Does the January effect exist in high-yield bond market?
Previous studies show that January returns in high-yield bond (HYB) markets are usually large. While these results are ubiquitous, their validity depends on the robustness of statistical procedures used. Virtually every study of seasonal variation in HYB markets has used mean/variance analysis despite it being well documented that returns in HYB markets are nonnormally distributed. This study uses stochastic dominance comparisons to audit previous parametric tests of the January effect in HYB markets in the U.S. from 1926 to 1993. Results indicate that the January effect in HYB markets is robust and that previous findings are not an artifact deriving from violations of distributional assumptions. (c) 2001 Elsevier Science Inc. All rights reserved.
JEL classification: G15; C32; E44
Keywords: January effect; High-yield bond; Stochastic dominance; Seasonality; Cumulative density function
The January effect (also called the turn-of-the-year effect) refers to the unusually large, positive average security returns during the last few days of December and first week of January.  The finance literature contains substantial evidence of seasonality in risky marketable securities. For example, stocks tend to exhibit unusually high returns in January not only in the U.S. but also around the world (Gultekin, 1983). The bond market also does not seem to be immune to seasonal effects; examples include consistently high returns in January (Chang & Pinegar 1986; Maxwell, 1998; Schneeweis & Woolridge, 1979; Smirlock, 1985; Wilson & Jones, 1990) and high (low) returns in the second (fourth) week of the month (Jordan & Jordan, 1991).
Schneeweis and Woolridge (1979) find evidence of a January effect in various municipal, corporate, public utility, and government bond series. Smirlock (1985) finds a January seasonal for low-grade corporate bonds but not for high-grade corporate or U.S. Government bonds. Chang and Pinegar (1986) also find a January seasonal for low-quality bonds. They investigate whether the results can be explained by tax-loss selling and find that it does not appear to be the only cause of the January seasonal. Wilson and Jones (1990) find a January seasonal for corporate bond and commercial paper returns. Maxwell (1998) reports that his findings are consistent with the increased strength of the January effect as bond ratings decline. Also, his study demonstrates a shift in demand for higher-rated bonds at yearend that is related to institutional "window dressing."
Researchers have found systematic differences among returns for different months of the year in low-grade bonds. No fully satisfactory explanation has been provided for this apparent violation of the trading hypothesis. In the absence of a theoretically acceptable explanation for an observed phenomenon, the question of appropriateness of research methods arises. Virtually all prior studies have relied on parametric t and F-tests to document the January effect in low-quality (high-yield) bonds. While researchers recognize that these parametric tests are not strictly appropriate for assets with nonnormally distributed returns, they assume that any deviation from normality is compensated for by the robustness of parametric methods.
However, this paper uses a stochastic dominance analysis to investigate the January effect in the high-yield bond (HYB) market. Stochastic dominance is a useful tool for making comparisons among distributions without relying on parametric assumptions. In this study, stochastic dominance comparisons are used to show that the January effect in HYB markets documented in earlier studies are robust and do not appear to result from deviations from normality that exist in sample data.
The remainder of this paper proceeds as follows: Section 2 briefly discusses data description and analysis, Section 3 introduces stochastic dominance research methods and results, and Section 4 summarizes.
2. Data description and analysis
Monthly returns of high-yield corporate bonds (bonds included in this series are weighted by rating single B and below) are obtained from Ibbotson Associates for the period of 1926-1993. However, the original data for this study were maintained by First Boston. Monthly returns on long-term high-grade corporate bonds (HGB) and long-term government bonds (LGB) from January 1926 to December 1993 are taken from Ibbotson and Sinquefeld's 1994 yearbook of Stocks, Bonds, Bills, and Inflation (Ibbotson Associates, Chicago). Furthermore, the spread (return of high-yield corporate bond - the return on LGB) is used in this study to eliminate the effect of changes in the term structure.
