The Short-Maturity Effect in Corporate Bonds

Transcription

1 The Short-Maturity Effect in Corporate Bonds Darrin DeCosta Managing Director Accretive Asset Management LLC 29 S. Webster St., Suite 395 Naperville, IL Fei Leng Associate Professor of Finance University of Washington Tacoma 1900 Commerce St. Tacoma WA Gregory Noronha Professor of Finance University of Washington Tacoma 1900 Commerce St. Tacoma WA July 2014

2 The Short-Maturity Effect in Corporate Bonds Abstract We find that short-maturity investment-grade corporate bonds tend to perform better on a riskadjusted basis than similar bonds with longer maturities. Since bonds with short maturities are also typically those with low volatilities, our results are equivalent to low-volatility bonds outperforming high-volatility bonds on a risk-adjusted basis. Our results are at least partially attributable to price pressures resulting from a demand and supply effect. We find that insurance companies purchases create a strong demand for long-term bonds and that their sales result in an excess supply of short-term bonds. This demand-supply imbalance is more pronounced among life insurers than among non-life insurers. Our results suggest that the increased market supply of short-term bonds resulting from insurers portfolio rebalancing activity lowers the prices of these bonds and contributes to their superior risk-adjusted performance. 1

3 The Short-Maturity Effect in Corporate Bonds 1. Introduction In the stock market, there is ample evidence that value, size, and momentum strategies outperform on a risk-adjusted basis. Recent evidence from Ang, Hodrick, Xing and Zhang (2006, 2009) shows that high-volatility stocks tend to underperform in the U.S. as well as globally. Blitz and van Vliet (2007) document that not only do high-volatility stocks exhibit abnormally low risk-adjusted returns, but also that low-volatility portfolios have significantly positive alpha. All these researchers find that their results hold after controlling for factors such as size, value, and momentum, and that the volatility effect is distinct from these other factors. The question we ask in this paper is whether such a phenomenon also exists in the investment-grade corporate bond market. That is, do low volatility corporate bonds, where low volatility is typically characterized by low duration or short maturity, have significantly better risk-adjusted performance than highvolatility bonds? More specifically, we inquire (1) whether, after controlling for factors traditionally related to bond returns, such as term, default risk, and liquidity, a short-maturity effect remains, and (2) if yes, what contributes to the effect. We use a sample of investment-grade, option-free corporate bonds to construct portfolios according to bond maturities. We show that Sharpe ratios of the shorter-maturity portfolios are higher than those of longer-maturity portfolios. This pattern persists even after we double-sort the bonds according to their credit quality and issuer sector. To further control for bond characteristics other than term to maturity, we match short-term bonds with longer-term bonds according to sector, credit score and average monthly trading volume. We find that portfolios with short-maturity bonds have significantly higher Sharpe ratios than matching portfolios that contain longer-term bonds. Using a factor regression model which controls for the bond factors 2

4 of term, default and liquidity, we demonstrate that portfolios consisting of short-term corporate bonds have positive and significant alpha. As the term to maturity increases, the outperformance disappears. Overall, our findings are strongly supportive of the thesis that short-term (low volatility) bonds have better risk-adjusted performance than otherwise similar long-term (high volatility) bonds. We next make inquiries into possible drivers of what appears to be a counterintuitive phenomenon namely, that low-risk financial instruments beget a higher risk-adjusted reward than otherwise equivalent high-risk ones. Based on the fact that insurance companies are major participants in the investment-grade corporate bond market, in that they both hold and transact in proportionately large dollar amounts of these bonds, we study their bond transaction data. We find that, because they must match the risk profiles of their assets to those of their long-term liabilities, insurance companies exhibit a strong demand for longer-term bonds and tend to sell shorter-term bonds. Moreover, life insurers differ from non-life insurers in their demand for bonds with different maturities. Specifically, the data indicate that life insurers engage in significant net sales of bonds with six years or less to maturity, whereas non-life insurers exhibit significant net sales of bonds with no more than three years to maturity. While all insurers exhibit strong demand for bonds with 10 years to maturity, only life insurers exhibit significant demand for bonds with more than 15 years to maturity. To further verify that the short-maturity effect is related to the bond trading behavior of insurance companies, we design a strategy that trades against the bond transactions of insurance companies. Specifically, if insurance companies, in aggregate, engage in a net purchase of a bond, we sell and include the bond in our short position portfolio. That is, we take the position of issuing the bond. If insurance companies, in aggregate, have a net sale of a bond, we purchase 3

5 and include it in our long position portfolio. That is, we buy and hold the bond. Using bond factor regressions, we document positive abnormal returns for this long-short strategy. This result suggests that the demand-supply imbalance induced by insurance companies bond transactions is significant enough to distort bond prices and contribute to the short-maturity anomaly. Moreover, we demonstrate that while trading against insurance companies generates positive abnormal returns, a parallel strategy using bonds that do not exhibit the insurer-induced demand-supply imbalance fails to produce positive alpha. This provides further support to the notion that insurance companies bond market behavior contributes to the short-maturity effect. Further analysis shows that it is mainly life insurers who contribute to the demand-supply imbalance in bond market and that other types of insurance firms have an inconsequential effect our empirical results based on all insurers are very similar to the results based on life insurers only, suggesting that life insurers are the significant drivers of the short-maturity anomaly. Overall, our results based on insurance companies bond transactions indicate that the high levels of demand for investment-grade corporate bonds at the long end of the yield curve, coupled with high levels of sales at the short end, creates an imbalance that drives up the prices of long-term instruments while depressing those of short-term ones, contributing to the superior risk-adjusted performance of these short-term bonds. 1 To the best of our knowledge, no work in the academic research community addresses the short-maturity effect. In the professional investment community we were able to find brief 1 The large quantity of bonds available for sale at the short-end of the yield spectrum, and concomitant price pressure, is attributable to causes other than sales by insurance companies. Several popular investment-grade indexes have rules which require that they delete bonds that have either three years or one year to maturity. Indextracking bond mutual funds are thus forced to sell these bonds as well, contributing to the excess supply. See DeCosta, Leng and Noronha (2013) for details. 4

