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An Optimal Corporate Bond Investment Strategy during The compressed spread periodC. Christopher LeeCentral Connecticut State University, USA.Benjamin B. BaeCalifornia State University, Bakersfield, USA.Katie WeckesserCompass Property Management, USA.ABSTRACTThis paper attempted to answer how we would invest in corporate bonds when the prevailing bond market spreads were very low. Sample data included 300 investment grade bonds and 300 junk bonds. We could construct an efficient frontier curve in terms of the bond investment risk & return, based on the results from the statistical analyses. Our empirical evidences suggest that BB-rated corporate bonds were the optimal investment choice. Key words:?risk, returns, portfolio, efficient frontier. JEL Codes:?G10, G11INTRODUCTIONA widely discussed topic among the finance and economic community is the actual returns of investment grade bonds versus non-investment grade bonds. It is known that non-investment grade bonds assume this quality rating due to their high degree of default risk, in relation to investment grade bonds. Due to this increased risk, non-investment grade bonds should generate greater returns. Drexel Burnham Lambert (1985) used this risk/return relationship as a sales mechanism for low-grade or ‘junk’ bonds. In this paper, we examine the return spread between investment grade bonds and non-investment grade bonds. When building a portfolio, an investor wants to generate the greatest return while staying diversified. Incorporating bonds would diversify a portfolio in terms of assets held, but will they generate a return? It is a focal question within this study. We hypothesize that non-investment grade bonds will outperform investment grade bonds, specifically BB bonds will generate the greatest return. To test this hypothesis empirically, we first applied a t-test model to our data followed by an ANOVA model. LITERATURE REVIEWWhile reviewing literature regarding bond yields of U.S. corporate, non-callable bonds there is consensus that investment grade bonds presume less default risk opposed to non-investment grade bonds, typically referred to as low-grade or high-yield bonds. Moeller and Molina (2003) showed that investment grade bonds have lower default rates than non-investment grade, making them more attractive to investors who are risk averse. Altman, Gonzalez-Heres, Chen, and Shin (2014) concluded that higher-volatility in the bond market will generate distressed returns relative to lower-volatility. Huang and Huang (2002) showed that credit risk accounts for only a small fraction of yield spreads for investment-grade bonds of all maturities, with the fraction lower for bonds of shorter maturities, and that it accounts for a much higher fraction of yield spreads for high-yield bonds. Greenwood and Hanson (2012) results demonstrated that a high degree of predictability in corporate bond returns is linked to the quality of the corporate debt financing. This corporate debt financing plays a significant role in what quality rating the corporate debt will obtain. By using issuer quality measures to forecast the excess returns on corporate bonds, Greenwood and Hanson (2012) concluded that in periods when issuer quality is high, corporate bonds will significantly outperform Treasury bonds, and the opposite for when the issuer quality is low. Default Risk and market volatility are not the only determining factors for when deciding which bond(s) to purchase; return is also a top concern. While reviewing literature on which category of bonds, investment grade or non-investment grade, yield greater returns there was much consensus on non-investment grade yielding higher returns. Phillips (2012) presents an argument for the purchase of high-yield bonds, stating that when combined with a low correlation to most assets, in a diversified portfolio, there are many scenarios for incorporating high-yield bonds. In her study she showed that high-yield bonds have produced an equity-like return with a materially lower volatility. Jostova, Nikolova, Philipov, and Stahel (2013) all found that high-yield bonds generate momentum payoffs that are associated only with non-investment grade bonds. Their findings state that momentum profits are 121 basis points per month concentrated to non-investment grade bonds, as this momentum strategy is not profitable for investment grade bonds, which is consistent with the findings of Gebhardt, Hvidkjaer, and Swaminathan (2005). Altman (1989) revealed that B-rated and CCC-rated bonds outperformed all other rating categories for the first four years after being issued, with BB-rating bonds outperforming all categories thereafter. Though there are few studies suggesting there is no difference in the yields of high-grade to low-grade bonds, Cornell and Green (1991) reported in their findings that there was statistically no difference in the returns. DATA AND METHODOLOGYData was collected using Yahoo Finance Bond Screener during the period of March and April 2014 when data was available to the Internet. The screener was set for corporate bonds, maturities 1-5 years, not callable, with bond ratings ranging AAA-BBB or BB-CCC, to allow us to gather separate data for investment grade bonds versus non-investment grade bonds. Out of thousands of investment grade bonds presented by the bond screener, 300 were randomly selected. These 300 comprise the first group of data, G1. Of the hundreds of non-investment grade bonds presented by the bond screener 300 were randomly selected to comprise (G2). Together the total count for data is 600, evenly divided between investment grade and non-investment grade. The distribution of bond ratings among these 600 bonds is presented in the following Table 1. Table SEQ Table \* ARABIC 1. Sample Data Distribution by Bond RatingsTable 2 presents descriptive statistics for bond ratings. BB ratings have the greatest number, 168 and followed by A ratings, 113. Out of the 600 bond entries collected, 168 were bonds with a BB rating. The BB rating bonds had the largest mean return at .22, with a standard deviation of .08, as shown in Table 2. This is considerably higher than all other bonds, with a risk, measured using standard deviation, only .0091 higher than AAA bonds. Table 2 Descriptive StatisticsNumerous studies argue that low-grade, high-yield bonds outperform high-grade bonds due to the steady high-income (coupon) provision, which has served as a cushion to the price volatility (Phillips, 2012; Gebhardt, et al., 2005; Altman, 1989; Wu, et al., 2012; Cici & Gibson 2012; Fama, et