- Email: [email protected]
Another look on bond market seasonally: a note
Journalof ELSEVIER
Jwrnal
of Banking
& Finance
14 (IYYS)
1047-- 1054
Another look on bond market seasonality: a note
Abstract This note provides evidence that there exists business cycle effects on the monthly returns of long-term government bond and low-grade corporate bond. In addition, the results of the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models suggest that the returns series exhibit significant autoregressive conditional heteroskedasticity Kr~ywwds: Bond market \easonality:
GARCIA:
Hand rtlturns:
Business
cycles
1. Introduction
Bond market seasonalities has received notable attention. Schneeweiss and Woolridge ( 1979). Keim and Stambaugh ( 198h), Chang and Pinegar (1988), and Wilson and Jones (1990) all document seasonalities in average monthly returns in fixed income securities. In other work, Fama and French (1989) contend that bond returns are higher during contractionary vis-a-vis expansionary periods, and Chan et al. (1993) provide evidence that the distribution of bond returns is a mixture of stable distributions, which implies that bond return series exhibit time-varying heteroskedasticity. The purpose of this note is to combine these separate strands of
1048
K.c‘
Ghan, H.K. Wu / Jourrd
of Hunkq
& Fmance
I9 (1995)
1047-1054
the bond literature by testing the effects of business cycles and of time-varying heteroskedasticity on the bond market seasonal. To do so, we employ a two-way ANOVA and Bollerslev’s (Bollerslev, 1986) Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models. The note is organized as follows. Section 2 discusses the data. Empirical methods and results are presented in Sections 3 and 4, and a brief summary is presented in Section 5.
2. Data The nominal returns series employed in this study are: long-term government bond (LGB), long-term high-grade corporate bond (LCB), and low-grade corporate bond (LOW). The LGB and LCB returns are from Stocks, Bonds, Bills, and fnflution (1989 Year-Book) (Ibbotson Associates. 1989). The LOW returns are from Ibbotson Associates Inc. The time period covered is from January, 1926 to December. 1988. The periods of economic expansion and contraction are defined by the National Bureau of Economic Research (NBERl and obtained from Business Condition Digest. The exact periods are given in the Appendix. ’
3. Methodology We first document a bond market seasonality over the business cycles. The methodology follows Keim (1983) with the inclusion of a business cycle variable. The model is as follows: R t lk = CL!+ Pk + 61, + C,,I
(1)
where R,,, is the returns of the ith bond in the jfh month in the k’h economic condition: k is 1 for returns in an economic expansion and is zero for returns in an economic contraction; ~1, is the mean effect of the jrh month to R,,,; Pk is the mean effect of the kth economic condition to R,,,; a,, is the interaction effect of the jlh month and the kth economic condition to Rllk; and ellk is the random error term.
Eq. (I 1 is a two-way analysis of variance (ANOVA) model which allows for the possible interactions between the monthly seasonality and business cycle
’ It i\ possible that bond prices predict changes in the economy in advance rather than waiting to respond until government ‘igencies habe de\lgnated the time as contractionary or expansionary (thanks to an rcferce mentioned this caveat). How~ever. the way we put the economic contractions and expanalons in the statistical model is operational. Set Liano and Gup (1989) for details.
K.C‘ Chun. H.K. Wu/Journul
of Bankmg
cY:Finance
19 (1995)
1047-1054
1049
conditions. For a two-way ANOVA model as Eq. (1) interaction has to be checked first [see Smith and Williams (1976. p. 51 l)]. The hypothesis of no interaction effects becomes: Hypothesis I: H,,: S,A= 0 HA: some 6,, # 0 where j = 1 (January). . . 12 (December). If Hypothesis 1 is not rejected, we will test the null hypotheses of equal means across calendar months ( ,u,‘s) and across business cycle conditions ( Pk’s). If H,, of Hypothesis 1 is rejected, the F tests (from the two-way ANOVA) of equal p,‘s and pk’s are no longer meaningful. In this case, we use Fisher’s least significant difference (LSD) tests comparing the average monthly returns. After establishing the bond market seasonality, we then incorporate the possible conditional heteroskedasticity of error term in the model. By using a dummy variable regression with a business cycle variable and Bollerslev’s (Bollerslev, 19X6) Generalized Autoregressive Conditional Heteroskedasticity (GARCH) errors specifications. the model becomes: R,, = h,,D,, + h,, D,, + . . +h,,,D,,, + C&D,, * B, + Q12(D,, * B,) 4 + @,,ADI?I * 4) + ‘I, where R,, = the returns of the ith bond over time = 1 for returns in January; otherwise 0; D,,
(3)
ii 121 B,
= I for returns in December; otherwise 0; = 1 for returns in economic expansions; = 0 for returns in economic contractions. b,‘s and Oi’s = coefficients to be estimated: = random error term with GARCH specification. kd the GARCH error term, e,, of orders p and 4, denoted as GARCH (p,q) is represented as: e, - F( 0.I ,) I,= a,, +t
a,cf I= I
i=l
(4) ,+ ip,~., ,= I
)
(5)
where p > 0 and (1> 0 are the orders of the process; a: ,) > 0; a ,, pj 2 0, for ,... p: j = 1. . ..q. F(0, l,,) = conditional distribution ot oI, with mean, 0 and conditional variance
l’,. The attractiveness of the GARCH model is due to its ability to capture the peakedness and fatty tails observed in empirical distributions [see Chan et al.
