

cCollege of Business Administration, Seoul National University, 151-742 San 56-01 Sillim-Dong,

Kwanak-Ku, Seoul, South Korea

Abstract

This study investigates the effectiveness of the Tokyo Stock Exchange (TSE)-traded Japanese 10-

year JGB futures contract to hedge portfolios of Japanese bonds of differing maturity and credit quality.

The bond portfolios examined are Government, AAA-, and AA-rated Eurobonds with maturities of 2,

3, 5, 7, 10, and 20 years. Consistent with the recent literature, the study employs univariate methods for

calculating hedge ratios based on levels, first differences, and percentage change of each series. Out-of-

sample forecasting is used to determine the effectiveness of the calculated hedge ratios for each of the

bond portfolios and to determine which approach to calculating hedge ratios is the most effective. The

results show that this particular futures contract does provide a good hedge, particularly for those bond

terms closest to the 10-year term of the contract. There is some evidence, although not strong, that JGBs

are better hedged than AAA andAA bonds. Investors should take some caution when using this futures

contract to hedge bond portfolios of different maturities and credit ratings.

D 2004 Elsevier Inc. All rights reserved.

JEL classification: G13

Keywords: Hedge ratios; Japanese bonds; Debt futures contracts

1057-5219/$ - see front matter D 2004 Elsevier Inc. All rights reserved.

doi:10.1016/j.irfa.2004.01.006

* Corresponding author. Fax: +82-2-882-0547.

E-mail addresses: [email protected] (M. Young), [email protected] (W. Hogan),

[email protected] (J. Batten).1 Fax: +64-6356-9099x2482.2 Fax: +61-2-9281-0364.

M. Young et al. / Int. Rev. Financ. Analy. 13 (2004) 13–2514

1. Introduction

This study investigates the effectiveness of the Tokyo Stock Exchange (TSE)-traded

10-year Japanese JGB futures contract to hedge portfolios of Japanese bonds of different

maturities and credit quality. The bond portfolios examined are Japanese JGBs, AAA-, and

AA-rated Eurobonds with maturities of 2, 3, 5, 7, 10, and 20 years. The 10-year JGB

futures contract is a highly liquid contract that can easily be used as a hedging tool, but its

effectiveness in carrying out this task is an important issue. This is particularly so if the

bond portfolio to be hedged is of a different maturity or credit quality from the 10-year

JGB, which will be the case in most situations. Given the fact that the JGB market is now

the largest bond market in the world, the ability to hedge portfolios of different maturities

and credit quality is critical.

Hedge ratios are calculated using the standard technique of regression analysis. This

is justified, given the significant cointegration or long-term equilibrium that exists

between the JGB and the Eurobonds of different credit quality and maturities. The

regression analysis is carried out for both daily and weekly data over the period covering

1 October 1993 to 21 October 1998. In the case of the daily data, the regressions are

carried out on levels data only. For the weekly analysis, levels, first differences, and

percentage change data are used. In the case of the daily data set, the period is divided

into three subperiods. These are from the beginning of the period under study until the

downgrading of the Sakura and Daiwa Banks in mid-June 1995, from then until the

Japanese Government announcement that it would inject funds into the Japanese banking

system at the beginning of December 1997, and from then until the end of the period.

Splitting the data this way enables the determination of the impact that significant events

in the Japanese banking industry have had on interest-rate volatility across the yield

curve and the effectiveness of using the Japanese 10-year JGB contract as a hedging

tool. The same splits could not be made for the weekly data set, as there were

insufficient observations.

Finally, forecast errors and hedging effectiveness through profit and loss analysis are

examined for out-of-sample periods so that comparisons can be made between the

different bonds being hedged to determine the bonds that can be hedged most effectively.

Given the importance of hedging interest-rate risk in the modern financial marketplace,

this study aims to provide a clearer understanding of hedging effectiveness as it relates to

Japanese bonds trading in the Euro markets.

2. Literature review

The role of the futures market as a vehicle for hedging continues to grow in importance,

as does the interest in determining optimal hedging strategies to protect value. The

effectiveness of hedge ratios calculated by traditional methods is therefore an important

issue. Due mainly to liquidity considerations, futures products seldom match positions

held in the cash market. This being the case, determining optimal hedge strategies is

usually carried out with the use of mismatched futures contracts. Also of importance is the

analysis of the effectiveness of standard hedging tools to hedge bonds of different credit

M. Young et al. / Int. Rev. Financ. Analy. 13 (2004) 13–25 15

quality and duration. This paper is mainly concerned with this second issue, but the issue

of the effectiveness of different hedging techniques is also addressed.