Table 1 presents the descriptive statistics of monthly returns for HYB, HGB, LGB, and the spread from 1926 to 1993. In the period of study, mean returns of HYB, HGB, and LGB are significantly different from zero, except the spread. In addition, all bond returns, except the spread, which has a negative skewness, have positive skewness and kurtosis. Jarque--Bera statistics for testing normality indicates that return distributions for HYB, HGB, LGB, and spread exhibit significant nonnormality. Furthermore, descriptive statistics for each individual monthly return for an illustrative sample of each bond series (HYB, HGB, LGB and spread) are given in Tables 2-5.
Table 2 shows that January, July, and December are the only months that have significantly positive mean returns among all months of the year for HYB. In addition, 6 months of mean returns show positive skewness and the other 6 months show negative skewness. Each-month-of-the-year distribution shows positive values of kurtosis.
3. Stochastic dominance research methods and results
Results of normality tests suggest that nonparametric methods, such as stochastic dominance, may lead to different conclusions if previous results are being driven by violations of parametric assumptions. Stochastic dominance requires no assumptions about thenature of underlying distributions and imposes few constraints on investor utility functions.
Stochastic dominance tests are used to establish preferences among cumulative probability distributions. There are three major types of stochastic dominance: first order (FSD), second order (SSD), and third order (TSD). Stochastic dominance is defined formally as follows: an asset X with a cumulative density function (CDF) [F.sub.1] would dominate an asset Y with a CDF
[G.sub.1] by FSD if, and only if,
[F.sub.1](x) [less than] [G.sub.1](x), for all possible outcome, x (1)
Hence, X dominates Y by FSD if CDF of X lies completely to the right of the CDF of Y. When Condition (1) is satisfied, the probability of realizing a return less than or equal to x is greater for asset Y than it is for asset X. Needless to say, Condition (1) is extremely stringent, which limits its applicability to everyday portfolio choice problems. Similarly, asset X would dominate asset Y by SSD if, and only if,
[F.sub.2](x) [less than] [G.sub.2](x), for all possible x, (2)
where [F.sub.2] and [G.sub.2] denote the areas under [F.sub.1] and [G.sub.1], respectively (Condition (2)). Hence, SSD allows CDFs to cross by small amounts as long as the area under CDF of X is always less than the area under the CDF of Y. Finally, an asset X would always dominate asset Y by TSD if, and only if,
[[micro].sub.(x)] [greater than] and [F.sub.3](x) [less than] [G.sub.3](x) for all possible x (3)
where [[micro].sub.x] and [[micro].sub.y] are the expected returns to assets X and Y, and [F.sub.3] and [G.sub.3] denote the areas under [F.sub.2] and [G.sub.2], respectively (Condition (3)). Stochastic dominance makes the following additional requirements on investors' utility functions. Investors must be nonsatiated under FSD, nonsatiated and risk averse under SSD, and nonsatiated risk averse, with decreasing absolute risk aversion, under TSD. If there is stochastic dominance, then the expected utility of the investor is always higher under the dominant asset than under the dominated asset. Consequently, the dominated asset would never be chosen. Stochastic dominance results imply hierarchy. FSD implies SSD, which, in turn, implies TSD. Hence, a finding that only TSD exists in turn implies that SSD or FSD does not exist. The decision rules for these three levels of stochastic dominance with discrete distributions are developed in Porter, Wart, and Ferguson (1973) and are used here to determine whether any m onth in high-bond return distributions are dominant.
To implement the S.D. approach, this study examines the distribution of HYB and the spread returns and compares them with HGB and LGB. To examine S.D. in January vs. non January returns, we construct the CDF. The n realized monthly January returns are ranked in increasing order. Since each observation has an equal probability of occurrence, each realized return is assigned a probability of 1/68.  Hence, the lowest realized return has a cumulative probability of 1/68 and the second lowest realized return has a cumulative probability of 2/68. Finally, the highest realized return has a cumulative probability of 68/68 or 1. Plotting these points produces the empirical CDF.