’
(1993)]. The conditional variance of P, (i.e., i’,l is modeled as the combination of the past conditional variance (l’, ,. ) and the past ‘forecast errors’ (ef- ,, . . . ). This follows the intuition that the pattern of bond returns volatility differs in stable and unstable periods.
4. Empirical
results
Table 1 presents the results of bond market seasonality over the business cycles. For the LCB, the FAB (the interaction effect) is not statistically significant at the conventional level. In addition, the F statistics (F,) in the LCB column indicates that we cannot reject equal p,‘s across calendar months. Thus, there is no seasonality in the average monthly returns of high-grade corporate bond. Nevertheless. F, is significant, i.e., average monthly returns during economic contractions and expansions are significantly different. An examination of the summary statistics (which are not shown here) indicates that the average returns during economic contractions are higher. The interaction term of LGB and LOW are significantly different as suggested by the F,,, statistics in Table 1. Therefore, LSD tests are performed. The results for LSD tests of LGB are in Table 2. First, the LSD tests of equal mean returns over the economic contractions and expansions are performed on a month by month basis. The results are in the last column of Table 2. LGB average monthly returns are significantly different over the business cycle in April and November. The average monthly returns are higher during economic contractions; for example. the average monthly return is 2.569% in November during economic contractions compared with 0.286% during economic expansions. Second, LSD tests are performed among the calendar months within each economic condition. Calendar months without significant difference are given either letter A or B. The results indicate that LGB average monthly returns exhibit seasonalities during economic contraction\ but not during economic expansions. The mean return in November
Table I ‘Two-w~I) :ZhOV.A model of buwus c!cli: grwcrnmcnt bond (LGBI. high-grade long-term (LOW) .____ ~LGB
and xas~nal cffccts corporate bond (LCB), l.(‘B
on the returns of long-term and low-grade corporate hond LOW
Notea (1) ‘l’hc b statistic\ is from two-wa> AN0V.A: (ii) F;% I- statistics for equal monthly mean rcturnb: Iii11 b,( -- F atat..t’.. IS KS f or cqu,d mean returns durmg cwpansions and contractions: (iv) F - f *vstatistic\ for Interaction between wasonal ;md husinesa cycle effects on the bond returns; (v) 1%
Least (LGB)
significant difkrcncc tests of equal mean percent during ccnnomx cxpanswns and contraction\ Contractions Mean and LSD
test
c~~r~w the months Nowmher April
2.3 Y I .O? x
Octohcr JUllC JUI!
I 4.i 5 I I75 I.07 i
Fehruar) September January .Augu\t
I.01 0.92 O.‘O II.15
May Dcccmher March
I).15 2 0.11) 4 (IOU 0
Notes:
(i) LSD
3 J h 7
= Icabt sigmficant
returns
Expansions Mean and LSD IIC’TI~ the months
test
ot the long-term
government
bond
LSD test of the equal mean over husincss cycle
A AB A8 AB .AB AH AB I3 B E B B diffcrencc.
aberage monthly returns during economic with the same Icttcrs (A or B) represent 5ignificant different.