6 research notes by Haesen, Houweling and Bus (2009), and by de Carvalho, Dugnolle, Lu and Moulin (2014), which broach the subject. Haesen et al. (2009) partition their bond sample into five groups according to terms to maturity of bonds and then compare their Sharpe ratios. They find that the group with the shortest bond maturity produces the highest Sharpe ratio while the group with the longest maturity has the lowest Sharpe ratio. de Carvalho et al. (2014) find similar results that remain invariant across bond classes and currencies. Our study differs from these two studies in two important aspects. Firstly, their results are supported by minimal statistical testing and secondly, they advance no explanation for their findings. In contrast, not only do we use a bond-level matching approach to carefully control for other bond characteristics in the test of Sharpe ratio difference, but we also adopt a bond factor regression model to test the outperformance of short-term bonds. Furthermore, we present a possible explanation for the short-maturity effect. To a certain extent, our work complements that of Ellul, Jotikasthira and Lundblad (2011). They report downward price pressure on bonds held by insurance companies that are downgraded to speculative grade and which these firms must collectively sell to comply with regulations, and for which liquidity provided by willing buyers may not exist. That is, other insurance companies are unable or unwilling to buy these downgraded bonds and liquidity must come from outside the insurance community. In a somewhat parallel manner, we posit that the asset-liability management needs of insurance firms compel them to maintain their asset portfolio durations by purchasing long-term bonds while divesting short-term bonds, thereby creating a demand-supply imbalance that exists even for investment-grade debt instruments. Other insurance companies are disinclined to buy these short-term bonds since they do not meet 5

7 liability-matching requirements, and so in this situation as well demand must come from elsewhere. Our research contributes to the existing corporate bond literature in two ways. We are the first to provide systematic empirical evidence of the short-maturity effect in the corporate bond market. In addition, we are the first to investigate why it arises, which we attribute, at least in part, to the bond transactions of insurance companies. We do not attempt to explore reasons why such an effect persists after it first appears. Haesen et al. (2009) conjecture that leverage and derivative-usage restrictions do not permit investors to easily arbitrage it away. However, this does not explain why less liability-minded investors such as bond mutual funds simply do not seize the opportunity to overweight their portfolios with underpriced short-term corporate bonds and hold them to maturity. Given that the discovery of the low-volatility anomaly in the equity market has inspired several subsequent papers using limitations-of-arbitrage arguments to explain the phenomenon, we leave the inquiry into the persistence of the short-maturity effect in the bond market for future research. The remainder of the paper is structured as follows. Section 2 describes our data. Section 3 examines the short-maturity effect in corporate bonds. Section 4 investigates a potential reason for this effect. Section 5 concludes. 2. Sample and Data Our sample period is 1996 to We obtain bond characteristics and rating information from the Mergent Fixed Investment Securities Database (FISD). We remove non-corporate bonds, non-us bonds and non-investment grade bonds (bonds rated lower than Baa3 by Moody s or BBB- by Standard and Poor s). We also exclude bonds with embedded options (e.g., 6

8 callable, putable, convertible, sinking-fund bonds) as well as bonds without a fixed cash coupon rate (e.g., floater, step-up coupons, pay-in-kind coupons, etc.) Bond transaction price data are from two sources: the Financial Industry Regulatory Authority (FINRA) Trade Reporting and Compliance Engine (TRACE), and National Association of Insurance Commissioners (NAIC). TRACE covers all secondary market transactions in publicly traded TRACE-eligible bonds. It was introduced in three phases. In phase I, starting in July 2002, TRACE only covered about five hundred US investment-grade corporate bonds with at least $1 billion issue size. In phase II, starting in March 2003, TRACE expanded its coverage to all A-rated bonds with at least $100 million issue size and 120 Baa-rated bonds with at least $1 billion size. In phase III, starting in October 2004, TRACE further expanded to cover all publicly traded corporate bonds. The NAIC transaction database contains the prices of all transactions in public corporate bonds by insurance companies since Since insurance companies collectively hold 30-40% of investment-grade corporate bonds (Schultz, 2001; Campbell and Taksler, 2003), researchers (e.g., Cai, Helwege and Warga, 2007; Lin, Wang and Wu, 2011; Ellul, Jotikasthira and Lundblad, 2011) believe that the NAIC data adequately represent corporate bond market transactions. Following prior research (e.g., Lin, Wang and Wu, 2011; Jostova, Nikolova, Philipov and Stahel, 2013), we supplement the TRACE data with the NAIC bond transaction data. Because TRACE has a more comprehensive coverage of bond transactions than NAIC, and because TRACE starts after NAIC, for a bond whose transactions are recorded by both databases we keep the NAIC records only if these transactions occur before the same bond is first covered by TRACE. Because TRACE contains some erroneous trade records, we follow Dick-Nielsen (2009) to clean the TRACE data. For a bond to be included in our sample, we require the bond to be issued in or after 1990, covered by TRACE and/or NAIC for at least six months, and have at 7