Fig. 1 shows the CDF of the January returns with the March, July, September, November, and December returns for the HYB bonds. Other months are omitted to reduce clutter. The January CDF is shifted to the right and does not overlap with any CDFs of other months of the year. Fig. 1 produces visual proof of first-order stochastic dominance of the January returns in HYB bonds over the non-January returns.
Using a version of stochastic dominance given in Levy and Sarnat (1985), Table 6 provides results for the January returns over non-January returns for HYB, HGB, LGB, and the spread. January returns generally exhibit dominance over non-January returns for HYB. For HYB, January returns dominated 9 of the other 11 months using FSD and 2 remaining months (April and August) using SSD. Therefore, January returns dominate non-January returns for all months using TSD.  January returns for HGB and LGB do not dominate non-January returns using any of the stochastic dominance criteria. However, January returns for the spread dominate non-January returns by SSD and TSD for 9 of the 11 months, and there is FSD for 2 remaining months (April and August). In order to have a strong seasonality result, we should have a first-degree stochastic dominance, because SSD and TSD capture small differences in return distribution, and more structure is imposed on investor preferences as one moves from FSD to TSD. The results in Tab le 6 indicate that there is no seasonality in long-term HGB, government bonds, and the spread. However, it indicates that there is seasonality in HYB.
To compare the S.D. results to a parametric and a nonparametric test of mean results, this paper examines the hypothesis of equal mean values in the same bond data series using the analysis of variance (ANOVA; parametric) test and the Kruskal--Wallis (K-W; nonparametric) test. The results of both the ANOVA and the K-W tests for each bond series are provided in Table 7. The F values for ANOVA indicate that the amount of variation explained by the seasonal model is significant for HYB at the 1% level but not for the remaining bond series (HGB, LGB, and spread). This implies that there is only monthly seasonality in HYB.
The results obtained using ANOVA test are susceptible to the effects of extreme returns. The nonparametric test based on ranks is less affected by the size of returns. Moreover, it is less restrictive than the parametric test due to the assumptions imposed on the parametric method. The K-W nonparametric test was run on the series of monthly holding-period returns to test whether the hypothesis of all 12 populations has identical population distributions. The test statistics is approximately distributed as [[chi].sup.2] with df = 11 and a one-tailed rejection region is appropriate.
The results of the K-W test shown in Table 7 indicate that at least one mean monthly return is different from other months of the year for the HYB, the HGB, and for the spread. This means that there is seasonality in the HYB, in the HGB, and in the spread but not for the LGB. In this study, the results of the three tests (ANOVA, K-W, and S.D.) show that there is a strong monthly seasonality in the HYB market.
Notice that the results of S.D. test shown in Table 6 and Fig. 1 indicate that the seasonality in the HYB market is caused by the month of January.  The advantage of using the S.D. method is that it tests for seasonality and discovers which month is causing the seasonality simultaneously. However, the ANOVA or the K-W method shows only whether there exists a significant variation in the monthly returns for bond data series. 
The stochastic dominance results show that the January effect in HYB markets is robust and does not appear to result from deviations from normality. In general, these results confirm the previously reported result that the January return distribution in high-yield (low-grade) bonds offers a high risk-return relationship compared with those of other months of the year. 
Kaplan and Urwitz (1979) and others have reported evidence of a positive relationship between firm size and bond rating. Accordingly, it is likely that low-grade bonds are primarily issued by "small" (relative to government and high-grade issuers) firms. Such a finding mirrors the results reported by Keim (1983) that the January seasonal effect in the stock market is concentrated in small firms. Blum, Keim, and Patel (1991) have reported that on the risk-return menu, low-grade bonds fall somewhere between high-grade bonds and common stock. Because of their shorter duration, low-grade bonds are less sensitive to movements in interest rates than high-grade bonds. On the other hand, low-grade bonds are more sensitive to changes in stock prices than high-grade bonds. Many fund managers assert that low-grade bond returns are more sensitive to changes in economic activity than to changes in interest rates. For example, Neal Litvack of Fidelty Fund stated that, "Interest rates are a secondary factor. The primary va riable that will impact high yield bonds is the performance of the economy."  Although the majority of the market is composed of bonds with fixed coupons, the high-return characteristics and general junior position in the capital structure makes this security class much closer to equity than traditional fixed income securities. Also, the returns of low-grade bonds display properties of both bonds and stocks and thus are more complex than for HGB. Keim and Stambaugh (1986) find that returns on small-firm stocks and low-grade bonds are more highly correlated in January than in the rest of the year with previous levels of asset prices, especially prices of small-firm stock. Hence, portfolio managers may be able to improve their performance by accounting for seasonal patterns in the debt and equity markets.