(ii I ’ ’ 1% t I 5’~ 1 Ggnificant different between the cxpawion and contraction\ in a particular month; (iii) Means rhc\ drc m the \ame group: otherwise the means are 1%
(Letter A) is Ggnificantly higher than that of January, August. May, December, and March (Letter B) during economic contractions. The LSD test results of LOW monthly returns arc in Table 3. The reporting format is the same as Table 2. The effect of the business cycle on low-grade
GARCHC I. I ) models ot w~)nal effects ,,n the returns ot long-term government bond (LGB) and low-grade cortxxate bond (LOW) over busince cvclcs Variables
C‘oefficients
LGB
LOW
0.21) lMO.24 ) I I I Sl2.S-J ) ’
(I.05 IHO.IO ) I 33 l(3.67 ) * 0 Oh S(O.13 1 I.Oh
O(lh7
I. 14 h(2.23
) )
0.35 l(O.SX ) OSX‘Kl.13 ) I I6 7C3.66 1 _ 1.78 3CS.11 ) 1 I .0x l(2.I)J 1 ’ Il.03 2lO.04 1 LOS S(2.04 ) (I.23 IM0.N ) I i3 42.X6 ) * 0.1’- 4(0.?’- ) il.64 5(0.0(1 ) 1.25 hl2.14 I Ci4Y 0(0.75 I (1.7h
l(1.35
)
(1.Y.i IK?.il ) I.51 Y(3.16) 11-J: I(1 79 1 ll.i'J
h(3.3
)
O.Cl.? x4.4x
)
OX? X(11 4) 0 03 39: ISll (II
2.63 3C3.17 ) * * 0.08 7CO.15) 1.08 (HZ.17 ) . 1.53 l(3.01 ) * ’ 0.33 MO.35 ) - 1.09 8C1.53 ) 0.68 9C1.03 ) 1.40 3C2.54 ) * ~ 0.41 2CO.741 0.03 l(O.07 1 1.16 l(2.77 ) * * 0.44 7CO.77) -0.70 Y(O.83 ) 0.25 8cO.39 ) -0.71 Z(1.21 ) - 1.41 2c2.44 ) * - 0.30 3CO.31) I .O4 4C1.37 ) 0.45 2CO.63) - 1.28 S(2.15 ) * 0.93 X(1.54 ) 0.24 3(0.46 1 -0.92 7C1.92 ) 0.40 3CO.65) 0.10 8C?.Y4 ) * * 0.17 2C7.52 ) * 0.83 Z47.7) I).04 584 - 1705.81
Notca: (1) ‘The ~octficicnts of all the dumm! vari;thlcs I /I‘\ and H‘s) have been multiplied by 100: (ii) Inside the parcnthcscb arc Cihsolute r-statistics: (iii) Jcc Ggnit’icant: * 5% significant: (iv) The notation\ of \ariahlc\ and cocfficicnt\ follow I:q5 (7) ,md (5)
corporate bonds ih different from that of LGB. January is the ‘impact month’. The average monthly returns in January within the group of economic contractions are significant higher than March, May. and September. Within the group of economic expansions. January has an average monthly returns higher than all other months. Nevertheless. there is no asymmetric January effect over the business cycles as no significant LSDs are found in January. However, there are asymmetric effects of monthl) returns in March, May. and August. As the bond market seasonals over the business cycles are confined to LGB and LOW. u’c then model LGB and lI)W series with GARCH models. Table 4 presents the results of GARC’H( 1.1 1 models of the bond market seasonality of
K.(‘. Chun, H.K. Wu/Journal
ofBanking B Finance I9 (1995) 1047-1054
1053
LGB and LOW over the business cycles. The conditional heteroskedasticity parameter estimates (a ,,, a 1, and fl,) are all significant at the 1% level. For the LGB, there are statistically significant monthly returns in February, April, July, October, November, and December. For the LOW, we find that there are significant monthly returns in January, March, April, August, and November. January has an extremely high return of 2.633%. Interestingly, the interaction dummy variables (D,, * B,) in both LGB and LOW also indicate negative signs if the coefficients are statistically significant different from zero. The negative signs of the estimated coefficients suggest that the average monthly returns during economic expansions are significantly lower than that of economic contractions. Hence, the business cycles exert asymmetric impact on some average monthly returns on LGB and LOW. 5. Summary The results indicate that there exist business cycle effects on the monthly returns of fixed income securities. In general, the return during economic contractions are higher. In addition, the GARCH models suggest that the returns series exhibit significant autoregressive conditional heteroskedasticity, but that heteroskedasticity-adjusted regression still exhibit seasonalities that differ (in some months) according to the state of the economy. 6. Appendix:
Business cycle expansions and contractions
Business cycle reference dates
Duration in months
Trough
Peak
Jul. 1924 Nov. lY27 Mar. 1933 Jun. lY38 Oct. 194s Oct. 194Y May. 1954 Apr. 1YSX Feb. 1961 Nov. 1Y70 Mar. 1975 Jul. 1980 Nov. 1982
Oct. 1426 Aug. lY2Y May. 1937 Feb. 194.5 Nov. 1948 Jul. 1Y5.1 Aug. 1957 Apr. 1960 Dec. 1YhY Nov. lY73 Jan. 1080 Jul. IYXI
Contractions (trough from previous peak) 13 4.7 13 8 11 10 ti 10 11 Ih h I6
in the U.S.
