The Bond Pricing Implications of Rating-Based Capital Requirements. Internet Appendix. This Version: December Abstract

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1 The Bond Pricing Implications of Rating-Based Capital Requirements Internet Appendix This Version: December 2017 Abstract This Internet Appendix examines the robustness of our main results and presents complete results of tests that are only summarized in the main paper. Section I investigates whether our results are robust when using alternative bond factor denitions. Section II repeats our main bond pricing tests using a sample that does not include returns calculated from matrix prices in the Lehman database. Section III demonstrates that our results are not driven by exposure to aggregate bond liquidity risk. Section IV compares the pricing of bonds rated BBB to that of better-rated bonds and the pricing of bonds rated A to that of other NAIC designation 1 bonds and BBB+ bonds. Section V investigates the impact of the nancial crisis period on our results. Section VI presents the complete results of the conditional portfolio analyses that examine the period. Section VII tests whether the negative relation between insurer holdings and bond performance is robust when using dierent samples of bonds and when using β CBMKT as the measure of systematic risk exposure. Section VIII presents complete results for the bond pricing tests that examine the period. Section IX demonstrates that our main results hold during the period.

2 I Alternative Factors In the main paper, we constructed our bond factors from Barclays indices. In this section, we demonstrate that our results are robust when using alternative versions of these factors constructed from the bonds in our sample. Specically, we dene CBMKT Alt as the dierence between the MV -weighted average return of the IG bonds in our sample and the return of a one-month U.S. Treasury bill, and DEF Alt as the dierence between the MV -weighted average return of the IG bonds in our sample and the return of the Barclays Long Maturity U.S. Treasury index. We then repeat the factor analyses whose results are shown in Tables 4-7 of the main paper. All aspects of these analyses remain the same as those in the main paper except that we now use CBMKT Alt and DEF Alt, instead of CBMKT and DEF, to calculate risk-adjusted returns. The results of these tests, shown in Tables A1-A4 of this Internet Appendix, demonstrate that our main results are qualitatively unchanged when we use the alternative factor denitions. During the period, the alphas of portfolios that are long bonds rated BBB and short other IG bonds are positive and statistically signicant regardless of which factor model is used. The β CBMKT 10 1 and β T ERM 10 1 portfolios have negative and signicant alphas with respect to all three factor models in both the conditional and unconditional analyses, and the β DEF 10 1 portfolio generates a statistically insignicant alpha in all analyses. Also consistent with our main results, when we use the alternative bond factors, we nd no evidence of the pricing eects during the period (Tables A5-A8). Finally, Table A9 demonstrates that the performance of the long-short portfolios duing the period is signicantly dierent than during the period. By construction, DEF Alt absorbs all excess return variation of the aggregate portfolio of bonds in our sample that is not captured by T ERM. One ramication of this is that the long-short portfolios we examine tend to have large post-formation exposure to DEF Alt. To test whether this potentially mechanically induced exposure has an impact on our results, we dene a second alternative version of the default factor. DEF Alt,BBB is the dierence between the MV -weighted average return of the bonds rated BBB+, BBB, or BBB and the MV -weighted average return of bonds rated AAA in our sample. This denition mimics 1

3 that of the default factor DEF used in the main paper, except that DEF Alt,BBB is generated from the bonds in our sample. The results of the bond pricing tests using DEF Alt,BBB instead of DEF, shown in Tables A10-A18 of this Internet Appendix, are qualitatively the same as those in the main paper. The pricing patterns are detected during the period, but not during the period, and the dierence in the performance of the long-short portfolios between these two periods is statistically signicant. Consistent with the focal analyses that use DEF as the proxy for the aggregate default factor, the long-short portfolios have economically small and in most cases statistically insignicant post-formation exposure to DEF Alt,BBB. II Matrix Prices The sample we examine in the main paper includes observations for which the bond return was calculated from a matrix price in Lehman. Sarig and Warga (1989) and Gebhardt, Hvidkjaer, and Swaminathan (2005) suggest that matrix prices in Lehman may be less accurate than those based on quotes. We therefore examine whether our results are robust when we exclude from our sample observations for which the bond return is calculated using a Lehman matrix price. We do so by repeating our main bond pricing tests, presented in Tables 4-7 of the main paper, using the non-matrix price sample. The results of these tests, shown in Tables A19- A22 of this Internet Appendix, are nearly unchanged when matrix prices are removed. This is not surprising since the Lehman data end in 1998 and these tests cover the period. However, the vast majority of the observations used in our tests of the period have returns calculated from Lehman. To ensure that the reason we do not detect pricing patterns during this period is not the noise introduced by matrix prices, we repeat the analyses using the non-matrix price sample. The results of these tests, shown in Tables A23-A26 of this Internet Appendix, are consistent with those summarized in Table 13 Panel A of the main paper. For the period, the alphas of long-short portfolios constructed using the non-matrix price sample are all economically small and statistically insignicant. Finally, Table A27 demonstrates that, consistent with the results in Table 14 of the main paper, when we use the non-matrix price sample, there is a signicant dierence in the TERM+DEF+STOCK alpha of the long-short portfolios (except for the β DEF

4 portfolio) during the period compared to the period. III Bond Liquidity Factor In this section, we examine the robustness of our results after controlling for the eect of aggregate bond liquidity risk by augmenting each of our factor models with a bond liquidity factor. We construct a tradable bond liquidity factor, BondLIQ, following Bai et al. (2017). Specically, for each bond i and month t we estimate the bond's eective bid-ask spread as in Roll (1984) to be two times the square root of the rst-order serial covariance of monthly bond returns, calculated using returns from months t 59 through t, inclusive. We then calculate the change in the bond's eective spread between month t and month t 1. At the end of each month t, we form 25 portfolios by sorting all bonds in our sample into ve quintile groups based on ascending values of MV, and then within each MV quintile, we sort bonds into ve quintile portfolios based on ascending values of the change in spread. We then calculate the MV -weighted returns in month t + 1 for each of the 25 portfolios and dene our bond liquidity factor, BondLIQ, to be the average return of the ve high-spread change portfolios minus the average return of the ve low-spread change portfolios. We then repeat the portfolio analyses in Tables 4-7 of the main paper using the augmented factor models. The results of these tests, shown in Tables A28-A31 of this Internet Appendix, are qualitatively the same as those in the main paper. Furthermore, regardless of which factor model is used, the results provide no evidence that the long-short portfolios have exposure to BondLIQ. In sum, the results demonstrate that our ndings are robust after controlling for exposure to aggregate corporate bond market liquidity risk. IV Other Downgrade Probability Tests As shown in Figure 3 of the main paper, bonds rated BBB have the second highest probability of being downgraded to NIG. Thus, it is possible that insurers are also averse to holding bonds rated BBB compared to better-rated bonds. While we would expect this aversion to be much less severe than insurers' aversion to holding bonds rated BBB, which have a much higher probability of being downgraded to NIG, it is nonetheless possible that aversion to bonds rated BBB impacts prices. We therefore test whether bonds rated BBB are underpriced 3