9 least five distinct dates with active trades. Our final sample contains 13,049 distinct corporate bonds. A given bond can remain in the sample for multiple years until its maturity or the end of our sample period. Table 1 summarizes the characteristics of the bonds in the sample. 2 <Insert Table 1> We follow DeCosta, Leng and Noronha (2013) to calculate a volume-weighted-average price (VWAP) for each day using transaction prices of bonds. Specifically, we compute the VWAP of a bond on a trading day if there are multiple trades in the bond on that day. If there is only one trade in the day, this price is the VWAP of the bond. If there is no trade on a day, we use the most recent VWAP of the bond as the VWAP of the day. To filter out potential price recording errors of TRACE and NAIC, we require that a valid VWAP (clean price) to be in the % range of its par value and in the % range of the previous VWAP. 3 We then calculate the return of a bond on day t as: ( VWAP t AI t ) Ct ( VWAP t 1 AI t 1 ) r t (1) VWAP AI t 1 t 1 where AI t is the accrued interest and C t is the coupon payment (if any) on day t. Monthly returns of the bond are computed by compounding daily returns. Summary statistics for sample bond returns and volatilities are presented in Table 2. In addition to the average monthly returns and 2 Table 1 contains the credit score information of the sample. The credit score of a bond is calculated as the average of the Moody s credit rating score and Standard & Poor s credit rating score. We assign 1 to Moody s (S&P s) Aaa (AAA) rating, 2 to Moody s (S&P s) Aa1 (AA+) rating, 3 to Moody s (S&P s) Aa2 (AA) rating, and so on, up to 10 for Baa3 (BBB-), which is the lowest rated bond still considered investment grade. 3 To avoid mixing results with the regulatory pricing pressure researched by Ellul et al. (2011), we only study bonds that have never been downgraded to speculative grade. So, a clean price that exceeds the ranges of % of the par value or % of the immediate previous price is suspicious. 8

10 volatilities of all bonds in the sample, the table also contains the average returns and volatilities of bonds with different terms to maturity. It can be seen, as expected, that bonds with longer terms generally produce higher returns, though at higher volatilities. <Insert Table 2> 3. The Short-Maturity Effect To measure the risk-adjusted performance of bonds with different terms to maturity, we first use the Sharpe ratio, which is defined as the mean of the excess returns over the risk-free rate divided by the standard deviation of the excess returns (Sharpe, 1994). We create eight portfolios according to the maturities of the bonds in the sample. Portfolio 1 includes bonds with 1-36 months (i.e., 3 years) to maturity 4, portfolio 2 contains bonds with months (i.e., 3-6 years) to maturity,, portfolio 7 consists of bonds with months (i.e., years) to maturity, and portfolio 8 includes bonds with no less than 253 months (i.e., >21 years) to maturity. Each portfolio is rebalanced monthly. We then calculate the market-value weighted average of monthly returns of each portfolio in excess of the monthly 1-month T-bill returns for the sample period Monthly T-bill returns are obtained from CRSP. Table 3 reports the Sharpe ratios of the eight term portfolios. It shows that the Sharpe ratios of the first two portfolios (particularly portfolio 1) are substantially higher than those of other portfolios which contain longer-term bonds. <Insert Table 3> 4 We exclude bonds with zero-months to maturity. This is because the exact maturity date in the maturity month varies among different bonds. Bonds that mature early in the month have fewer days to accumulate returns than bonds that mature late in the month, resulting in un-comparable monthly returns among different bonds. 9

11 Table 3 shows that portfolio Sharpe ratios tend to drop as the term to maturity increases. However, it only provides preliminary evidence of the short-maturity effect because the eight portfolios may be different in other characteristics and thus it is difficult to ascribe their Sharpe ratio differentials only to the maturity difference. For instance, the table shows that the average credit quality of portfolio seems to deteriorate somewhat as the term to maturity of the portfolio lengthens. In addition, longer-term portfolios are largely composed of non-financial-sector bonds whereas shorter-term portfolios have a predominant proportion of financial-sector bonds. To account for such differences, we assign each bond in each month to one of the three credit quality categories (i.e., high quality with a credit score of 1-4, medium quality with a credit score of 4-7, and low quality with a credit score of 7-10) and one of the two issuer sector classes (financials vs. non-financials). We thus partition the entire bond sample into six (3 2) doublesorted subsamples according to bond credit qualities and issuer sectors. We then create six term portfolios using bonds from the same subsample. Portfolios 1, 2,, 5, and 6 include bonds with 1-36 months (i.e., 3 years), months (i.e., 3-6 years),, months (i.e., years), and 181 or above months (i.e., >15 years) to maturity. We create six, instead of eight, term portfolios here because the number of bonds quickly decreases as the term to maturity increases as Table 3 shows, the average number of bonds included in portfolios 6 and 7 in a month drops to 47 and 42, respectively, and having too many term portfolios within each credit quality-issuer sector subgroup would result in too few bonds in some longer-term portfolios. <Insert Table 4> It can be seen from Table 4 that within each credit quality-sector subgroup portfolio Sharpe ratios tend to decrease as the portfolio term increases. Also observable is that the Sharpe ratio of a non-financial-sector bond portfolio tends to be higher than that of a bond portfolio 10