Expansions (trough to peak) 27 21 50 80 37 4s 39 24 106 36 5x 12
Source: Business Condition Digest. Bureau of Economic Analysis, U.S. Department of Commerce, July 1989. p. 104.
Acknowledgements Helpful comments from two anonymous referees are gratefully acknowledged. We are responsible for any remaining errors. The content of the paper does not necessarily reflect the views of Secor Bank, USA.
References Bollersle\ I I YXh. Generalized Autoregre\\~vc (‘onditional Hetcroxkcdasticity. Journal of Econometric\ il. 307-327 Ghan. K.(‘. MS. Pan and H.K. Wu, IYYi. An investigation of the empirical distribution of bond return\. Journal of Economics and Business AS. lYY3, ISY- 168. Chang. k. and J.M. Pinegar. 1988. Does the market reward risk in non-January months? Journal of Portfolio Management 1.5, Fall. 55-57. Fama. E. and K. French. IYXY, Forccaxting ruturn\ on corporate bonds and common stocks, Journal of Financial Economics 25. 23-4Y. Ibbotsun Aswclates. Inc.. 1489. Stock\. bond\, bills. and inflation (lhbotson Associates, Inc.). Krim, D.. IY83. Size-related anomalic\ and stock return \casonality: further empirical evidence, Journal of Financial Economics I 1. L3-32 Kcim. D. and R.F. Stambaugh, 1986. Prcdictmg return\ in the stock and bond market. Journal of Financial Economics 15. 357-3YO. Liano. K. and B.i?. Gup, 1989, The Day-of-the-week effect in stock returns over business cycles, Financial .Analysts Journal 4.5, July/Augwt. 74-77. Schncewci\s. T and J.R. Woolridge. lY7Y. Capital market aeasonality: the case of bond returns, Journal I,f Financial and Quantitative Analvxi> 13. Y3Y-YiX. Smith. L.11. and D.R. Williams, 1976, Stat&al Analysi\ for Business: A Conceptual Approach, 2nd cdn. (Wadsworth Publishing Company. InL~.) Wilson. J.W .Ind C.P. Jones, lYY0, Is thcrc Y tanuary cffcct in corporate bond and paper returns? Financi,ll Review 25. 55-79.
Jwrnal
of Banking
& Finance
14 (IYYS)
1047-- 1054
Another look on bond market seasonality: a note
Abstract This note provides evidence that there exists business cycle effects on the monthly returns of long-term government bond and low-grade corporate bond. In addition, the results of the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models suggest that the returns series exhibit significant autoregressive conditional heteroskedasticity Kr~ywwds: Bond market \easonality:
GARCIA:
Hand rtlturns:
Business
cycles
1. Introduction
Bond market seasonalities has received notable attention. Schneeweiss and Woolridge ( 1979). Keim and Stambaugh ( 198h), Chang and Pinegar (1988), and Wilson and Jones (1990) all document seasonalities in average monthly returns in fixed income securities. In other work, Fama and French (1989) contend that bond returns are higher during contractionary vis-a-vis expansionary periods, and Chan et al. (1993) provide evidence that the distribution of bond returns is a mixture of stable distributions, which implies that bond return series exhibit time-varying heteroskedasticity. The purpose of this note is to combine these separate strands of
1048
K.c‘
Ghan, H.K. Wu / Jourrd
of Hunkq
& Fmance
I9 (1995)
1047-1054
the bond literature by testing the effects of business cycles and of time-varying heteroskedasticity on the bond market seasonal. To do so, we employ a two-way ANOVA and Bollerslev’s (Bollerslev, 1986) Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models. The note is organized as follows. Section 2 discusses the data. Empirical methods and results are presented in Sections 3 and 4, and a brief summary is presented in Section 5.