This study uses stochastic dominance comparisons to audit previous parametric tests of the January effect in HYB market from 1926 to 1993. Since stochastic dominance does not require assumptions about the nature of distributions being compared, it can be used to compare nonnormal distributions without making the compromises inherent in using mean/variance analysis. Stochastic dominance tests confirm the previously reported result that January return distribution offers a high risk-return relationship compared with those of other months of the year. January returns dominate returns of other months of the year by FSD.
Since stochastic dominance tests do not rely on assumptions about the distribution of returns, and assumptions about normality are clearly violated by monthly HYB return, one may be confident that this result is not an artifact arising from violations of distributional assumptions underlying the tests. These results therefore confirm the robustness of previous work on the January effect in HYB and that the January effect does not exist for high-grade bonds.
Researchers have reported evidence of a positive relationship between firm size and bonds rating. Returns on small-firm stocks and low-grade bonds are more highly correlated in January than in the rest of the year. Accordingly, it is likely that low-grade bonds are primarily issued by "small" (relative to government and high-grade issuers) firms. Results in this study show a significant January effect in HYB that mirrors Keim's (1983) findings that the January seasonal effect in the stock market is concentrated in small firms.
The author thanks the anonymous referees and the Editor of the Journal who provided many useful and insightful comments that helped improved the paper.
(1.) Early papers on stock return seasonality and size effect include Banz (1981), Branch (1977), and Rozeff and Kinney (1976). For evidence of other seasonalities in security returns, see Ariel (1987), French (1980), and Lakonishok and Smidt (1988).
(*.) Tel.: +971-6-505-5320; fax: +971-6-558-5065.
E-mail address: email@example.com (O.M. Al-Khazali).
(2.) The number of years in the study is 68.
(3.) FSD implies SSD, which, in turn, implies TSD.
(4.) Due to the assumptions of parametric analysis, researchers prefer to use stochastic dominance analysis.
(5.) Chang and Pinegar (1986) and Smirlock (1985) conducted pair-wise comparisons among 12 months and repeated the ANOVA and the K-W tests on 11 months without January. They reached the same conclusion as in this paper; that is, the month of January is causing the seasonality in the HYB.
(6.) See Chang and Pinegar (1986), Maxwell (1998), and Smirlock (1985) for further discussions.
(7.) Wall Street Journal, June 6, 1989.
Ariel, R. A. (1987). A monthly effect in stock returns. Journal of Financial Economics, 18, 161-174.
Banz, R. W. (1981). The relationship between return and market value of common stocks. Journal of Financial Economics, 9, 3-18.
Blum, R., Keim, D., & Patel, S. (1991). Return and volatility of low-grade bonds, 1977-1989. Journal of Finance, 46, 49-74.
Branch, B. (1977). A tax-loss trading rule. Journal of Business, 50, 198-207.
Chang, E. C., & Pinegar, J. (1986). Return seasonality and tax-loss selling in the market for long-term government and corporate bonds. Journal of Financial Economics, 17, 391-415.
French, K. R. (1980). Stock returns and the weekend effect. Journal of Financial Economics, 8, 44-77.
Gultekin, N. (1983). Stock market returns and inflation: evidence from other countries. Journal of Finance, 38, 663-673.
Jordan, S. D., & Jordan, B. D. (1991). Seasonality in daily bond returns. Journal of Financial and Quantitative Analysis, 26, 269-285.