5 relative to better-rated bonds by examining the performance of long-short portfolios that are long bonds rated BBB and short either bonds with an NAIC designation of 1 (NAIC 1), bonds rated BBB+, or all bonds with a rating better than BBB (NAIC 1 and BBB+). These tests are similar to those in Table 4 of the main paper, which examine whether bonds rated BBB are relatively underpriced. The results, shown in Table A32 of this Internet Appendix, indicate that the long-short portfolios have positive (with one exception) but economically small and statistically insignicant alphas, suggesting either that insurers are not that averse to bonds rated BBB, or that if they are, the price impact of this aversion is negligible. If a bond rated A is downgraded, it will incur a higher required capital charge. However, as shown in Table 1 of the main paper, the increase in required capital for a bond downgraded from an NAIC designation 1 to an NAIC designation 2 is small and, as discussed in Becker and Ivashina (2015), is likely the reason why investors do not exhibit a strong preference for NAIC designation 1 bonds over NAIC designation 2 bonds. Nonetheless, we examine whether the prices of bonds rated A are aected by these bonds being at the threshold between NAIC designation 1 and 2. Table A33 presents the results of portfolio analyses examining the performance of NAIC designation 1 bonds not rated A, bonds rated A, and bonds rated BBB+, as well as that of a long-short portfolio that is long bonds rated A and short other NAIC designation 1 bonds ([A ] NAIC 1 No A ) and a long-short portfolio that is long bonds rated BBB+ and short bonds rated A ([BBB+] A ). The results provide no evidence that bonds rated A generate dierent risk-adjusted returns relative to better-rated bonds or bonds rated just a notch lower, since both of the long-short portfolios produce economically small and statistically insignicant alphas relative to all three factor models. V Financial Crisis Period The nancial crisis of was a period characterized by a large number of credit rating downgrades and substantial price volatility in xed-income markets. To ensure that our results are not driven by the events of this period, we remove the nancial crisis period from our sample and repeat the bond pricing tests whose results are shown in Tables 4-7 of the main paper. Specically, we remove return months t + 1 from December 2007 through 4

6 June 2009, inclusive, the period characterized by the NBER as recessionary. The results of the tests with the nancial crisis period removed, shown in Tables A34-A37 of this Internet Appendix, are qualitatively the same as those in the main paper. There is no evidence that our results are driven by the nancial crisis. VI Complete Results of Conditional Portfolio Analyses Panels B of Tables 5-7 of the main paper, which present the results of the conditional portfolio analyses for portfolios sorted on β CBMKT, β T ERM, and β DEF, do not display alphas or post-formation risk factor sensitivities for the individual decile portfolios, or post-formation risk factor sensitivities for the long-short portfolios. Tables A38-A40 of this Internet Appendix display the complete results of these analyses. The results demonstrate that the exposures of the long-short portfolios are consistent with those of the unconditional analyses. Conditional portfolios formed by sorting on β CBMKT or β T ERM have strong positive post-formation exposure to CBM KT or T ERM, respectively. There is no evidence that conditional portfolios sorted on β DEF have post-formation exposure to DEF. VII Insurer Holdings and Bond Pricing - Additional Results In the main paper, our analyses of the relation between insurer holdings and risk-adjusted bond returns used a sample that included only NAIC designation 2 bonds. Here, we demonstrate that our results are robust when we repeat the analyses using either all bonds or only bonds rated BBB or BBB. Specically, at the end of each month t we sort all bonds in the given sample into deciles based on an ascending ordering of β T ERM. We also separate the bonds into those rated BBB and those with any other rating. The intersections of the 10 β T ERM groups and the two NIG downgrade probability groups form the 20 portfolios, whose MV -weighted month t+1 returns we examine. We then repeat the regression analyses whose results are shown in Table 11 of the main paper, this time using each of these alternative samples. The results using all IG bonds (bonds rated BBB and BBB ), shown in Table A41 (Table A42) of this Internet Appendix, are similar to those in the main paper. Regardless of 5

7 which sample of bonds we use, the regressions detect a negative and statistically signicant relation between %InsHeld and risk-adjusted bond performance. We also investigate whether the relation between insurer holdings and risk-adjusted bond returns is robust when using β CBMKT, instead of β T ERM, as the measure of systematic risk exposure. Specically, at the end of each month t we sort all bonds with NAIC designation 2 into deciles based on an ascending ordering of β CBMKT. We also separate these bonds into those rated BBB and those with any other rating. The intersections of the 10 β CBMKT groups and the two NIG downgrade probability groups form the 20 portfolios, whose MV - weighted month t + 1 returns we examine. We then repeat the regression analyses whose results are shown in Table 11 of the main paper. Table A43 of this Internet Appendix demonstrates that the results are once again similar to those in the main paper. In all analyses, the coecient on %InsHeld is negative and statistically signicant. VIII Complete Results of Bond Pricing Tests In Table 13 Panel A of the main paper we presented summary results for our bond pricing tests covering the period. In Tables A44-A47 of this Internet Appendix, we present the complete results of these tests. These tests are identical to those whose results are shown in Tables 4-7 of the main paper, except that here the sample covers the period. As shown in the main paper, the alphas of the long-short portfolios are small and insignicant during Not shown in the main paper are the post-formation factor sensitivities for these portfolios. As in the period, portfolios sorted on β CBMKT or β T ERM have strong positive post-formation exposure to CBM KT or T ERM, respectively, during IX Results of Bond Pricing Tests Rating-based capital requirements for banks were introduced through the implementation of Basel II in 2007, thus giving banks investment incentives that are similar to those of insurers. However, banks are relatively small players in the corporate bond market compared to insurers, and corporate bonds make up only a small portion of banks' investment portfolios. It is therefore unlikely that demand from banks is the primary driver of the pricing patterns 6