A standard approach to calculating hedge ratios is to regress adjusted historical price

data from the physical market onto the equivalently adjusted price data from the futures

market. Such a regression analysis will produce a beta that is the estimated hedge ratio.

Contributions to this methodology include Ederington (1979), Figlewski (1984, 1985),

and Hill and Schneeweis (1981, 1982). As pointed out by Wilkinson, Rose, and Young

(1999), in applying regression analysis, the data can be presented in a number of different

ways. The regressions can be carried out using price levels (Witt, Schroeder, & Hayenga,

1987), first differences (Hill & Schneeweis, 1981), or percentage change (Brown, 1985).

While there is no real agreement on the best approach to adopt, the time frame being

considered and the variability of returns in both the cash and futures market will have an

influence on results. For longer time frames, using weekly or monthly data, it can be

argued that the first differences or the percentage change data are best. Data presented in

this way focus on the variability of returns, which is the investor’s primary concern when

considering hedging a portfolio. However, for shorter time frames when daily, or even

more frequent, data are used, levels data may be more appropriate in determining

appropriate hedge ratios. This is because any nonsynchronous trading between cash and

futures markets, or any short-term differing perceptions between markets, could lead to

unreliable results if using first differences or percentage change data.

While the methodologies mentioned above have been widely accepted as appropriate

for the determination of hedge ratios, researchers, such as Myers (1991), argue that there

are fundamental problems with these approaches. In particular, these methodologies

assume that optimal hedge ratios, and therefore basis risk, are constant over time. While

this is certainly a problem that needs to be considered, it can be argued the traditional

methodologies are still appropriate as long as there are no structural breaks in the series

under consideration. Those calculating hedge ratios should therefore look carefully to see

if any particular time period is likely to show different volatility risk as compared to

another.

In an attempt to solve the problem of variable basis risk, cointegration techniques may

be applied (see Engle & Granger, 1987; Granger, 1981; Johansen, 1988). Furthermore, this

cointegration methodology has been used in a number of different situations to estimate

optimal hedge ratios. As detailed by Wilkinson et al. (1999), these include treasury bond

futures (Cecchetti, Cumby, & Figlewski, 1988), wheat futures (Myers, 1991), stock index

futures (Ghosh, 1993; Park & Switzer, 1995), and currency futures (Ghosh, 1995). The

study by Wilkinson et al. applies both univariate and multivariate error correction models

to estimate optimal hedge ratios for the Australian and New Zealand debt markets. These

studies show that the time-varying hedge ratios perform either marginally better or no

better than the traditional hedge ratios. This study employs the traditional methodologies

but also takes into account the possibility that major events within the Japanese banking

sector could have led to structural breaks in the series under consideration.

There has been little research to date on the effectiveness of various JGB contracts to

hedge bond portfolios of differing credit quality and duration. Cornell and Green (1991)

find evidence of lower-grade bonds having more sensitivity to stock price movements than

higher-quality bonds, thus suggesting that a combination of a U.S. Treasury futures and a


U.S. Stock Price futures might be more effective than a straight U.S. Treasury futures for

hedging a lower-grade bond portfolio. Marcus and Ors (1996) supported this finding when

looking at hedging bonds close to default. Work by Ioannides and Skinner (1998) also

finds that credit quality and maturity are important sources of basis risk when hedging

lower-grade corporate bonds.

3. Data and method

Due to declining deficits and debt levels in G10 countries, most governments have

issued fewer and shorter maturities, while the Japanese Government has faced the reverse

situation. To meet its monetary objectives, the Japanese Government traditionally issues

fixed-rate bonds with maturities from 2 to 20 years, although most have a maturity of 10

years [80% in 1997 and 1998; see Bank for International Settlements (BIS) Quarterly

Review, 1998] in domestic bond markets. These bonds represent approximately 50% of

total issues of Japanese Government securities with the balance comprising issues of

treasury bills. These bills carry a maturity of between 3 and 6 months. The effect of the

zero-interest-rate policy has seen short-end cash rates approach 0%. More recently, longer-

term inflation expectations have pushed the 20- and 30-year bonds above 2%.