Kaplan, R., & Urwitz, G. (1979). Statistical models of bond ratings: a methodology inquiry. Journal of Business, 52, 231-262.
Keim, D. (1983). Size-related anomalies and stock return seasonality; further empirical evidence. Journal of Financial Economics, 12, 13-32.
Keim, D., & Stambaugh, R. (1986). Predicting returns in the stock and bond markets. Journal of Financial Economics, 17, 357-390.
Lakonishok, J., & Smidt, S. (1988). Are seasonal anomalies real? Ninety-year perspective. Review of Financial Studies, 1, 403-425.
Levy, H., & Sarnat, M. (1985). Investment, and portfolio analysis. New York: Wiley.
Maxwell, W. (1998). The January effect in corporate bond market: a systematic examination. Financial Management, 27, 18-34.
Porter, R. B., Wart, J. R., & Ferguson, D. L. (1973). Efficient algorithms for conduction stochastic dominance tests on large numbers of portfolios. Journal of Financial and Quantitative Analysis, 8, 71-81.
Rozeff, M., & Kinney, W. (1976). Capital market seasonality: the case of stock returns. Journal of Financial Economics, 3, 379-402.
Schneeweis, T., & Woolridge, J. (1979). Capital market seasonality: the case of bond returns. Journal of Financial and Quantitative Analysis, 14, 939-958.
Smirlock, M. (1985). Seasonality and bond market returns. Journal of Portfolio Management, 11, 42-44.
Wilson, J. W., & Jones, C. P. (1990). Is there a January effect in corporate bond and paper returns. The Financial Review, 25, 55-79.
Table 1 Descriptive statistics of monthly mean returns from 1926 to 1993 Bond Mean S.D. t statistics Skewness Kurtosis Jarque-Bera HYB 0.60 3.15 5.45 *** 0.30 9.46 1047840 *** HGB 0.47 1.96 6.90 *** 0.83 10.14 1827 *** LGB 0.48 2.53 5.60 *** 3.97 52.46 85329 *** Spread 0.00007 1.67 1.12 -9.11 177.60 1074840 *** Bond N HYB 816 HGB 816 LGB 816 Spread 816 (1) Spread = HYB - LGB; (2) N = Observation. (***) Significant at 1% Table 2 Descriptive statistics of returns for HYB in each calendar month from 1926 to 1993 Month Mean S.D. t statistics Skewness Kurtosis N Jan. 2.96 3.12 6.88 *** 2.12 10.14 68 Feb. 0.24 2.66 0.73 -1.92 8.46 68 Mar. -0.14 3.10 -0.35 -2.23 9.22 68 Apr. 0.73 3.56 1.65 0.74 4.13 68 May. -0.03 4.28 -0.05 -0.38 7.98 68 Jun. 0.30 2.46 0.96 0.33 0.60 68 Jul. 1.25 2.91 3.43 *** 2.53 12.36 68 Aug. 0.38 3.45 0.88 4.52 29.09 68 Sep. -0.03 3.33 -0.07 -1.64 6.30 68 Oct. 0.25 2.61 0.78 -0.84 2.45 68 Nov. 0.16 2.53 0.53 0.15 1.06 68 Dec. 0.85 2.67 2.54 ** -0.59 2.87 68 (**)Significant at 5%. (***)Significant at 1%. Table 3 Descriptive statistics of returns for HGB in each calendar month from 1926 to 1993 Month Mean S.D. t statistics Skewness Kurtosis N Jan. 0.86 1.94 3.63 *** -0.70 3.11 68 Feb. 0.18 1.98 0.76 -0.17 4.54 68 Mar. 0.26 1.33 1.62 -0.09 0.51 68 Apr. 0.16 2.45 0.53 2.09 14.88 68 May. 0.46 2.02 1.88 * 1.36 4.24 68 Jun. 0.53 1.45 3.06 *** -0.55 2.65 68 