8 we document. Nonetheless, to ensure that our results are not completely driven by banks' investment demand induced by rating-based capital requirements, we repeat our main bond pricing tests, whose results are shown in Tables 4-7 of the main paper, using the period. The results of these tests, shown in Tables A48-A51 of this Internet Appendix, demonstrate that our main results hold during the period. Thus, while banks may contribute to the eects after 2007, the eects are not completely driven by banks' investment demand. 7

9 References Bai, Jennie, Turan G. Bali, and Quan Wen, 2017, Common risk factors in the cross-section of corporate bond returns, Working paper available at Becker, Bo, and Victoria Ivashina, 2015, Reaching for yield in the bond market, Journal of Finance 70, Fama, Eugene F., and James D. MacBeth, 1973, Risk, return, and equilibrium: empirical tests, Journal of Political Economy 81, Gebhardt, William R., Soeren Hvidkjaer, and Bhaskaran Swaminathan, 2005, The crosssection of expected corporate bond returns: betas or characteristics?, Journal of Financial Economics 75, Newey, Whitney K., and Kenneth D. West, 1987, A simple, positive semi-denite, heteroskedasticity and autocorrelation consistent covariance matrix, Econometrica 55, Roll, Richard, 1984, A simple implicit measure of the eective bid-ask spread in an ecient market, Journal of Finance 39, Sarig, Oded, and Arthur Warga, 1989, Bond price data and bond market liquidity, Journal of Financial and Quantitative Analysis 24,

10 Table A1: Performance of Portfolios Sorted on NIG Downgrade Probability - Alternative Factors This table presents the results of a portfolio analysis examining the performance of portfolios formed by sorting on NIG downgrade probability. The analysis here is identical to that in Table 4 of the main paper, except that the factor analysis of the bond returns uses CBMKT Alt and DEF Alt as factors, which are constructed from the returns of bonds in our sample, instead of CBMKT and DEF, which are constructed from the returns of Barclays indices. NAIC 1 NAIC 2 No BBB IG No BBB Model Excess Return Excess Return (3.83) (4.11) (3.97) (4.25) (4.90) (3.14) (2.76) (3.30) (2.18) CBMKT α ( 1.91) (0.86) ( 4.13) (1.73) (3.96) (3.72) (3.48) (4.01) (3.16) β CBMKT,Alt (74.74) (52.12) (237.26) (42.81) (22.18) ( 0.41) ( 1.19) ( 0.61) ( 0.97) TERM+DEF α ( 1.93) (0.84) ( 4.58) (1.72) (4.26) (4.06) (3.47) (4.33) (3.11) (59.54) (45.19) (223.83) (38.32) (22.98) (0.72) ( 0.07) (0.56) ( 0.05) β DEF,Alt (34.58) (29.91) (150.69) (26.90) (18.22) (1.87) (1.70) (1.95) (1.41) TERM+DEF+STOCK α ( 1.08) (0.33) ( 3.85) (1.32) (3.57) (3.20) (3.29) (3.64) (2.45) (58.93) (44.29) (202.23) (36.27) (18.62) ( 0.05) ( 0.28) ( 0.05) ( 0.58) β DEF,Alt (34.24) (27.58) (131.03) (24.79) (14.59) (0.67) (0.97) (0.85) (0.22) ost ( 1.83) (1.28) ( 1.22) ( 0.29) (1.23) (1.52) (0.64) (1.25) (1.24) ost ( 0.10) ( 0.04) (0.02) ( 0.39) ( 0.14) ( 0.10) ( 0.12) ( 0.13) (0.04) ost ( 0.67) (1.00) (0.27) ( 0.41) ( 0.65) ( 0.31) ( 1.47) ( 0.63) ( 0.55) ost (1.20) ( 0.96) ( 0.05) (0.08) ( 0.89) ( 1.02) ( 0.47) ( 0.83) ( 0.88) ( 1.93) (1.42) ( 1.51) (0.72) (1.97) (2.05) (1.41) (1.94) (1.72) BBB BBB [BBB ] NAIC 1 [BBB ] NAIC 2 No BBB [BBB ] IG No BBB [BBB ] BBB 9

11 Table A2: Performance of Portfolios Sorted on β CBMKT - Alternative Factors This table presents the results of an unconditional (Panel A) and conditional portfolio analysis (Panel B) examining the performance of portfolios formed by sorting on β CBMKT. The analysis here is identical to that in Table 5 of the main paper, except that the factor analysis of the bond returns uses CBMKT Alt and DEF Alt as factors, which are constructed from the returns of bonds in our sample, instead of CBM KT and DEF, which are constructed from the returns of Barclays indices. Panel A: Unconditional Portfolio Analysis β CBMKT 1 β CBMKT 2 β CBMKT 3 β CBMKT 4 Model Excess Return Excess Return (6.86) (4.43) (3.86) (3.50) (3.65) (3.80) (4.15) (3.81) (3.71) (3.34) (1.46) CBMKT α (7.17) (1.69) (0.34) ( 0.04) ( 0.30) ( 0.25) (0.41) ( 0.72) ( 1.33) ( 2.23) ( 4.54) β CBMKT,Alt (13.39) (15.01) (18.80) (20.89) (33.72) (36.65) (47.49) (51.58) (44.94) (36.40) (20.97) TERM+DEF α (7.13) (1.67) (0.27) ( 0.08) ( 0.36) ( 0.29) (0.39) ( 0.67) ( 1.28) ( 2.19) ( 4.57) (13.26) (15.16) (18.06) (18.89) (34.39) (35.29) (45.07) (49.05) (44.23) (34.36) (19.57) β DEF,Alt (11.01) (13.94) (14.97) (15.13) (28.54) (28.72) (32.58) (34.62) (32.89) (23.27) (12.88) TERM+DEF+STOCK α (7.49) (1.55) (0.44) ( 0.12) (0.11) (0.10) (0.65) ( 0.47) ( 1.34) ( 2.72) ( 5.21) (13.55) (16.88) (22.04) (16.66) (36.74) (31.66) (41.83) (49.81) (39.48) (28.80) (16.73) β DEF,Alt (10.84) (16.42) (20.67) (13.49) (32.59) (25.46) (29.89) (34.64) (27.04) (17.92) (9.45) ost ( 2.04) ( 2.02) ( 1.58) ( 0.47) ( 3.58) ( 1.02) (0.43) (0.85) (0.65) (2.97) (3.38) ost (0.86) ( 0.45) (0.43) ( 0.89) ( 1.34) ( 1.17) ( 1.67) (0.10) (1.50) (0.70) (0.13) ost ( 0.07) ( 0.50) ( 0.59) ( 0.27) ( 0.93) ( 1.12) ( 0.63) (0.10) (0.86) (1.73) (1.69) ost ( 0.47) (0.71) ( 1.10) (1.32) (1.64) ( 0.58) ( 2.00) (1.63) ( 0.00) (0.14) (0.31) ( 2.09) (0.57) (0.80) (0.05) ( 1.17) (0.22) (0.98) ( 2.39) (0.40) (0.57) (1.27) β CBMKT 5 β CBMKT 6 β CBMKT 7 β CBMKT 8 β CBMKT 9 β CBMKT 10 β CBMKT