12 made up of financial-sector bonds with similar credit quality and term to maturity. Moreover, for both financial and non-financial bond portfolios, Sharpe ratios increase as their credit quality falls (i.e., credit score rises). These findings indicate that besides term to maturity, bond characteristics such as credit quality and issuer sector also affect portfolio Sharpe ratios, making it necessary to control for these factors while studying the short-maturity effect. To better control for these characteristic differences in verifying the short-term effect, we reconstruct bond portfolios using a characteristic matching approach as follows. In each month of the sample period , we create eight bond pools. Pool 1 contains bonds with exactly 36 months to maturity, pool 2 with bonds with 72 months to maturity,, and pool 8 with bonds with 288 months (i.e., 24 years) to maturity. Because all the longer-term, option-free bonds will eventually become shorter-term bonds as time passes and more bonds are issued at shorter maturities, the number of bonds included in a bond pool decreases as we move from lower to higher pool numbers. That is, pool 1 always contains the most bonds. Thus, we treat pool 1 as the matching pool, from which we choose a bond that best matches a sample bond in the other pools on characteristics other than term to maturity. We adopt a search process with three criteria to select a bond from pool 1 that matches a bond in pool 2 in a given month. 5 First, the pool 1 bond must be in the same sector (i.e., financial, industrial, utility) as the pool 2 bond. Second, the difference in credit scores of the two bonds at the beginning of the month cannot exceed one 5 Our characteristics matching approach is somewhat comparable to the matching method suggested by Bessembinder, Kahle, Maxwell and Xu (2009). However, they only match on term to maturity, which they break into three matching categories (i.e., 0-5 years, 5-10 years, and 10 years or more), and credit ratings, which they break into six categories (i.e., Aaa, Aa, A, Baa, Ba, and B). We adopt a stricter matching standard than they do by using more granular credit categories and matching on sector and trading volume as well. We drop the term to maturity criterion because we intentionally keep the maturities of the sample and matching bonds different. 11

13 ratings increment. Third, the average trading volume 6 of the pool 1 bond in the prior 12 months must be within the % range of the trading volume of the pool 2 bond. Finally, from all the pool 1 bonds that satisfy the above three criteria, we choose the one with the average monthly trading volume closest to that of the pool 2 bond under consideration. In case that multiple matches result from this selection procedure, we choose the bond with the closest credit rating and (if their credit ratings are equally close) closest total par value outstanding to the pool 2 bond. Once we identify the pool 1 bond that best matches a pool 2 bond in a given month, we include it in portfolio 1 and the pool 2 bond in portfolio 2, and hold them in their respective portfolios for 36 months. In cases where we are unable to find a matching bond in pool 1 according to the above criteria, we do not add bonds to either portfolio. In the next month, the bonds added to portfolio 1 (portfolio 2) in the previous month have 35 months (71 months) to maturity, and a new batch of bonds selected according to the matching procedure, all with 36 months (72 months) to maturity, enter into portfolio 1 (portfolio 2). In each monthly rebalancing, the bonds included in a portfolio more than 36 months ago are removed from the portfolio. This process ensures that portfolio 1 consists of bonds with 1-36 months to maturity and portfolio 2 contains bonds with only months to maturity. Through the bond-level matching, portfolio 1 and portfolio 2 are similar in characteristics other than time to maturity. We then repeat the 6 Trading volume in a month is calculated as the total par value traded in the month. Par value is used to measure trading volume because TRACE uses par value as the volume measure. We use trading volume as a matching criterion to control for bond liquidity. Prior researchers (e.g., Mahanti, Nashikkar, Subrahmanyam, Chacko and Mallik, 2008; Bao, Pan and Wang, 2011) have used other measures of the liquidity characteristics of corporate bonds. But those measures either require special private data unavailable to us, or impose very stringent bond price data requirements, which result in a final sample too small for us to proceed with our study. 12

14 process and construct six additional portfolio 1s that match portfolios 3, 4,, and 8, respectively. Note that the portfolio 1 that matches portfolio 2 is not identical to the portfolio 1 that matches portfolio 3. This is because the former portfolio 1 includes the pool 1 bonds that best match the pool 2 bonds whereas the latter portfolio 1 consists of the pool 1 bonds that best match the pool 3 bonds. Thus, the seven portfolio 1s created to match portfolios 2-8 are all unique. We next calculate the value weighted monthly returns of the portfolios created by the matching procedure. Because our sample period is , we start adding bonds to a portfolio in January 1996, but the portfolio only consists of limited number of bonds in the first year. To avoid the erratic returns of a small portfolio, we drop the year of 1996 and only compute portfolio monthly returns for the period. For the same reason, we require that the portfolio in a given month consists of at least five bonds in order for the portfolio return in the month to be used in our study. Using monthly returns of 1-month T-bills and monthly returns of portfolios 2-8 and their respective matching portfolio 1s, we first compute the Sharpe ratios of the sample portfolios and their corresponding matching portfolios, and then test the Sharpe ratio difference of the portfolio pairs using the Jobson and Korkie (1981) test with the Memmel (2003) correction. The results are presented in Table 5. <Insert Table 5> Table 5 shows that both the average excess returns and volatilities of the short-term matching portfolios (i.e., portfolio 1s) are lower than their corresponding longer-term portfolios (i.e., portfolios 2, 3,, 8). The Sharpe ratios of the short-term matching portfolios are all higher than their corresponding longer-term counterparts, and except for portfolio 7 the Sharpe ratio differentials are all statistically significant. The economic significance of the Sharpe ratio 13