Jul. 0.32 1.87 1.42 0.18 3.01 68 Aug. 0.40 2.07 1.60 0.68 3.07 68 Sep. 0.43 1.59 2.24 ** 0.60 2.73 68 Oct. 0.80 2.48 2.69 *** 0.13 4.99 68 Nov. 0.60 2.17 2.28 ** 2.53 14.01 68 Dec. 0.66 1.85 2.94 *** 0.18 2.92 68 (*)Significant at 10%. (**)Significant at 5%. (***)Significant at 1%. Table 4 Descriptive statistics of returns for LGB in each calendar month from 1926 to 1993 Month Mean S.D. t statistics Skewness Kurtosis N Jan. 0.20 2.10 0.78 -0.26 2.83 68 Feb. 0.41 2.26 1.47 1.58 8.48 68 Mar. 0.41 1.89 1.79 * 0.70 2.97 68 Apr. 0.33 2.65 1.02 2.58 14.49 68 May. 0.31 2.33 1.09 0.44 3.11 68 Jun. 0.77 1.75 3.62 *** 0.83 1.18 68 Jul. 0.26 2.05 1.04 0.28 2.03 68 Aug. 0.20 2.09 0.75 0.72 2.54 68 Sep. 0.18 2.04 0.75 -0.14 2.00 68 Oct. 0.94 2.51 3.10 *** -0.10 2.96 68 Nov. 0.73 2.47 2.44 ** 2.80 12.62 68 Dec. 0.43 2.03 1.74 * -0.23 2.54 68 (*)Significant at 10%. (**)Significant at 5%. (***)Significant at 1%. Table 5 Descriptive statistics of returns for spread in each calendar month from 1926 to 1993 Month Mean S.D. t statistics Skewness Kurtosis N Jan. 1.83 2.13 4.18 *** 1.33 8.14 68 Feb. 0.06 1.06 0.23 -1.54 7.66 68 Mar. -0.40 4.13 -0.85 -1.65 9.56 68 Apr. 0.57 5.16 1.05 0.84 8.13 68 May. -0.49 3.23 -1.55 -0.78 9.98 68 Jun. -0.23 2.56 -0.76 0.68 1.60 68 Jul. 0.93 3.61 2.53 ** 3.87 11.36 68 Aug. -0.02 1.54 -0.27 3.42 22.09 68 Sep. -0.46 2.13 -0.97 -0.61 8.30 68 Oct. -0.55 1.31 -1.68 -0.76 3.45 68 Nov. -0.44 3.13 -0.83 0.10 2.16 68 Dec. 0.19 2.77 1.34 ** -0.39 3.67 68 (**)Significant at 5%. (***)Significant at 1%. Table 6 Stochastic dominance of January returns over non-January returns from 1926 to 1993 Bond Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec HYB FSD FSD SSD FSD FSD FSD SSD FSD FSD FSD FSD HGB SSD NSD SSD NSD NSD NSD NSD NSD SSD NSD NSD LGB NSD NSD NSD NSD NSD NSD NSD NSD NSD NSD NSD Spread SSD TSD NSD TSD TSD TSD NSD TSD SSD TSD SSD There are 68 monthly observations for HYB from 1926 to 1993. The notation FSD denotes first order, SSD denotes second order, and TSD denotes third order, respectively. An entry in the table means that the January return for the HYB, HGB, LGB, and spread on the left dominates its non-January return indicated across the top. Table 7 Test of equal mean returns in each calendar month from 1926 to 1993 Bond F value P(F) KW P(K) HYB 4.09 .0001 55.49 .0001 HGB 1.50 .15 25.31 .008 LGB 0.89 .54 11.98 .37 Spread 1.23 .25 18.41 .07 (1)The statistics is from one-way ANOVA; (2)K-W statistics is from K-W one-way AVONA by ranks; (3) (*)10% significant; (**)5% significant; (***)1% significant.
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|Title Annotation:||seasonal high returns|
|Author:||Al-Khazali, Osamah M.|
|Publication:||Review of Financial Economics|
|Article Type:||Statistical Data Included|
|Date:||Jan 1, 2001|
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