12 Table A2: Performance of Portfolios Sorted on β CBMKT - Alternative Factors continued Panel B: Conditional Portfolio Analysis - Control for Capital Charge β CBMKT 1 β CBMKT 2 β CBMKT 3 β CBMKT 4 β CBMKT 5 β CBMKT 6 β CBMKT 7 NAIC (1.52) ( 3.86) ( 3.96) ( 4.05) NAIC (1.35) ( 4.44) ( 4.23) ( 5.78) NAIC Avg (1.48) ( 4.84) ( 4.82) ( 6.05) β CBMKT 8 β CBMKT 9 β CBMKT 10 β CBMKT 10 1 CBMKT α TERM+DEF α TERM+DEF+STOCK α 11

13 Table A3: Performance of Portfolios Sorted on β T ERM - Alternative Factors This table presents the results of an unconditional (Panel A) and conditional portfolio analysis (Panel B) examining the performance of portfolios formed by sorting on β T ERM. The analysis here is identical to that in Table 6 of the main paper, except that the factor analysis of the bond returns uses CBMKT Alt and DEF Alt as factors, which are constructed from the returns of bonds in our sample, instead of CBM KT and DEF, which are constructed from the returns of Barclays indices. Panel A: Unconditional Portfolio Analysis β T ERM 1 β T ERM 2 β T ERM 3 β T ERM 4 Model Excess Return Excess Return (5.88) (5.01) (4.29) (3.75) (3.84) (3.52) (4.27) (3.76) (3.41) (3.28) (1.22) CBMKT α (6.24) (3.48) (1.80) ( 0.57) ( 0.11) ( 1.16) (0.72) ( 2.37) ( 2.55) ( 2.00) ( 3.73) β CBMKT,Alt (12.03) (17.88) (22.60) (29.25) (35.93) (39.91) (44.97) (59.05) (29.99) (30.12) (15.27) TERM+DEF α (6.22) (3.60) (1.76) ( 0.72) ( 0.20) ( 1.29) (0.78) ( 2.33) ( 2.38) ( 1.98) ( 3.90) (13.93) (21.16) (24.72) (31.51) (35.68) (40.09) (48.21) (58.54) (31.58) (30.04) (14.94) β DEF,Alt (13.03) (21.38) (26.56) (31.09) (31.61) (34.89) (38.48) (42.52) (25.31) (19.11) (7.59) TERM+DEF+STOCK α (7.51) (4.00) (1.96) ( 0.44) (0.38) ( 0.82) (0.94) ( 2.56) ( 3.28) ( 2.78) ( 5.10) (17.41) (24.04) (24.74) (31.60) (36.28) (36.74) (39.51) (53.62) (33.45) (28.03) (14.82) β DEF,Alt (16.97) (25.26) (24.71) (31.56) (29.88) (29.05) (29.87) (35.70) (25.62) (15.35) (5.72) ost ( 1.91) ( 2.35) ( 3.30) ( 1.29) ( 2.96) ( 0.19) ( 1.93) (1.05) (2.27) (3.49) (3.44) ost (0.65) (0.77) (0.05) ( 2.05) (0.36) ( 1.33) ( 0.40) ( 0.75) (0.78) (0.90) (0.35) ost ( 0.10) ( 1.28) ( 0.22) (0.03) ( 1.35) ( 1.60) (0.26) (1.14) (1.98) (1.26) (1.10) ost ( 1.94) ( 0.04) (0.47) (1.06) ( 0.36) ( 0.08) (0.60) (0.83) ( 0.10) ( 0.58) (0.54) ( 2.92) ( 1.45) (0.14) ( 1.22) ( 0.68) ( 0.52) (0.03) (0.34) (2.81) (2.16) (2.92) β T ERM 5 β T ERM 6 β T ERM 7 β T ERM 8 β T ERM 9 β T ERM 10 β T ERM

14 Table A3: Performance of Portfolios Sorted on β T ERM - Alternative Factors continued Panel B: Conditional Portfolio Analysis - Control for Capital Charge β T ERM 1 β T ERM 2 β T ERM 3 β T ERM 4 β T ERM 5 β T ERM 6 β T ERM 7 NAIC (1.29) ( 3.54) ( 3.67) ( 4.78) NAIC (1.22) ( 3.55) ( 3.42) ( 4.56) NAIC Avg (1.29) ( 3.80) ( 3.86) ( 5.23) β T ERM 8 β T ERM 9 β T ERM 10 β T ERM 10 1 CBMKT α TERM+DEF α TERM+DEF+STOCK α 13