15 improvement of shorter-term portfolios is also meaningful. The Sharpe ratios of the short-term matching portfolios are 48% (portfolio 1 vs 3) to 139% (portfolio 1 vs 8) higher than those of their longer-term counterparts. Our results indicate that even after we control for other bond characteristics, short-term bonds still outperform longer-term bonds on a risk-adjusted basis. Also noteworthy is that the Sharpe ratios of the seven portfolio 1s tend to drop as we move their matching target to higher-numbered pools, as do the Sharpe ratios of the higher-numbered pools themselves. Because all seven portfolio 1s have the same term to maturity, this Sharpe ratio pattern suggests that bond characteristics other than term to maturity contribute to the high Sharpe ratios of the shorter-term portfolios, and that our matching approach successfully screens out these confounding factors while retaining the maturity effect. In Table 5, we note that the number of months of portfolio data and the average monthly number of bonds included in the portfolios progressively drop as we move comparisons from the short end (e.g., portfolio 1 vs. 2) to the long end (e.g., portfolio 1 vs. 8). This is because the number of bonds quickly decreases as the term to maturity increases. With the smaller sample to begin with, it becomes more difficult to find matching bonds for longer-term bonds which satisfy all the matching criteria and portfolio construction requirements and produce a valid portfolio return for a month. Consequently, the number of missing monthly portfolio returns increases and the number of bonds in each non-missing month decreases as the time to maturity lengthens. To check whether the missing months and the small number of bonds in non-missing months affect the Sharpe ratio comparisons on the long end (e.g., portfolio 1 vs. 8, portfolio 1 vs. 7), we drop the % trading volume range constraint. 7 This effectively reduces the number of missing 7 Instead of dropping the % trading volume range completely, we first relax it to %. While this relaxation does not qualitatively change the Table 5 results, it only marginally reduces the number of missing 14

16 months and increases the average monthly number of bonds included in portfolios for the long end comparison, 8 but the results (untabulated) remain similar. Thus far, we have relied on Sharpe ratio to measure risk-adjusted performance and use bond-level characteristic matching to control for the bond return differentials caused by reasons other than maturity. As in the case of stock returns, there is no agreement among researchers about whether cross-sectional bond returns are determined by characteristics or factor loadings. According to Gebhardt, Hvidkjaer and Swaminathan (2005), bond returns are determined by bonds sensitivity to the common factors of bond term and default risk. Besides these two bond factors, Lin, Wang and Wu (2011) further include a liquidity factor. Elton, Gruber, Agrawal and Mann (2001) argue that stock market factors also affect bond returns and they include the three Fama and French (1993) factors. We follow these prior researchers and use the six factors of bond term, bond default, bond liquidity, stock market risk (RMRF), stock size (SMB), and stock value (HML). 9 We follow Gebhardt, Hvidkjaer and Swaminathan (2005) and Lin, Wang and Wu (2011) to construct the term and default factors. We follow Lin, Wang and Wu (2011) to months and increases the average monthly number of bonds included in portfolios for the long end comparison. To gain more improvement on this data issue, we remove the constraint of trading volume range. 8 For example, for the comparisons of portfolio 1 vs 5, portfolio 1 vs 6, portfolio 1 vs 7, and portfolio 1 vs 8, the numbers of non-missing months are 200, 191, 134, and 143, respectively, and the average monthly numbers of bonds included in a portfolio are 24, 29, 25, and 25, respectively. 9 Jostova, Nikolova, Philipov and Stahel (2013) document a momentum effect in the corporate bond market. However, the momentum effect largely exists for speculative-grade bonds. We study only investment-grade bonds in this paper. 15

17 construct the Pastor-Stambaugh liquidity factor for bonds 10, and use the three stock factors obtained from WRDS. To use factor regression models to study the short-maturity effect, we create eight monthly rebalanced portfolios with different maturities. Portfolio 1 includes bonds with 1-36 months (i.e., 3 years) to maturity, portfolio 2 contains bonds with months (i.e., 3-6 years) to maturity,, portfolio 7 consists of bonds with months (i.e., years) to maturity, and portfolio 8 includes bonds with no less than 253 months (i.e., >21 years) to maturity. We calculate the monthly value-weighted returns of each portfolio for the entire sample period Unlike our earlier characteristic matching approach where a restrictive screening procedure is imposed before bonds can be included in a portfolio, the eight portfolios we construct in the factor regression approach do not require a prescreening process. As a result, portfolios contain more bonds and we have portfolio returns for every month in our sample period. Thus, for each portfolio, we have 216 monthly returns. We regress portfolio monthly returns on risk factors for bonds using the equation: r it i iterm t 2iDefault t 3 iliquidity t 4iRMRF t 5iSMBt 6i 1 HML (2) t t where r it is the return on a bond portfolio i in month t in excess of the 1-month Treasury bill return of the same month. Term is the difference between the return on the 10-year Treasury bond and the return on 1-month Treasury bill in month t, Default is the difference between the 10 Lin, Wang and Wu (2011) provide two different ways to construct the bond liquidity factor. The first method is similar to how Pastor and Stambaugh (2003) construct a stock liquidity factor. They call the bond liquidity factor constructed this way the Pastor-Stambaugh liquidity measure. The second method is similar to the stock illiquidity measure proposed by Amihud (2002). They call the bond liquidity factor constructed using this second way the Amihud liquidity measure. As a separate check, we also use the Amihud bond liquidity factor in our factor regressions. The results are qualitatively unchanged. 16