While the Japanese domestic bond market is dominated by government issues (67% in

1998), the reverse is the case with yen-denominated Eurobond markets, which comprise

largely private sector issues. Japanese Government issues in Eurobond markets normally

are for longer maturities (10 to 20 years), while private sector issues tend to have a

maturity of less than 5 years. This variation in the maturity distribution of JGBs is a trade-

off between the maturity demands of investors and the reduction in the level of liquidity

when too few issues are offered for a specific maturity (BIS Quarterly Review, 1999). In

addition, many non-Japanese borrowers have been attracted by the low yields demanded

on Japanese-denominated securities in both domestic and Eurobond markets.

To provide an insight into the issue of hedging bond portfolios of differing credit

quality and durations, we investigate JGBs and high-quality AAA and AA yen-denomi-

nated fixed-rate Eurobonds (henceforth, yen Eurobonds). For simplicity, this investigation

excludes bonds with embedded options, such as callable, puttable, or convertible bonds.

The high rating class of yen-denominated Eurobonds (AAA and AA) with six different

maturities (2, 3, 5, 7, 10, and 20 years) from 1 June 1993 to 21 October 1998 (total of 1382

observations) in secondary bond markets was investigated inasmuch as this credit class

accounts for the majority (70%) of outstanding bonds on issue. Trading in JGBs occurs

over the counter with new JGBs issued by way of competitive auctions held either

monthly or bimonthly, while 20-year bonds are usually auctioned quarterly. This study

excludes the new 30-year JGB inasmuch as this instrument was first offered through a

yield-based Dutch bidding auction, after our sample period, on 2 September 1999.

Inasmuch as Eurobonds are largely unsecured, most issues are by high-quality issuers,

with AAA and AA ratings being the most liquid. There are few non-investment-grade

Eurobond issues. These aggregated rating classes represent portfolios of AAA- and AA-

rated Eurobonds issued by a variety of issuers from different industrial, Japanese

Government, and supranational sectors.


The fixed-rate yields were collected from the credit-spread pages provided by Reuters’

Information Services and are based on secondary market bond prices at 4 p.m. London

time. The yields for the benchmark maturities for the different rated bonds were calculated

from bond yields from various maturities and interpolated into a benchmark set of yields

(t= 2, 3, 5, 7, 10, and 20 years) using cubic spline techniques. A cubic spline produces a

zero curve, which is both smooth in its first derivation and continuous in the second-order

derivation (see Kim, Moon, & Lee, 1998). The values of the second derivations can be

solved using a set of tri-diagonal equations that enable the calculation of any interpolated

value of t. In this instance, interpolated values of t= 2, 3, 5, 7, 10, and 20 were determined.

There are a number of important features about the structure of the JGB market based

on evidence provided by the Reuters Fixed Income database and Inoue (1999). First, it is

much larger (more than eight times) than the yen Eurobond market. Second, AA-rated

Eurobonds have the largest outstandings (about 50%), and AAA-grade issues the second

largest (20%). Based on this fact, our empirical modeling of risky bonds focuses on AA-

and AAA-rated Eurobonds. Third, the distribution of JGBs was generally concentrated

across maturities from 5 to 10 years, with the 10-year bond being traded as the key

benchmark instrument. There were 9% of issues with maturities longer than 10-year

maturities, although the longest bond maturity at the end of our sample period was 20

years. Thus, in this study, six different maturities (2, 3, 5, 7, 10, and 20 years) were

investigated inasmuch as there is very little liquidity in yen Eurobonds with longer

maturities and lesser credit ratings, although the second phase of Japan’s program of

deregulation, which took effect from 1 December 1998, may have caused changes in the

levels of liquidity of the Japanese fixed-income markets. Some important aspects of

deregulation include the use of the on-the-run 10-year JGB as the market benchmark, the

lowering of the small lot trading size of JGBs from 1 million to 100,000 yen, and a

shortening of the settlement dates from 3 days after the trade date to 1 day after the trade

date.