2. Data The nominal returns series employed in this study are: long-term government bond (LGB), long-term high-grade corporate bond (LCB), and low-grade corporate bond (LOW). The LGB and LCB returns are from Stocks, Bonds, Bills, and fnflution (1989 Year-Book) (Ibbotson Associates. 1989). The LOW returns are from Ibbotson Associates Inc. The time period covered is from January, 1926 to December. 1988. The periods of economic expansion and contraction are defined by the National Bureau of Economic Research (NBERl and obtained from Business Condition Digest. The exact periods are given in the Appendix. ’
3. Methodology We first document a bond market seasonality over the business cycles. The methodology follows Keim (1983) with the inclusion of a business cycle variable. The model is as follows: R t lk = CL!+ Pk + 61, + C,,I
(1)
where R,,, is the returns of the ith bond in the jfh month in the k’h economic condition: k is 1 for returns in an economic expansion and is zero for returns in an economic contraction; ~1, is the mean effect of the jrh month to R,,,; Pk is the mean effect of the kth economic condition to R,,,; a,, is the interaction effect of the jlh month and the kth economic condition to Rllk; and ellk is the random error term.
Eq. (I 1 is a two-way analysis of variance (ANOVA) model which allows for the possible interactions between the monthly seasonality and business cycle
’ It i\ possible that bond prices predict changes in the economy in advance rather than waiting to respond until government ‘igencies habe de\lgnated the time as contractionary or expansionary (thanks to an rcferce mentioned this caveat). How~ever. the way we put the economic contractions and expanalons in the statistical model is operational. Set Liano and Gup (1989) for details.
K.C‘ Chun. H.K. Wu/Journul
of Bankmg
cY:Finance
19 (1995)
1047-1054
1049
conditions. For a two-way ANOVA model as Eq. (1) interaction has to be checked first [see Smith and Williams (1976. p. 51 l)]. The hypothesis of no interaction effects becomes: Hypothesis I: H,,: S,A= 0 HA: some 6,, # 0 where j = 1 (January). . . 12 (December). If Hypothesis 1 is not rejected, we will test the null hypotheses of equal means across calendar months ( ,u,‘s) and across business cycle conditions ( Pk’s). If H,, of Hypothesis 1 is rejected, the F tests (from the two-way ANOVA) of equal p,‘s and pk’s are no longer meaningful. In this case, we use Fisher’s least significant difference (LSD) tests comparing the average monthly returns. After establishing the bond market seasonality, we then incorporate the possible conditional heteroskedasticity of error term in the model. By using a dummy variable regression with a business cycle variable and Bollerslev’s (Bollerslev, 19X6) Generalized Autoregressive Conditional Heteroskedasticity (GARCH) errors specifications. the model becomes: R,, = h,,D,, + h,, D,, + . . +h,,,D,,, + C&D,, * B, + Q12(D,, * B,) 4 + @,,ADI?I * 4) + ‘I, where R,, = the returns of the ith bond over time = 1 for returns in January; otherwise 0; D,,
(3)
ii 121 B,
= I for returns in December; otherwise 0; = 1 for returns in economic expansions; = 0 for returns in economic contractions. b,‘s and Oi’s = coefficients to be estimated: = random error term with GARCH specification. kd the GARCH error term, e,, of orders p and 4, denoted as GARCH (p,q) is represented as: e, - F( 0.I ,) I,= a,, +t
a,cf I= I
i=l
(4) ,+ ip,~., ,= I
)
(5)
where p > 0 and (1> 0 are the orders of the process; a: ,) > 0; a ,, pj 2 0, for ,... p: j = 1. . ..q. F(0, l,,) = conditional distribution ot oI, with mean, 0 and conditional variance
l’,. The attractiveness of the GARCH model is due to its ability to capture the peakedness and fatty tails observed in empirical distributions [see Chan et al.
’
(1993)]. The conditional variance of P, (i.e., i’,l is modeled as the combination of the past conditional variance (l’, ,. ) and the past ‘forecast errors’ (ef- ,, . . . ). This follows the intuition that the pattern of bond returns volatility differs in stable and unstable periods.