15 Table A4: Performance of Portfolios Sorted on β DEF - Alternative Factors This table presents the results of an unconditional (Panel A) and conditional portfolio analysis (Panel B) examining the performance of portfolios formed by sorting on β DEF. The analysis here is identical to that in Table 7 of the main paper, except that the factor analysis of the bond returns uses CBMKT Alt and DEF Alt as factors, which are constructed from the returns of bonds in our sample, instead of CBMKT and DEF, which are constructed from the returns of Barclays indices. Panel A: Unconditional Portfolio Analysis β DEF 1 β DEF 2 β DEF 3 β DEF 4 Model Excess Return Excess Return (4.55) (4.49) (4.70) (4.00) (4.17) (4.27) (3.94) (3.65) (3.79) (3.70) (1.42) CBMKT α (2.09) (1.42) (1.49) (0.55) (1.03) (1.01) ( 0.21) ( 1.88) ( 0.90) (0.23) ( 0.99) β CBMKT,Alt (17.64) (38.64) (32.32) (29.13) (35.02) (35.95) (50.02) (50.03) (60.82) (35.69) (7.04) TERM+DEF α (1.97) (1.43) (1.60) (0.57) (1.13) (1.12) ( 0.11) ( 1.74) ( 0.87) (0.08) ( 1.08) (17.71) (33.50) (26.93) (27.03) (36.87) (33.41) (46.21) (47.25) (56.75) (34.20) (6.80) β DEF,Alt (13.28) (21.55) (17.04) (20.02) (28.19) (25.24) (32.49) (33.76) (40.81) (26.38) (5.02) TERM+DEF+STOCK α (2.41) (1.27) (1.15) (0.52) (1.16) (0.79) (0.32) ( 1.12) ( 0.77) ( 0.00) ( 1.25) (20.16) (33.98) (29.35) (27.09) (37.24) (35.62) (43.55) (43.00) (44.45) (34.52) (7.09) β DEF,Alt (15.58) (21.59) (19.71) (21.09) (32.42) (28.83) (29.35) (29.94) (31.07) (21.88) (4.26) ost ( 0.07) ( 0.32) ( 1.09) ( 1.61) ( 2.11) ( 1.14) ( 3.18) ( 1.28) ( 0.56) (0.95) (0.80) ost (1.10) (0.26) ( 0.33) ( 0.79) ( 2.31) ( 1.62) ( 0.61) (0.12) ( 0.43) ( 1.21) ( 1.32) ost (1.95) (2.13) (0.24) (0.48) (0.20) ( 0.15) (0.28) ( 0.50) ( 1.91) ( 0.85) ( 1.44) ost (0.00) (0.81) (2.22) (2.23) (0.26) (1.32) ( 0.58) ( 1.56) (0.61) ( 0.75) ( 0.38) ( 3.00) ( 1.41) ( 0.93) ( 0.53) (0.67) (1.61) ( 0.23) (0.48) (0.71) (0.79) (2.20) β DEF 5 β DEF 6 β DEF 7 β DEF 8 β DEF 9 β DEF 10 β DEF

16 Table A4: Performance of Portfolios Sorted on β DEF - Alternative Factors continued Panel B: Conditional Portfolio Analysis - Control for Capital Charge β DEF 1 β DEF 2 β DEF 3 β DEF 4 β DEF 5 β DEF 6 β DEF 7 NAIC (0.62) ( 1.51) ( 1.48) ( 1.24) NAIC (1.82) ( 0.84) ( 1.01) ( 1.32) NAIC Avg (1.46) ( 1.40) ( 1.46) ( 1.44) β DEF 8 β DEF 9 β DEF 10 β DEF 10 1 CBMKT α TERM+DEF α TERM+DEF+STOCK α 15

17 Table A5: Performance of Portfolios Sorted on NIG Downgrade Probability - Alternative Factors This table presents the results of a portfolio analysis examining the performance of portfolios formed by sorting on NIG downgrade probability. The analysis here is identical to that in Table 4 of the main paper, except that the factor analysis of the bond returns uses CBMKT Alt and DEF Alt as factors, which are constructed from the returns of bonds in our sample, instead of CBMKT and DEF, which are constructed from the returns of Barclays indices. The analysis covers portfolio formation (return) months t (t + 1) from December 1977 (January 1978) to November (December) 1992, inclusive. NAIC 1 NAIC 2 No BBB IG No BBB Model Excess Return Excess Return (0.92) (1.23) (0.97) (1.28) (1.06) (0.64) ( 0.82) (0.49) ( 1.05) CBMKT α ( 1.70) (2.14) ( 0.42) (2.27) (0.51) (0.71) ( 1.19) (0.51) ( 1.58) β CBMKT,Alt (285.63) (61.88) (910.32) (49.78) (39.90) ( 0.56) (2.61) ( 0.20) (3.73) TERM+DEF α ( 1.82) (2.16) ( 0.18) (2.33) (0.27) (0.53) ( 1.56) (0.27) ( 1.85) (291.61) (51.85) ( ) (45.46) (51.78) (2.59) (4.74) (3.00) (5.14) β DEF,Alt (83.42) (22.38) (288.42) (19.71) (24.09) (5.35) (5.80) (5.64) (5.18) TERM+DEF+STOCK α ( 1.26) (1.55) ( 0.00) (1.65) ( 0.09) (0.12) ( 1.29) ( 0.09) ( 1.61) (306.78) (58.05) ( ) (49.84) (47.76) (1.68) (4.28) (2.09) (4.90) β DEF,Alt (95.36) (25.01) (322.38) (21.91) (27.72) (5.58) (6.30) (5.98) (5.60) ost ( 2.98) (2.64) ( 1.71) (2.68) (1.58) (1.79) (0.11) (1.60) (0.02) ost ( 2.66) (2.46) ( 1.02) (2.48) (1.69) (1.88) (0.06) (1.68) ( 0.07) ost ( 1.41) (1.11) ( 0.91) (1.10) (0.20) (0.34) ( 0.42) (0.23) ( 0.56) ost (0.54) ( 0.21) (0.62) ( 0.14) ( 0.04) ( 0.10) (0.06) ( 0.07) (0.04) (0.56) ( 0.23) (0.56) ( 0.35) ( 0.36) ( 0.40) ( 0.27) ( 0.38) ( 0.16) BBB BBB [BBB ] NAIC 1 [BBB ] NAIC 2 No BBB [BBB ] IG No BBB [BBB ] BBB 16