Yen Eurobond yields generally fell over the sample period (20-year bond yields fell

from near 5.8% in June 1993 to below 2.0% in October 1998). The different yields were

also highly correlated. While bond yields generally fell for much of the sample period,

following well-documented and extensive central bank intervention, a series of Japanese

fiscal initiatives, and a pickup in growth in the U.S. economy, the U.S. dollar (USD)

appreciated for most of the later part of 1998 from the sample period highs of 140 yen per

USD to 110 yen per USD.

Hedge ratios are calculated for the AA, AAA, and Japanese JGBs, using both daily and

weekly data, with the individual bonds being the dependent variables and the TSE

Japanese 10-year JGB futures contract being the independent variable. The 10-year JGB

futures contract was the first financial futures contracts in Japan and began trading on

October 19, 1985. In addition to the 10-year JGB futures, TSE began trading 20-year JGB

futures contracts on July 8, 1988, and 5-year JGB futures contracts on February 16, 1996;

the 10-year contract remains the most active and forms the focus of our analysis. All these

contracts have a face value of 100 million yen and are deliverable with the underlying cash

instrument. This key future also applies to contracts traded on both LIFFE (face value of

100 million yen) and the Chicago Board of Trade (face value of 20 million yen). All open

positions on LIFFE are closed out at the close of a business day at the first subsequent


opening price on the TSE for the same delivery month and cash settlement made

accordingly through variation margin. Hedge ratios were also calculated using the LIFFE

and SIMEX Japanese 10-year JGB futures contracts. However, these ratios were found to

be of no significant difference to those calculated using the TSE contract; these results are

therefore not presented here. This was due to the very high correlations between the

different futures contracts (all levels were at least .999 correlated, while changes in levels

varied between .78 and .85 for the three different contracts). A constant term was also used

in all regressions. All futures contract data was obtained from the DataStream data set.

For the daily data set, the ratios were calculated for levels, first differences, and

percentage change, but only the levels results are presented here. This is because the first

differences and percentage change results had very low R-squared values, most likely on

account of the very small, but somewhat uncorrelated, daily movements. There is also a

noncontemporaneous problem with the daily data, as the bond data is at 4 p.m. London

time while the futures data is at 7 a.m. London time. As stated above, the LIFFE and

SIMEX contracts did not help in addressing this problem. The daily data was further split

into three subperiods as the Japanese economic world changed significantly over the

sample period. The first of these periods runs from 1 October 1993 to 16 June 1995,

coinciding with the downgrading of the Sakura and Daiwa Banks in mid-June 1995. The

second of these periods runs from 19 June 1995 to 5 December 1997, as on 8 December

1997, the Japanese Government announced that it would inject funds into the banks. The

final period, therefore, runs from 8 December 1997 until 21 October 1998. As well as

calculating hedge ratios for these subperiods, hedge ratios were also calculated for the

whole period. The robustness of the hedge ratios calculated was examined by looking at

out-of-sample forecast errors and hedging profits and losses. The out-of-sample periods for

the three subperiods and the whole period are detailed in the results tables.

As well as examining hedge ratios calculated from daily data, weekly data for the whole

period were also used to calculate hedge ratios. The ratios were again calculated for levels,

first differences, and percentage change, and the results are presented here for all three

approaches. As with the daily data, out-of-sample forecast errors and hedging profits and

losses were calculated.

The estimation of the hedge ratios is carried out by using a regression of the following

form:

Ct ¼ aþ bFt þ et ð1Þ

where Ct and Ft are cash and futures prices at time t, respectively, and et is the random

disturbance term.

The hedge ratio, b, is found by regressing historical prices of the underlying bond

security on the TSE Japanese 10-year JGB futures contract. The regressions are carried out

using price levels, first differences, and percentage change. For the daily data, only the

price levels results are reported, but for the weekly data analysis, all three methods are

reported.

Having calculated all the hedge ratios, we then compare the forecast errors for the

differing credit qualities and durations. Finally, a rolling hedge is set up on a daily basis for

the daily results and on a weekly basis for the weekly results to determine the effectiveness

of using just one highly liquid futures contract for the hedging process. A perfect hedge


should yield no profit or loss in the long run, besides transaction costs. This is examined

for out-of-sample periods. While daily hedging may be too frequent and weekly hedging

to infrequent, this analysis should give a good indication as to the effectiveness of such

hedging strategies.