4. Empirical
results
Table 1 presents the results of bond market seasonality over the business cycles. For the LCB, the FAB (the interaction effect) is not statistically significant at the conventional level. In addition, the F statistics (F,) in the LCB column indicates that we cannot reject equal p,‘s across calendar months. Thus, there is no seasonality in the average monthly returns of high-grade corporate bond. Nevertheless. F, is significant, i.e., average monthly returns during economic contractions and expansions are significantly different. An examination of the summary statistics (which are not shown here) indicates that the average returns during economic contractions are higher. The interaction term of LGB and LOW are significantly different as suggested by the F,,, statistics in Table 1. Therefore, LSD tests are performed. The results for LSD tests of LGB are in Table 2. First, the LSD tests of equal mean returns over the economic contractions and expansions are performed on a month by month basis. The results are in the last column of Table 2. LGB average monthly returns are significantly different over the business cycle in April and November. The average monthly returns are higher during economic contractions; for example. the average monthly return is 2.569% in November during economic contractions compared with 0.286% during economic expansions. Second, LSD tests are performed among the calendar months within each economic condition. Calendar months without significant difference are given either letter A or B. The results indicate that LGB average monthly returns exhibit seasonalities during economic contraction\ but not during economic expansions. The mean return in November
Table I ‘Two-w~I) :ZhOV.A model of buwus c!cli: grwcrnmcnt bond (LGBI. high-grade long-term (LOW) .____ ~LGB
and xas~nal cffccts corporate bond (LCB), l.(‘B
on the returns of long-term and low-grade corporate hond LOW
Notea (1) ‘l’hc b statistic\ is from two-wa> AN0V.A: (ii) F;% I- statistics for equal monthly mean rcturnb: Iii11 b,( -- F atat..t’.. IS KS f or cqu,d mean returns durmg cwpansions and contractions: (iv) F - f *vstatistic\ for Interaction between wasonal ;md husinesa cycle effects on the bond returns; (v) 1%
Least (LGB)
significant difkrcncc tests of equal mean percent during ccnnomx cxpanswns and contraction\ Contractions Mean and LSD
test
c~~r~w the months Nowmher April
2.3 Y I .O? x
Octohcr JUllC JUI!
I 4.i 5 I I75 I.07 i
Fehruar) September January .Augu\t
I.01 0.92 O.‘O II.15
May Dcccmher March
I).15 2 0.11) 4 (IOU 0
Notes:
(i) LSD
3 J h 7
= Icabt sigmficant
returns
Expansions Mean and LSD IIC’TI~ the months
test
ot the long-term
government
bond
LSD test of the equal mean over husincss cycle
A AB A8 AB .AB AH AB I3 B E B B diffcrencc.
aberage monthly returns during economic with the same Icttcrs (A or B) represent 5ignificant different.
(ii I ’ ’ 1% t I 5’~ 1 Ggnificant different between the cxpawion and contraction\ in a particular month; (iii) Means rhc\ drc m the \ame group: otherwise the means are 1%
(Letter A) is Ggnificantly higher than that of January, August. May, December, and March (Letter B) during economic contractions. The LSD test results of LOW monthly returns arc in Table 3. The reporting format is the same as Table 2. The effect of the business cycle on low-grade
GARCHC I. I ) models ot w~)nal effects ,,n the returns ot long-term government bond (LGB) and low-grade cortxxate bond (LOW) over busince cvclcs Variables
C‘oefficients
LGB
LOW
0.21) lMO.24 ) I I I Sl2.S-J ) ’
(I.05 IHO.IO ) I 33 l(3.67 ) * 0 Oh S(O.13 1 I.Oh
O(lh7
I. 14 h(2.23
) )
0.35 l(O.SX ) OSX‘Kl.13 ) I I6 7C3.66 1 _ 1.78 3CS.11 ) 1 I .0x l(2.I)J 1 ’ Il.03 2lO.04 1 LOS S(2.04 ) (I.23 IM0.N ) I i3 42.X6 ) * 0.1’- 4(0.?’- ) il.64 5(0.0(1 ) 1.25 hl2.14 I Ci4Y 0(0.75 I (1.7h
l(1.35
)