18 Table A6: Performance of Portfolios Sorted on β CBMKT - Alternative Factors This table presents the results of an unconditional (Panel A) and conditional portfolio analysis (Panel B) examining the performance of portfolios formed by sorting on β CBMKT. The analysis here is identical to that in Table 5 of the main paper, except that the factor analysis of the bond returns uses CBMKT Alt and DEF Alt as factors, which are constructed from the returns of bonds in our sample, instead of CBM KT and DEF, which are constructed from the returns of Barclays indices. The analysis covers portfolio formation (return) months t (t + 1) from December 1977 (January 1978) to November (December) 1992, inclusive. Panel A: Unconditional Portfolio Analysis β CBMKT 1 β CBMKT 2 β CBMKT 3 β CBMKT 4 Model Excess Return Excess Return (1.83) (1.07) (0.91) (0.84) (0.89) (0.88) (0.88) (0.90) (0.95) (0.98) (0.52) CBMKT α (2.89) (0.58) ( 0.02) ( 0.76) ( 1.02) ( 1.89) ( 1.49) ( 0.99) ( 0.40) ( 0.15) ( 1.28) β CBMKT,Alt (18.96) (18.78) (24.39) (41.62) (93.95) (126.04) (96.50) (64.49) (50.44) (36.65) (18.82) TERM+DEF α (3.09) (0.38) ( 0.39) ( 1.41) ( 1.44) ( 1.90) ( 1.45) ( 0.92) ( 0.17) (0.27) ( 1.32) (18.93) (21.07) (30.75) (60.08) (125.36) (102.36) (86.87) (64.94) (59.36) (54.46) (23.19) β DEF,Alt (9.97) (12.91) (20.29) (32.60) (65.45) (32.89) (32.32) (22.88) (22.99) (18.73) (4.09) TERM+DEF+STOCK α (1.47) (0.07) ( 0.07) ( 0.65) ( 0.46) ( 0.52) ( 0.61) ( 0.34) ( 0.18) ( 0.15) ( 0.93) (21.53) (22.17) (30.44) (56.74) (122.47) (112.47) (95.48) (65.40) (56.66) (49.19) (24.34) β DEF,Alt (10.92) (13.44) (19.90) (29.46) (75.06) (38.06) (37.33) (23.81) (22.70) (17.15) (4.42) ost (2.68) (0.92) (0.11) ( 0.95) ( 2.30) ( 3.13) ( 2.75) ( 1.89) ( 0.39) (1.65) ( 0.14) ost (1.96) (1.60) (1.89) (1.29) (1.15) (0.09) ( 0.81) ( 1.53) ( 1.53) ( 0.99) ( 1.77) ost (2.67) (1.49) ( 0.40) ( 1.44) ( 2.46) ( 2.74) ( 2.16) ( 1.72) (0.43) (1.84) ( 0.47) ost (0.38) ( 0.78) ( 1.88) ( 1.55) ( 0.18) (0.49) (0.92) (0.80) (0.82) (0.02) ( 0.22) (0.45) (0.60) (1.43) (0.89) ( 0.09) ( 0.20) ( 1.64) ( 1.43) ( 0.95) ( 0.42) ( 0.49) β CBMKT 5 β CBMKT 6 β CBMKT 7 β CBMKT 8 β CBMKT 9 β CBMKT 10 β CBMKT

19 Table A6: Performance of Portfolios Sorted on β CBMKT - Alternative Factors continued Panel B: Conditional Portfolio Analysis - Control for Capital Charge β CBMKT 1 β CBMKT 2 β CBMKT 3 β CBMKT 4 β CBMKT 5 β CBMKT 6 β CBMKT 7 NAIC (0.50) ( 1.25) ( 1.28) ( 0.74) NAIC (0.48) ( 1.35) ( 1.30) ( 1.23) NAIC Avg (0.50) ( 1.42) ( 1.44) ( 1.09) β CBMKT 8 β CBMKT 9 β CBMKT 10 β CBMKT 10 1 CBMKT α TERM+DEF α TERM+DEF+STOCK α 18

20 Table A7: Performance of Portfolios Sorted on β T ERM - Alternative Factors This table presents the results of an unconditional (Panel A) and conditional portfolio analysis (Panel B) examining the performance of portfolios formed by sorting on β T ERM. The analysis here is identical to that in Table 6 of the main paper, except that the factor analysis of the bond returns uses CBMKT Alt and DEF Alt as factors, which are constructed from the returns of bonds in our sample, instead of CBM KT and DEF, which are constructed from the returns of Barclays indices. The analysis covers portfolio formation (return) months t (t + 1) from December 1977 (January 1978) to November (December) 1992, inclusive. Panel A: Unconditional Portfolio Analysis β T ERM 1 β T ERM 2 β T ERM 3 β T ERM 4 Model Excess Return Excess Return (1.76) (1.18) (0.90) (0.92) (0.91) (0.85) (0.88) (0.91) (0.94) (0.99) (0.57) CBMKT α (2.83) (1.02) ( 0.16) ( 0.24) ( 1.10) ( 2.21) ( 1.33) ( 0.76) ( 0.35) ( 0.02) ( 1.27) β CBMKT,Alt (21.07) (20.89) (26.52) (47.31) (123.07) (103.14) (82.23) (58.10) (43.33) (39.30) (20.45) TERM+DEF α (2.96) (0.91) ( 0.60) ( 0.68) ( 1.45) ( 2.16) ( 1.27) ( 0.62) ( 0.04) (0.46) ( 1.25) (20.15) (22.67) (34.42) (64.58) (121.39) (84.46) (76.18) (67.61) (58.77) (56.96) (24.12) β DEF,Alt (10.67) (13.20) (21.67) (34.55) (57.65) (28.74) (25.05) (25.27) (22.77) (20.95) (5.30) TERM+DEF+STOCK α (1.41) (0.42) ( 0.46) ( 0.34) ( 0.27) ( 0.91) ( 0.48) ( 0.18) ( 0.12) (0.32) ( 0.64) (22.82) (24.89) (34.70) (63.31) (122.66) (87.86) (80.15) (70.19) (58.89) (56.34) (27.59) β DEF,Alt (11.93) (14.26) (21.18) (32.99) (63.31) (31.47) (27.56) (26.96) (22.24) (19.95) (5.96) ost (2.34) (1.09) (0.12) ( 0.68) ( 2.00) ( 4.00) ( 3.68) ( 2.12) (0.77) (2.06) ( 0.21) ost (1.86) (1.57) (1.51) (1.74) (1.00) (0.27) ( 1.19) ( 2.04) ( 1.92) ( 1.22) ( 1.81) ost (2.57) (1.48) ( 0.13) ( 1.17) ( 2.88) ( 2.86) ( 2.39) ( 1.43) (0.82) (1.66) ( 0.75) ost ( 0.07) ( 0.86) ( 1.13) ( 0.76) ( 0.71) (0.66) (0.86) (0.84) (0.40) ( 0.84) ( 0.48) (0.85) (0.88) (1.30) (0.76) (0.83) (0.34) ( 0.86) ( 0.63) ( 0.78) ( 0.61) ( 0.80) β T ERM 5 β T ERM 6 β T ERM 7 β T ERM 8 β T ERM 9 β T ERM 10 β T ERM