4. Results

4.1. Cointegration relationships

Before undertaking cointegration tests on the series, it is appropriate to first determine

the presence of a unit root in the time series. Augmented Dickey–Fuller and Phillips–

Perron tests were undertaken for testing the hypothesis that the series are integrated with

order one I(1); although, for the sake of brevity, detailed results are not reported. For each

yen Eurobond with AAA and AA ratings and maturities of 2, 3, 5, 7, 10, and 20 years and

the equivalent maturity Japanese Government security, the unit root null hypothesis is

accepted even at the 10% level, whereas the hypothesis is strongly rejected for all

difference series. Thus, the data strongly supports the proposition that all series are I(1).

Expectations Theory (Hall, Anderson, & Granger, 1992) also predicts that the series

should be cointegrated with a cointegration vector (1,� 1).

Next, cointegration tests, employing the Johansen (1988) maximum likelihood proce-

dure, were conducted to determine the degree of cointegration between the various

Eurobonds and the JGBs, and between both these groups of bonds and the 10-year TSE

futures contract. Table 1 reports the results of these tests. In all cases, the tests support

cointegration between the equivalent maturity Eurobonds and JGBs, generally at the 1%

level. This supports the existence of a long-run equilibrium between equivalent maturity

corporate bonds and JGBs, as suggested by the Expectations Hypothesis (Hall et al.,

1992). The results support a cointegration relationship between the TSE 10-year contract

and Eurobonds with 7- and 10-year maturities, and between the TSE 10-year contract and

JGBs of 7, 10, and 20 years, but not for other maturities. The very low likelihood statistics

for shorter bond maturities suggest that hedging bonds using the TSE 10-year contract

may generate poor results.

4.2. Hedge ratios

The hedge ratios and their R-squared results for the daily data analysis are presented in

Table 2. As can been seen from the whole period results, the ratios are in line with what

would be expected given the varying bond terms ranging from 0.2375 for 2-year JGBs to

1.9962 for 20-year JGBs. The R-squared results are high in all cases ranging from a low of

87.15% to a high of 99.09%. The results are less consistent between bond terms for the

three subperiods, as presented in Table 2, but remain relatively consistent between the

varying bond qualities. For Periods 1 and 2, the hedge ratios are generally lower,

particularly for the 20-year bond terms. In the case of Period 3, the hedge ratios are

again lower for the shorter terms but significantly higher for the 20-year bond term. R-

squared results are also lower, particularly for those bonds with terms furthest away from

Table 1

Johansen Likelihood Test for cointegration of eurobond and equivalent maturity JGB and TSE 10-year contract

Bivariate cointegration Likelihood ratio

Eurobond to government bonds

AAA2-G2 44.8**

AAA3-G3 29.3**

AAA5-G5 18.9*

AAA7-G7 21.7**

AAA10-G10 45.2**

AAA20-G20 23.4**

AA2-G2 46.6**

AA3-G3 31.2**

AA5-G5 20.1*

AA7-G7 20.7**

AA10-G10 32.8**

AA20-G20 20.5**

Eurobond to TSE 10-year

AAA2-TSE 10 3.5

AAA3-TSE 10 3.7

AAA5-TSE 10 5.5

AAA7-TSE 10 15.2

AAA10-TSE 10 30.1**

AAA20-TSE 10 18.1*

AA2-TSE 10 3.3

AA3-TSE 10 3.7

AA5-TSE 10 6.2

AA7-TSE 10 17.6*

AA10-TSE 10 24.5**

AA20-TSE 10 13.2

Government bond to TSE 10-year

G2-TSE 10 3.9

G3-TSE 10 3.9

G5-TSE 10 8.2

G7-TSE 10 37.3**

G10-TSE 10 46.2**

G20-TSE 10 16.1*

The table reports the cointegration between two bonds of different credit class but the same maturity.

*The likelihood ratio > 15.4 supports cointegration at the 5% level.