18 value-weighted average return on 10-year investment-grade corporate bonds and the return on 10-year Treasury bond in month t, Liquidity is the Pastor-Stambaugh liquidity factor calculated as in Lin et al. (2011), RMRF, SMB, and HML are the three Fama-French factors, and ε is the error term. We use the Newey-West (1987) adjusted standard errors in the regression estimation. Table 6 reports the regression results. <Insert Table 6> Table 6 shows that the three bond factors of term, default and liquidity play a more important role in the determination of portfolio returns than the three stock factors RMRF, SMB and HML. The coefficients of the bond factors are significant in most regressions whereas those of the stock factors are generally insignificant. Most notably, the coefficients of the Term factor in the eight portfolios are all significant and their sizes strictly increase as we move from portfolio 1 to portfolio 8. This indicates that the term factor captures the return differences caused by different terms to maturity of the eight portfolios. The interesting thing in the regression results is the intercept (i.e., alpha) term. In general, as the term to maturity of the portfolio increases, the portfolio alpha decreases. Portfolios 1 and 2 are able to deliver an average of basis points of abnormal return per month after relevant risk factors (including the Term factor) are controlled for. In light of the 44 basis points of average annual pre-fee alpha produced by fixed-income active managers (Ng and Phelps, 2011), this outperformance of the shorter-term portfolios is quite large. The alphas of longer-term portfolios fall and even turn negative for portfolio 8. Given that the average monthly portfolio excess returns increase from 20 basis points to 46 basis points as bond term increases, it is noteworthy that alphas decrease from basis points to 7 basis points. This suggests that the risks of short-term bonds are overcompensated by the market whereas those of long-term bonds are undercompensated. 17

19 Furthermore, the t-statistics of the alpha terms gradually decrease as bond terms increase. The alphas of portfolios 1 and 2 are positive at the 1% significance level and that of portfolio 3 at the 5% significance level. The positive alphas of portfolios 4-7 are not significant at the conventional level and the negative alpha of portfolio 8 is significant at the 5% level. Overall, the bond factor regression approach produces similar results as the previous approach based on bond characteristics: Shorter-term bonds tend to outperform longer-term bonds on a risk-adjusted basis Demand and Supply in the Corporate Bond Market and the Short-Maturity Effect Many investors hold bonds, especially high-quality, option-free bonds, to match their liability structures. If investors have long-term, fixed-rate liabilities, they would demand longterm bonds. At the same time, the number and quantity of long-term bond issues is smaller than that of short-term issues. In such a situation, prices of long-term bonds are likely to be bid up and expected as well as realized returns likely to drop. As bonds approach their maturities, these liability-matching investors will sell shorter-term bonds, resulting in lower prices and higher subsequent returns for these bonds. Thus, the market demand differential may be a factor that contributes to the superior performance of shorter-term bonds. In this section, we investigate this potential reason for the short-maturity effect. To conduct such an investigation, ideally we would have the liability structure data of all major bond investors as well as bond transactions data of these investors. Though such 11 As with any results based on an asset-pricing model, ours are subject to the limitations of the model s adequacy in determining equilibrium returns. As Fama (1998) points out, model limitations affect most anomaly studies in the finance literature. 18

20 comprehensive databases are unavailable, the NAIC database provides the bond transaction data of insurance companies. As the largest investors in the corporate bond market, insurance companies hold 30-40% of investment-grade corporate bonds (Schultz, 2001; Campbell and Taksler, 2003). At the same time, corporate bonds are also the most important asset class in insurance companies investment portfolios. 12 Although insurance companies are not the only investors influencing demand and supply conditions for corporate bonds, Ellul, Jotikasthira and Lundblad (2011) rely on NAIC transaction data to study the impact of insurance company trading behavior on bond prices in the event of a credit downgrade. In this section, we also use the NAIC transaction data to study the short-maturity effect. In addition to data availability, another benefit of studying insurance companies is that they have a quasi-fiduciary duty to fund future benefits and claims of policyholders. So, when deciding what type of bonds to invest in, insurance companies generally match bond characteristics with those of their liabilities to minimize the risk of underfunding the liability. In each month of , as before, we partition investment-grade bonds into eight groups according to their terms to maturity. Group 1 contains bonds with 1-36 months (i.e., 3 years) to maturity 14, group 2 consists of bonds with months (i.e., 3-6 years) to maturity, 12 As of year-end 2013, 68% of the US insurance industry s $5.54 trillion asset portfolio is bonds, 53% of its bond holding is corporate bonds, and 95% of the corporate bond holding is investment-grade. (See Capital Markets Special Reports published by NAIC s Capital Markets Bureau, May 2014.) 13 Instead of using the entire sample period of , we use the period of because the 2012 and 2013 NAIC transaction data was still unavailable when this research was conducted. 14 If an insurance company holds a bond to maturity, the NAIC transactions database treats the total maturity value of the insurance company s holding as a bond sale by the insurance company on the maturity date. To avoid counting redemption at maturity as a bond sale, we exclude a bond once it reaches its maturity month. 19