21 Table A7: Performance of Portfolios Sorted on β T ERM - Alternative Factors continued Panel B: Conditional Portfolio Analysis - Control for Capital Charge β T ERM 1 β T ERM 2 β T ERM 3 β T ERM 4 β T ERM 5 β T ERM 6 β T ERM 7 NAIC (0.51) ( 1.30) ( 1.31) ( 0.64) NAIC (0.51) ( 1.41) ( 1.36) ( 1.28) NAIC Avg (0.51) ( 1.50) ( 1.51) ( 1.06) β T ERM 8 β T ERM 9 β T ERM 10 β T ERM 10 1 CBMKT α TERM+DEF α TERM+DEF+STOCK α 20

22 Table A8: Performance of Portfolios Sorted on β DEF - Alternative Factors This table presents the results of an unconditional (Panel A) and conditional portfolio analysis (Panel B) examining the performance of portfolios formed by sorting on β DEF. The analysis here is identical to that in Table 7 of the main paper, except that the factor analysis of the bond returns uses CBMKT Alt and DEF Alt as factors, which are constructed from the returns of bonds in our sample, instead of CBMKT and DEF, which are constructed from the returns of Barclays indices. The analysis covers portfolio formation (return) months t (t + 1) from December 1977 (January 1978) to November (December) 1992, inclusive. Panel A: Unconditional Portfolio Analysis β DEF 1 β DEF 2 β DEF 3 β DEF 4 Model Excess Return Excess Return (0.82) (0.87) (0.99) (0.96) (0.98) (1.04) (1.05) (1.03) (1.12) (1.24) (1.87) CBMKT α ( 1.26) ( 1.01) (0.23) ( 0.16) (0.17) (0.82) (0.90) (0.65) (1.65) (1.83) (1.84) β CBMKT,Alt (48.36) (44.34) (85.12) (55.32) (66.62) (89.30) (77.25) (74.66) (75.99) (67.90) ( 0.03) TERM+DEF α ( 1.15) ( 0.86) (0.47) ( 0.16) (0.05) (0.72) (0.75) (0.39) (1.59) (1.74) (1.79) (48.69) (46.78) (96.10) (48.08) (62.34) (80.52) (92.84) (122.66) (72.12) (51.73) (1.42) β DEF,Alt (15.73) (20.85) (38.80) (25.81) (32.12) (40.48) (40.86) (48.72) (34.46) (21.95) (2.87) TERM+DEF+STOCK α ( 1.01) ( 0.56) (0.56) (0.06) ( 0.04) (0.47) (0.52) (0.25) (1.17) (1.45) (1.43) (48.15) (45.63) (82.69) (46.98) (61.90) (81.62) (91.25) (129.29) (74.21) (54.82) (0.92) β DEF,Alt (15.05) (21.83) (35.88) (25.21) (30.93) (43.04) (40.58) (50.08) (37.71) (23.64) (2.35) ost ( 0.46) ( 0.54) ( 0.11) ( 1.16) ( 0.27) (0.33) (0.79) (1.56) (2.19) (1.62) (1.19) ost ( 1.17) ( 1.39) ( 0.85) ( 0.12) (0.44) (0.19) (0.18) (0.71) (1.95) (1.80) (2.01) ost ( 0.76) ( 0.87) ( 0.35) (0.64) (0.07) (0.62) (0.35) (0.23) (1.84) (1.23) (1.30) ost (1.16) ( 0.17) ( 0.56) ( 0.80) (0.10) (0.17) ( 0.17) ( 0.70) ( 1.27) ( 0.18) ( 0.72) ( 1.08) (1.13) (2.02) (0.71) (0.62) ( 0.41) (0.27) ( 0.25) ( 0.46) ( 1.07) ( 0.22) β DEF 5 β DEF 6 β DEF 7 β DEF 8 β DEF 9 β DEF 10 β DEF

23 Table A8: Performance of Portfolios Sorted on β DEF - Alternative Factors continued Panel B: Conditional Portfolio Analysis - Control for Capital Charge β DEF 1 β DEF 2 β DEF 3 β DEF 4 β DEF 5 β DEF 6 β DEF 7 NAIC (0.86) (1.40) (1.29) (1.13) NAIC (1.04) (0.22) (0.13) ( 0.58) NAIC Avg (1.43) (1.00) (0.85) (0.31) β DEF 8 β DEF 9 β DEF 10 β DEF 10 1 CBMKT α TERM+DEF α TERM+DEF+STOCK α Table A9: Change in Portfolio Alphas versus Alternative Factors This table presents alphas and factor sensitivities from factor analyses of zero-cost long-short portfolio excess returns using the full sample period. The analyses here are identical to those in Table A9 of the main paper, except that the factor analyses of the bond returns use CBMKT Alt and DEF Alt as factors, which are constructed from the returns of bonds in our sample, instead of CBMKT and DEF, which are constructed from the returns of Barclays indices. 22

24 Table A9: Change in Portfolio Alphas versus Alternative Factors - continued [BBB ] NAIC 1 [BBB ] NAIC 2 No BBB [BBB ] IG No BBB α (0.12) ( 1.29) ( 0.09) ( 1.61) ( 0.93) ( 0.64) (1.43) α (2.24) (3.30) (2.58) (2.90) ( 3.15) ( 3.35) ( 1.89) (1.68) (4.28) (2.09) (4.90) (24.34) (27.59) (0.92) β DEF,Alt (5.58) (6.30) (5.98) (5.60) (4.42) (5.96) (2.35) ost (1.79) (0.11) (1.60) (0.02) ( 0.14) ( 0.21) (1.19) ost (1.88) (0.06) (1.68) ( 0.07) ( 1.77) ( 1.81) (2.01) ost (0.34) ( 0.42) (0.23) ( 0.56) ( 0.47) ( 0.75) (1.30) ost ( 0.10) (0.06) ( 0.07) (0.04) ( 0.22) ( 0.48) ( 0.72) ( 0.40) ( 0.27) ( 0.38) ( 0.16) ( 0.49) ( 0.80) ( 0.22) βp T ost, ERM ( 0.62) ( 1.84) ( 0.80) ( 2.17) (4.53) (2.18) (5.58) β DEF,Alt, ( 2.15) ( 2.31) ( 2.37) ( 2.45) (4.57) (1.00) (1.67) ost, (0.38) (0.43) (0.12) (1.07) (2.95) (3.05) (0.09) ost, ( 1.30) ( 0.13) ( 1.18) (0.07) (1.44) (1.60) ( 2.33) ost, ( 0.46) ( 0.49) ( 0.59) (0.12) (1.42) (1.24) ( 1.95) ost, ( 0.52) ( 0.28) ( 0.38) ( 0.54) (0.36) (0.72) (0.23), (1.68) (0.96) (1.47) (1.10) (1.18) (2.54) (1.71) [BBB ] BBB β CBMKT 10 1 β T ERM 10 1 β DEF