**The likelihood ratio > 20.4 supports cointegration at the 1% level.


the futures contract’s 10-year term, indicating that more care needs to be taken with hedge

ratios estimated in this manner, over shorter time frames, for substantially different bond

terms. These results also suggest that interest-rate volatility across the yield curve was

somewhat different for the three periods under consideration. An analysis of the hedge

ratios was also conducted for weekly data. For the levels data, these results are similar to

those for the weekly data with the hedge ratios ranging from 0.2286 for 2-year JGBs to

2.0222 for 20-year JGBs. The R-squared results range from a low of 86.32% to a high of

98.82%. In the case of the first differences and percentage change data, however, the R-

Table 2

Hedge ratio estimates, daily levels

Japanese bond type Period 1 Period 2 Period 3 Whole period

Hedge

ratio

R2

(%)

Hedge

ratio

R2

(%)

Hedge

ratio

R2

(%)

Hedge

ratio

R2

(%)

2-year Euro bonds AA 0.2481 88.31 0.1582 51.70 0.1444 73.48 0.2646 87.58






2-year Euro bonds AAA 0.2618 88.12 0.1536 51.15 0.1446 73.48 0.2597 88.11






2-year JGBs 0.2628 86.54 0.1475 48.50 0.1252 69.84 0.2375 87.15

3-year JGBs 0.4904 91.95 0.2552 56.27 0.2497 83.68 0.3786 89.61

5-year JGBs 0.8878 95.29 0.5961 88.44 0.5664 93.28 0.6519 96.93

7-year JGBs 1.0150 95.40 0.8605 94.57 0.8317 95.49 0.9149 99.09

10-year JGBs 0.9897 92.00 1.0070 89.40 1.1660 94.99 1.1832 98.35

20-year JGBs 0.8648 57.35 1.4719 86.36 2.3463 94.52 1.9962 95.63

Hedge Ratios for Japanese bonds, daily data estimates at levels. The period from October 1993 to 16 June 1998 is

used for the estimation of the hedge ratios for the whole period, while the subperiods are (1) 1 October 1993 to 10

February 1995; (2) 19 June 1995 to 1 August 1997; and (3) 8 December 1997 to 16 June 1998.


squared results are much lower, as the hedge ratios themselves also are. For the first

difference data, the hedge ratios range from 0.1149 for 2-year JGBs to 0.8459 for 20-year

JGBs. For the percentage change data, the range is from 0.1272 to 0.8043, respectively. R-

squared values are lowest for the 2-year JGBs in both cases at approximately 17% and

highest for the 5-year AAA bonds at approximately 46%.

Forecast errors for the daily results are presented in Table 3. These give the mean

absolute error (MAE) and standard deviation of errors (SDE) for the various hedge ratios.

For the daily full period results, the lowest errors are for the 2-, 3-, 5-, and 7-year JGBs and

the 10- and 20-year AAA bonds. For the varying bond terms, the lowest errors are for

those terms closest to the 10-year futures contract, as would be expected. The highest

errors occur for the 20-year bonds. Looking at the three subperiods, the error levels

themselves tend to be lower than for the whole period, indicating that shorter time frames

do give better hedge ratio estimates. This would also be consistent with the view that

interest-rate volatility was different to some extent over the three time frames selected.

Results were mixed in relation to the lowest error over the varying bond qualities,

indicating that the Japanese 10-year JGB futures contract was just as effective as a hedging

tool for all grades of bonds. Across maturities, errors were again highest on the 20-year

bonds but tended to be lowest on the shorter-term bonds.

An investigation of the forecast errors was also conducted for the weekly series.

Although not reported, the errors were highest for the levels analysis. The pattern was

similar as for the daily levels results, with the highest MAEs being recorded for the 20-year

Table 3

Forecast errors, daily levels

Japanese bond type hedged Period 1 Period 2 Period 3 Whole period

MAE

(Abs)

SDE MAE

(Abs)

SDE MAE

(Abs)

SDE MAE

(Abs)