21 , group 7 includes bonds with months (i.e., years) to maturity, and group 8 contains bonds with no less than 253 months (i.e., >21 years) to maturity. We then compute insurance companies aggregate purchase, sale and net purchase of a particular group of bonds. The bond buy, sell and net buy are defined as the total par value traded during a month scaled by total par value outstanding of the bond at the beginning of the month and we express this ratio as a percentage. Table 7 Panel A reports the bond trading patterns of all insurance companies. <Insert Table 7> In this panel, insurance companies, as a whole, exhibit significant net sales (i.e., negative net buys) of bonds with 72 months to maturity or less (in particular bonds with 36 months to maturity or less), whereas they engage in net purchases of longer-term bonds. Specifically, insurance companies have significant net purchase of bonds with months and more than 180 months to maturity. These trading results are consistent with the previous bond performance results in Tables 3-6. For instance, in Table 7 Panel A insurance companies exhibit the strongest net sale of bonds with 36 months or less to maturity, which corresponds to portfolio 1 in Tables 3-6. Portfolio 1 has the highest Sharpe ratios in Tables 3-5 and it has the most significant positive alpha in Table 6. As another example, Panel A of Table 7 shows that insurance companies have stronger net buys of bonds with months to maturity (corresponding to portfolio 4 in Tables 3-6) than bonds with and months to maturity (corresponding to portfolios 3 and 5 in Tables 3-6). In Table 3, the Sharpe ratio of portfolio 4 is substantially lower than those of portfolios 3 and 5. In Table 6, the alpha of portfolio 4 and its t-statistic are lower than those of portfolios 3 and 5. Additionally, Table 7 shows that insurance companies conduct significant net purchases of bonds with more than 180 months to maturity (corresponding to portfolios 6-8 in Tables 3, 5 and 6). In Tables 3, 5 and 6, portfolios 6-8 show signs of underperformance on a risk- 20

22 adjusted basis. Hence, our results provide the initial evidence that insurance companies divestiture of shorter-term bonds contributes to these bonds relatively low prices and better riskadjusted performance. To further investigate the bond trading behavior of insurance companies, we divide insurers into three types: life, property and casualty (P&C), and others (e.g., health). This partition is meaningful because the various insurer types differ in their liability structures. Life insurance companies have long-term liabilities, and many of their liabilities (e.g., annuities and guaranteed investment contracts) are sensitive to interest rate changes. To match their liabilities, they need portfolios of long-term bonds. In comparison, liabilities of non-life insurance companies tend to have shorter durations and be less sensitive to interest rate risk (Maginn, Tuttle, Pinto and McLeavey, 2007, p.112). As a result, non-life insurers demand for long-term bonds is not as strong as that of life insurers. Panels B, C and D of Table 7 report the trading results of the three types of insurance companies. Panels B-D show that all types of insurers exhibit significant net sales of bonds with 36 months, or less, to maturity and life insurers even engage in significant net sales of bonds up to 72 months to maturity. Hence, the bond sales of all the three types of insurers contribute to the strong outperformance of portfolio 1 in Tables 3-6, whereas the bond sales of only life insurers are related to the weaker outperformance results of portfolio 2 in these tables. Neither life nor non-life insurance companies have significant net purchases or net sales of bonds with months (i.e., 6-9 years) to maturity. While all insurers exhibit significant net purchases of bonds with months (i.e., 9-12 years) to maturity 15, none engages in significant trading activity 15 For the Other type of insurance companies, their net buy of bonds with months to maturity has mean of 0.11% and median of 0.01% of the bond par value outstanding. These numbers are rather small in terms of 21

23 in bonds with months (i.e., years) to maturity. This is because most corporate bonds are issued at 3, 5, 7 and 10 years to maturity and fewer bonds are issued with more than 10 years to maturity. Unless their liabilities have long durations, insurance companies in general prefer bonds with a relatively more active issuing market. For bonds with more than 180 months (i.e., >15 years) to maturity, only life insurers engage in significant net purchases, a result consistent with life insurers need to hedge their longer-term liabilities. So, the relative underperformance results of portfolio 4 in previous tables are related to the bond purchases of all types of insurers, whereas the underperformance of portfolios 6-8 is largely attributable to life insurers. From Panels B-D of Table 7, it seems that life insurers exert more influence on bond market demand than non-life insurers, as both the mean and median of monthly aggregate buy, sell, and net buy of life insurers are substantially greater in size than those of non-life insurers. This explains why the results in Tables 3-6 are more consistent with the results in Panel B than those in Panels C and D of Table 7. Table 7 suggests that that insurance companies liability-hedging need increases the market demand for longer-term bonds and increases the supply of shorter-term bonds, contributing to inferior (superior) risk-adjusted performance of longer-term (shorter-term) bonds. If this explanation of the short-maturity anomaly is indeed correct, a strategy that trades against insurance companies should generate abnormal returns on a risk-adjusted basis. Specifically, when insurance companies, in aggregate, exhibit strong demand for a bond, the excess demand economic significance. In addition, while the signed rank test result is significant at the 1% level, the t test is not significant. However, as is shown in Table 8 below, bond transactions of other insurers are much smaller in terms of number and size than the transactions of life insurers and P&C insurers. Therefore, other insurers play a negligible role in the corporate bond market. Despite this, we include other insurers in subsequent tables for the sake of completeness. 22