25 Table A10: Performance of Portfolios Sorted on NIG Downgrade Probability - Alternative Factors This table presents the results of a portfolio analysis examining the performance of portfolios formed by sorting on NIG downgrade probability. The analysis here is identical to that in Table 4 of the main paper, except that the factor analysis of the bond returns uses CBMKT Alt and DEF Alt,BBB as factors, which are constructed from the returns of bonds in our sample, instead of CBMKT and DEF, which are constructed from the returns of Barclays indices. NAIC 1 NAIC 2 No BBB IG No BBB Model Excess Return Excess Return (3.83) (4.11) (3.97) (4.25) (4.90) (3.14) (2.76) (3.30) (2.18) CBMKT α ( 1.91) (0.86) ( 4.13) (1.73) (3.96) (3.72) (3.48) (4.01) (3.16) β CBMKT,Alt (74.74) (52.12) (237.26) (42.81) (22.18) ( 0.41) ( 1.19) ( 0.61) ( 0.97) TERM+DEF α (2.62) (2.58) (2.63) (2.74) (3.66) (3.26) (3.50) (3.55) (2.50) (8.20) (8.71) (8.48) (8.14) (5.83) ( 1.85) ( 3.54) ( 2.26) ( 2.83) β DEF,AltBBB (0.91) (2.73) (1.66) (2.14) (2.27) (2.72) (0.66) (2.27) (1.09) TERM+DEF+STOCK α (1.42) (1.42) (1.42) (1.67) (2.61) (2.73) (3.20) (3.12) (1.99) (11.06) (11.70) (11.61) (10.83) (7.91) ( 1.18) ( 2.99) ( 1.65) ( 2.03) β DEF,AltBBB (0.21) (2.36) (1.05) (1.72) (2.01) (2.82) (0.54) (2.31) (1.00) ost (3.20) (3.36) (3.43) (2.78) (3.41) (1.59) (1.14) (1.38) (1.53) ost (1.28) (1.45) (1.38) (1.20) (1.07) (0.13) ( 0.02) (0.07) (0.12) ost (1.32) (1.55) (1.43) (1.07) (0.63) ( 0.66) ( 1.29) ( 0.87) ( 0.64) ost ( 0.80) ( 1.52) ( 1.12) ( 1.02) ( 1.50) ( 0.94) ( 0.58) ( 0.80) ( 0.90) (0.87) (1.27) (1.10) (1.12) (1.56) (2.25) (1.48) (1.99) (1.60) BBB BBB [BBB ] NAIC 1 [BBB ] NAIC 2 No BBB [BBB ] IG No BBB [BBB ] BBB 24

26 Table A11: Performance of Portfolios Sorted on β CBMKT - Alternative Factors This table presents the results of an unconditional (Panel A) and conditional portfolio analysis (Panel B) examining the performance of portfolios formed by sorting on β CBMKT. The analysis here is identical to that in Table 5 of the main paper, except that the factor analysis of the bond returns uses CBMKT Alt and DEF Alt,BBB as factors, which are constructed from the returns of bonds in our sample, instead of CBMKT and DEF, which are constructed from the returns of Barclays indices. Panel A: Unconditional Portfolio Analysis β CBMKT 1 β CBMKT 2 β CBMKT 3 β CBMKT 4 Model Excess Return Excess Return (6.86) (4.43) (3.86) (3.50) (3.65) (3.80) (4.15) (3.81) (3.71) (3.34) (1.46) CBMKT α (7.17) (1.69) (0.34) ( 0.04) ( 0.30) ( 0.25) (0.41) ( 0.72) ( 1.33) ( 2.23) ( 4.54) β CBMKT,Alt (13.39) (15.01) (18.80) (20.89) (33.72) (36.65) (47.49) (51.58) (44.94) (36.40) (20.97) TERM+DEF α (5.98) (3.19) (2.49) (2.12) (2.28) (2.33) (2.76) (2.47) (2.39) (1.80) ( 1.07) (6.26) (5.56) (5.97) (6.62) (6.63) (7.28) (7.95) (8.00) (9.08) (9.15) (8.75) β DEF,AltBBB (0.90) (0.50) (1.33) (1.51) (1.77) (1.87) (2.25) (1.61) (1.72) (1.35) (1.44) TERM+DEF+STOCK α (5.41) (2.18) (1.50) (1.10) (1.38) (1.44) (1.77) (1.27) (0.98) (0.24) ( 2.81) (7.76) (6.83) (7.40) (8.30) (8.06) (9.29) (10.58) (10.79) (12.54) (13.31) (12.72) β DEF,AltBBB (0.57) (0.03) (0.79) (1.02) (1.28) (1.23) (1.73) (0.89) (0.91) (0.68) (0.68) ost (1.76) (1.91) (1.85) (2.47) (1.78) (2.83) (3.54) (4.14) (3.63) (4.60) (5.10) ost (1.58) (0.64) (1.60) (0.54) (0.61) (0.35) (0.39) (1.18) (2.17) (1.54) (1.07) ost (1.12) (0.93) (0.85) (0.92) (0.86) (0.73) (0.92) (1.49) (1.66) (2.07) (2.21) ost ( 1.13) ( 0.45) ( 1.66) ( 0.21) ( 0.38) ( 1.18) ( 1.73) ( 0.63) ( 1.16) ( 1.20) ( 0.90) (0.02) (1.23) (1.27) (0.93) (0.72) (1.09) (1.36) (0.50) (1.43) (1.38) (1.83) β CBMKT 5 β CBMKT 6 β CBMKT 7 β CBMKT 8 β CBMKT 9 β CBMKT 10 β CBMKT