SDE

2-year Euro bonds AA 0.6763 0.7447 0.2699 0.3080 0.2483* 0.3151 1.7024 1.7622

3-year Euro bonds AA 0.8012 0.9199 0.5710 0.6145 0.3748* 0.4426 2.3178 2.4005

5-year Euro bonds AA 0.9415* 1.1231 0.5793 0.6778 0.3441* 0.4093 2.0760 2.1416


10-year Euro bonds AA 2.3904 2.8554 1.0490* 1.2981 1.2353 1.6026 1.1156 1.5402

20-year Euro bonds AA 3.0184 3.8744 2.3333* 2.5880 3.7034 4.5259 5.0427 7.3701

2-year Euro bonds AAA 0.6021 0.6622 0.2408* 0.2734 0.3036 0.3746 1.6807 1.7472




10-year Euro bonds AAA 1.5163 1.9353 1.5886 1.6951 1.1420 1.4761 0.9797* 1.3348

20-year Euro bonds AAA 2.8176* 4.1679 4.5486 4.6652 3.7582 4.5719 4.8034* 7.1588

2-year JGBs 0.2656* 0.3573 0.2743 0.3051 0.2849 0.3143 1.6482* 1.6930

3-year JGBs 0.3125* 0.3979 0.4419 0.4825 0.4836 0.5586 2.2685* 2.3400

5-year JGBs 1.3668 1.5478 0.4550 0.5227 0.6974 0.8197 1.9305* 2.0279

7-year JGBs 0.8007* 1.0215 0.4242 0.5139 0.3758* 0.4518 0.6783* 0.7636

10-year JGBs 0.8458* 1.1197 1.9500 2.0405 0.8902* 1.2092 1.4664 1.8154

20-year JGBs 5.8139 6.3621 4.8377 5.0751 2.2739* 3.2262 5.9590 6.9282

Summary statistics for one-step-ahead forecasts for Japanese bond hedge ratios, daily data estimates at levels. For

the whole period, 1 October 1993 to 16 June 1998 is used for the estimation, and 17 June 1998 to 21 October

1998 is used for forecasting. For Period 1, October 1993 to 10 February 1995 is used for the estimation, and 13

February 1995 to 16 June 1995 is used for forecasting. For Period 2, 19 June 1995 to 1 August 1997 is used for

the estimation, and 4 August 1997 to 5 December 1997 is used for forecasting. For Period 3, 8 December 1997 to

16 June 1998 is used for the estimation, and 17 June 1998 to 21 October 1998 is used for forecasting.

*Denotes the minimum value of the absolute MAE for each bond term.


bonds and the lowest errors being recorded for those terms nearest 10 years. There was no

obvious consistency across bond qualities in terms of lowest error. In three cases, the JGBs

showed the lowest error; in two cases, it was the AAA bonds; and in one case, the lowest

error was recorded by the AA bond. In the case of the first differences and percentage

change data, the MAEs are consistently lower than for the levels data, with the lowest errors

being recorded for the shorter-term bonds and the highest error being recorded for the 20-

year bonds. Across bond qualities, the JGBs have the lowest errors in all cases, indicating

that for first differences and percentage change data at least, the Japanese 10-year JGB

contract is better for hedging JGBs than bonds of lower credit quality. It should be noted,

however, that the errors are only slightly higher for the AAA and AA bonds.

The final set of tables present the profit and loss data from hedging in the out-of-sample

periods using the calculated hedge ratios. Transaction costs are not included in these

calculations. Tables 4 and 5 present the results for the daily levels analysis. In general,

these tables show that the calculated hedge ratios are effective for hedging against adverse

movements in interest rates. If the hedge is performing perfectly, there should be no profit

or loss from the hedging activity. For the whole period and the three subperiods, the least

successful hedge is on the 20-year bonds in all but one case. The period when hedging was

Table 4

Profit/loss from hedging, daily levels for Periods 1 and 2

Japanese bond type Period 1 Period 2

hedgedMean S.D. Minimum Maximum Mean S.D. Minimum Maximum

2-year Euro bonds AA 8.12 167.34 � 414.18 741.85 0.66 77.30 � 188.52 262.86

3-year Euro bonds AA 11.04 284.33 � 736.09 1167.66 � 3.91 138.30 � 547.71 357.27





2-year Euro bonds AAA 7.06 161.22 � 327.26 550.74 1.10 72.36 � 187.84 262.55

3-year Euro bonds AAA 8.97 268.85 � 698.01 943.38 � 2.02 146.01 � 542.18 354.50

5-year Euro bonds AAA 15.38 503.53 � 1284.81 1694.15 � 0.22 241.64 � 770.76 610.82




2-year JGBs 6.70 194.19 � 492.51 538.40 � 1.30 73.63 � 224.03 268.49

3-year JGBs 2.22 323.24 � 738.62 873.48 � 3.67 116.55 � 364.08 348.05

5-year JGBs � 13.30 569.47 � 1259.76 1345.15 � 2.73 252.47 � 684.97 663.22

7-year JGBs � 8.43 749.95 � 1738.90 1853.35 � 3.43 347.46 � 817.43 859.25

10-year JGBs 28.30 887.43 � 2640.59 2364.87 2.62 441.95 � 956.65 1640.85

20-year JGBs 77.88 1227.56 � 3773.59 4020.03 22.65 671.13 � 2560.62 1769.87

Average profit or loss (price times 1000) from hedging Japanese bonds; daily data estimates at levels. Profits and

losses for Period 1 are calculated from 13 February 1995 to 16 June 1995. Profits and losses for Period 2 are

calculated from 4 August 1997 to 5 December 1997.