(1.Y.i IK?.il ) I.51 Y(3.16) 11-J: I(1 79 1 ll.i'J
h(3.3
)
O.Cl.? x4.4x
)
OX? X(11 4) 0 03 39: ISll (II
2.63 3C3.17 ) * * 0.08 7CO.15) 1.08 (HZ.17 ) . 1.53 l(3.01 ) * ’ 0.33 MO.35 ) - 1.09 8C1.53 ) 0.68 9C1.03 ) 1.40 3C2.54 ) * ~ 0.41 2CO.741 0.03 l(O.07 1 1.16 l(2.77 ) * * 0.44 7CO.77) -0.70 Y(O.83 ) 0.25 8cO.39 ) -0.71 Z(1.21 ) - 1.41 2c2.44 ) * - 0.30 3CO.31) I .O4 4C1.37 ) 0.45 2CO.63) - 1.28 S(2.15 ) * 0.93 X(1.54 ) 0.24 3(0.46 1 -0.92 7C1.92 ) 0.40 3CO.65) 0.10 8C?.Y4 ) * * 0.17 2C7.52 ) * 0.83 Z47.7) I).04 584 - 1705.81
Notca: (1) ‘The ~octficicnts of all the dumm! vari;thlcs I /I‘\ and H‘s) have been multiplied by 100: (ii) Inside the parcnthcscb arc Cihsolute r-statistics: (iii) Jcc Ggnit’icant: * 5% significant: (iv) The notation\ of \ariahlc\ and cocfficicnt\ follow I:q5 (7) ,md (5)
corporate bonds ih different from that of LGB. January is the ‘impact month’. The average monthly returns in January within the group of economic contractions are significant higher than March, May. and September. Within the group of economic expansions. January has an average monthly returns higher than all other months. Nevertheless. there is no asymmetric January effect over the business cycles as no significant LSDs are found in January. However, there are asymmetric effects of monthl) returns in March, May. and August. As the bond market seasonals over the business cycles are confined to LGB and LOW. u’c then model LGB and lI)W series with GARCH models. Table 4 presents the results of GARC’H( 1.1 1 models of the bond market seasonality of
K.(‘. Chun, H.K. Wu/Journal
ofBanking B Finance I9 (1995) 1047-1054
1053
LGB and LOW over the business cycles. The conditional heteroskedasticity parameter estimates (a ,,, a 1, and fl,) are all significant at the 1% level. For the LGB, there are statistically significant monthly returns in February, April, July, October, November, and December. For the LOW, we find that there are significant monthly returns in January, March, April, August, and November. January has an extremely high return of 2.633%. Interestingly, the interaction dummy variables (D,, * B,) in both LGB and LOW also indicate negative signs if the coefficients are statistically significant different from zero. The negative signs of the estimated coefficients suggest that the average monthly returns during economic expansions are significantly lower than that of economic contractions. Hence, the business cycles exert asymmetric impact on some average monthly returns on LGB and LOW. 5. Summary The results indicate that there exist business cycle effects on the monthly returns of fixed income securities. In general, the return during economic contractions are higher. In addition, the GARCH models suggest that the returns series exhibit significant autoregressive conditional heteroskedasticity, but that heteroskedasticity-adjusted regression still exhibit seasonalities that differ (in some months) according to the state of the economy. 6. Appendix:
Business cycle expansions and contractions
Business cycle reference dates
Duration in months
Trough
Peak
Jul. 1924 Nov. lY27 Mar. 1933 Jun. lY38 Oct. 194s Oct. 194Y May. 1954 Apr. 1YSX Feb. 1961 Nov. 1Y70 Mar. 1975 Jul. 1980 Nov. 1982
Oct. 1426 Aug. lY2Y May. 1937 Feb. 194.5 Nov. 1948 Jul. 1Y5.1 Aug. 1957 Apr. 1960 Dec. 1YhY Nov. lY73 Jan. 1080 Jul. IYXI
Contractions (trough from previous peak) 13 4.7 13 8 11 10 ti 10 11 Ih h I6
in the U.S.
Expansions (trough to peak) 27 21 50 80 37 4s 39 24 106 36 5x 12
Source: Business Condition Digest. Bureau of Economic Analysis, U.S. Department of Commerce, July 1989. p. 104.
Acknowledgements Helpful comments from two anonymous referees are gratefully acknowledged. We are responsible for any remaining errors. The content of the paper does not necessarily reflect the views of Secor Bank, USA.
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