24 drives up the bond price and lowers the yield. One can take the position of issuing such bonds that is, going short the bond. Likewise, when insurance companies, in aggregate, sell a specific bond, one can take the position of lender and buy the bond. Because at any point in time the bonds with excess insurance company demand coexist with the bonds with excess insurance company supply, we can pair the long position with the short position to establish a long-short strategy. We expect this strategy to deliver abnormal returns on a risk-adjusted basis. If it does not, that would be an indication that insurance companies trading behavior is not influential enough to impact bond prices and create the short-maturity anomaly. We use the following procedure to construct the strategy that trades against insurance companies. At the beginning of a month, we calculate the aggregate net buys, defined as aggregate purchases minus aggregate sales, of a bond by all insurance companies in the last month, last two months, and last three months. If any of the aggregate net buys in the prior 1-3 months exceeds 10% of the total par value of the bond, we take the position of selling the bond and add it to the short portfolio. 16 This bond remains in the short portfolio until any of the three 16 We use 10% mark to screen bonds to ensure a meaningful demand-supply imbalance created by insurance companies and to reduce noise in the portfolio. We use an up-to-three-month evaluation window because corporate bonds can be quite illiquid and it is not unusual that a corporate bond does not have a single transaction for several consecutive months. Therefore, an aggregate net buy of 10% par value in three months is significant. Instead of using a uniform three-month evaluation window, we use three windows: past one month, past two months, and past three months. If the aggregate net buy in any window is 10% or more of the par value, the bond is selected. We believe this three-window approach is better than using a uniform window approach. For example, if the aggregate net buy of a bond in month -1 is 10% of the total par value, but those in month -2 and month -3 are 0.5% and 1%. Although the 0.5% and 1% aggregate net buy in a month likely results from random noise, the 10% aggregate buy does not. Under the uniform three-month approach, this bond is not chosen. But under the three-window approach, it 23

25 aggregate net buys in the prior 1-3 months exceeds 10% 17 of the total par value. Similarly, if any of the three aggregate net buys in the prior 1-3 months exceeds 10% of the total par value of the bond, we buy the bond and add it to the long portfolio. The bond remains in the long portfolio until any of the three aggregate net buys in the prior 1-3 months exceeds 10% of the total par value. We calculate differences between the value-weighted monthly returns of the long portfolio and those of the short portfolio and obtain the monthly returns for the strategy. We start adding bonds to the long-short strategy in January As in previous portfolio construction using the bond-level matching approach (i.e., Table 5), we drop the year of 1996 because the long and short portfolios of the strategy consist of fewer bonds in the first year of implementation than in subsequent years. Thus, we compute the monthly returns for the period. To control for the risks of the long-short strategy and obtain the abnormal returns, we apply the previous factor regression model (2) to calculated monthly returns of the strategy. Table 8 reports the regression results. <Insert Table 8> Table 8 shows that the alpha term of the regression on all insurance companies as a whole is significantly positive, suggesting that the demand-supply imbalance induced by insurance companies bond transactions contributes to the short-maturity anomaly. Since the long-short portfolio directly trades against insurance companies, the 5-6 basis points outperformance of this portfolio is indicative of the costs that insurance companies have to bear in order to maintain their liability hedge. Based on constituent bonds market capitalization, the monthly average size is selected. A close examination of our sample reveals that there exist a large number of noisy months, and the threewindow approach helps to mitigate the impact of random noise. 17 Note that 10% net buy means that the aggregate net sell on the bond exceeds 10% of the total par value. 24

26 of the long-short portfolio is $83 billion. Given that insurance companies collectively hold 30-40% of investment-grade corporate bonds (Schultz, 2001; Campbell and Taksler, 2003), we roughly estimate that the insurance industry in aggregate incurs an annual loss of at least $ million (= $83 billion 30-40% 5-6 basis points 12) due to the price distortions they themselves induce in the corporate bond market. 18 Ellul et al. (2011) also study the price distortions that insurance companies collectively cause to corporate bonds, but in a different context. They find that due to insurance companies fire sale triggered by the downgrade of a bond from investment to speculative grade, the price drop in the 6-week period starting from the downgrade week is 2.8% for bonds that are not likely subject to strong insurance company sale and 8.7% for bonds that are likely subject to the strong sale. In comparison, our result of 5-6 basis points of monthly abnormal return is much smaller in magnitude. This is because insurance companies in their study conduct a fire sale on the downgraded bonds to comply with regulations whereas in our paper insurance companies need to match asset duration with liability duration is not as urgent as immediate regulation compliance and thus insurers can adopt a trading strategy that minimizes the adverse price impact of their bond transactions. Nevertheless, even in our setting, insurance companies bond transactions exert non-trivial pressure on bond price due to their massive holdings of corporate bonds and the illiquidity of the corporate bond market. Another noteworthy difference from Ellul et al. (2011) is that while they study a less frequent event where corporate bonds are downgraded to speculative grade, in our paper the short- 18 The $ million annual loss is estimated using the bonds included in the long-short portfolio. To be included in this portfolio, a bond must satisfy the sample and data requirements described in section 2 and exhibit substantial demand-supply imbalance induced by insurance companies transactions (see footnote 15). Because insurance companies also hold bonds that do not satisfy these criteria and these bonds prices may also be affected, the actual loss of insurance companies is likely to be greater than our estimated size of loss. 25