Table 5

Profit/loss from hedging, daily levels for Period 3 and for the whole period

Japanese bond type Period 3 Whole period

hedgedMean S.D. Minimum Maximum Mean S.D. Minimum Maximum

2-year Euro bonds AA � 3.58 91.37 � 262.69 280.01 � 10.63 115.53 � 289.64 260.47




10-year Euro Bonds AA 34.81 531.68 � 1453.88 1954.18 27.34 550.00 � 1538.41 1945.26


2-year Euro bonds AAA � 4.56 78.06 � 223.47 280.97 � 11.31 104.58 � 303.91 260.26






2-year JGBs � 3.67 62.89 � 199.08 198.14 � 10.26 91.57 � 377.67 211.40

3-year JGBs � 7.91 119.13 � 330.98 407.67 � 15.47 150.90 � 535.91 403.92

5-year JGBs � 14.04 267.38 � 786.62 741.12 � 19.05 288.17 � 922.47 697.55

7-year JGBs � 2.23 379.39 � 1160.42 961.83 � 7.11 399.22 � 1292.64 919.42

10-year JGBs 11.62 694.24 � 2714.30 1778.34 10.62 697.60 � 2715.16 1769.57

20-year JGBs 38.63 1249.73 � 3590.74 3536.39 59.17 1184.58 � 3385.68 3714.94

Average profit or loss (price times 1000) from hedging Japanese bonds; daily data estimates at levels. Profits and

losses for both Period 3 and for the whole period are calculated from 17 June 1998 to 21 October 1998.



most successful overall was the second period. In relation to the varying bond qualities, the

JGBs were generally better hedged; although, it should be pointed out again that as with

the daily levels results, all grades of bonds were well hedged by the Japanese 10-year JGB

contract. The profit and loss outcomes were also determined for the weekly series. The

weekly levels results are again consistent with the daily levels results for the whole period,

with the hedging of the 20-year bonds being the least effective and there being little

difference in outcomes between the different bond qualities. In the case of the first

differences and percentage change data, there is a tendency for the shorter bond terms to be

better hedged, with the hedging for 20-year bonds again being the least effective. For all

bond terms, the JGBs are more effectively hedged than their AAA and AA counterparts.

5. Conclusions

This study examines the effectiveness of using the Japanese 10-year JGB contract as

traded on the TSE to hedge Japanese Eurobonds of different terms and quality. In relation

to the bonds of different terms, the general findings are that this futures contract provides a

good hedge, particularly for those bond terms closest to the 10-year term of the futures

contract, as would be expected. The least successful hedging is for 20-year bonds. When

considering different bond quality, there is little evidence that the JGBs are better hedged

than the AAA and AA bonds for the levels data. However, for weekly first differences and

percentage change data, there is evidence that the JGBs are better hedged by the Japanese

10-year JGB futures contract than the AAA and AA bonds.

For the daily levels data, three subperiods were examined to see if major events

within the Japanese banking industry had any effect on the hedging ability of the

futures contract. From the hedge ratios produced, there was some evidence that the

volatility across the yield curve altered between the three periods, as the hedge ratios

declined for the shorter-term bonds and increased for the longer-term bonds between

these periods. However, there is no real evidence of the hedge ratios calculated being

any more or less effective across the three periods.

Acknowledgements

This paper was presented at the 11th Annual PACAP-FMA Conference, Seoul Korea,

July 2001 and at the 2002 FMA-Europe Conference, June 6 to June 8, Copenhagen,

Denmark. The authors wish to thank participants and referees for their comments, which

have benefited the paper.

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Documents

The effectiveness of interest-rate futures contracts for hedging Japanese bonds of different credit quality and duration