al., 2008; Greenwood, et al., 2010; Hodrick & Edward, 1997; Ivashina & Zheng, 2011; Ivashina & Scharfstein, 2010). Contrary to risk and return, in terms of the financial theory, CCC bonds do not outperform BB bonds. Altman concluded in 1989, bonds with a BB rating will outperform all other bonds held for four years or longer, we have hypothesized this for bonds with maturities of one to five years (Altman, 1989; Strebulaev, et al., 2011).H1a:Among the non-investment grade bonds (G2), BB rated bonds will outperform all other bonds on the efficient frontier in terms of return.H1b:Among the non-investment grade bonds (G2), BB rated bonds will outperform all other bonds on the efficient frontier in terms of risk. In summary, a main hypothesis for this research states that there is no difference in risk with the purchase of corporate investment grade bonds to non-investment grade bonds; in fact, non-investment grade bonds, specifically BB rating, will produce the most return, outperforming all other bonds. To test Hypothesis 2a and 2b, ANOVA model was employed. Figure 1 Research FrameworkEMPIRICAL RESULTSDescriptive Statistics in Table 2 show statistical significance on the Levene’s test of homogeneity of variances (p<0.000). Accordingly, we employ Welch model instead of ANOVA model because data violates the ANOVA model’s homogeneity of variances assumption. Table 3 shows Welch model results which reports a statistical significance (p<0.000). Therefore, there is a significant difference among the seven groups of bonds in terms of returns. Table 3 Welch Robust Test of Equality of MeansWelch Statisticsdf1df2p-valueYield372.2536181.475.000Now the question remaining, which bond rating will be the optimal investment is assessed using a Games-Howell Post-Hoc Analysis. This test compares each bond rating to the other bond ratings, assigning p values to each pairing. The analysis shows that BB rated bonds have the most significance, with only moderate significance in relation to B rated bonds. Table 4 below depicts the Post-Hoc test results.Table 4 Games-Howell Post-Hoc Test Results of yieldAn interesting finding in this study is BB rated bonds and the other non-investment grade bonds have a negative correlation among them in terms of return and risk. As the bond rating decreases, becoming riskier, the return in theory would increase to compensate the investor for the additional default risk. Figure 2 shows below that as the bonds with a non-investment grade rating decreases return decreases too; opposing the financial theory. To test Hypothesis 3 that taking the high return of junk bond outweighs the high risk of junk bond as the spread between the return of junk bond and investment grade bond is at least 200 points. 200 points come from industry practice where bond investors use a threshold of 200 spread points when they decide the junk bond is worth investing over the investment grade bond. The group statistics of the two groups (BB-rated bonds, and AA-rated bonds) and the results of t-test Model for testing the equality of means of yield between the two groups are shown in Table 5 below.Table 5. T-test ResultsGroupnYieldMeanStd. DeviationMean Differencedft-statisticsBB-rated bonds 168.2288.0849.3012119.04429.444***AA-rated bonds48-.0722.0544***p<0.001Evidences of this study support findings on investment grade bond returns compared to non-investment grade bond returns in the literature (Phillips, 2012; Gebhardt, et al., 2005; Altman, 1989). Contrary to risk-return in terms of financial theory CCC bonds do not outperform all other bonds, considering the risk associated with them. A limited sample size may be the causation; extensive research with more bond data collected over a specified period may result in alternate findings. Figure 3 shows how financial theory can only be practiced to a certain point, as CCC bonds are not the outperformer. Figure 3 also show that the investment grade bonds have the negative yields. This may indicate that bond markets are still under the US economic slowdown which could lead to more defaults in the future. The?US stock market crash?of?2008?occurred on September 29, 2008. The Dow Jones Industrial Average fell 777.68 points in intra-day trading. That was the largest point drop in any single day in history. In 2014 when we collected bond data in Yahoo Finance, the US economy was still in recession. This recession and possible deflation may explain why the investment grade bonds show the negative yields. Finance theories indicate that in the recessionary economy investors may take investment strategies where they like to pay up now and get less nominal amount of money in the future. This could be profitable if the prices are going to fall significantly in the near future. Furthermore, investors tend to be more risk averse in the aftermath of a big financial crisis such as the?US stock market crash?of?2008. In this case, investors are more likely to buy the investment grade bonds as highly liquid but safe investment opportunities at the cost of low or even negative yields.AAA-rated bonds show the highest risk with the negative 0.08 yield. AA-rated bonds have the negative yield of 0.07 and relatively low risk 0.05. A-rated bonds present slightly lower yield than AAA bonds but their risk is lower than AAA-rated bonds. BBB-rated bonds have the lowest yield as their risk is also lowest as well. It is well known that lower rated bonds have higher yields due to higher default risk compared to higher rated bonds. Partly to confirm this well-known fact and partly to check the robustness of our data, two additional hypotheses are developed and tested, accordingly.H2aNon-Investment grade bonds (G2) produce greater returns compared to Investment grade bonds (G1).H2bNon-Investment grade bonds (G2) produce greater risk compared to Investment grade bonds.To test Hypothesis 2a and 2b, a t-test model was applied. The t-test model measured t-statistics on group mean differences using the sample means and sample standard deviations of the two groups, to see if there was any significant difference between Group 1 (investment grade bonds) and Group 2 (non-investment grade bonds).The results obtained in the group statistics are congruent with hypotheses, 2a and 2b, being that non-investment grade bonds will yield greater returns than investment grade, even with the assumed risk increase. Table 6 shows junk bonds, are riskier with a standard deviation of .139 compared to investment grade bonds that have a standard deviation of .064. Associated with this risk is return, with junk bonds having a mean of .19, while investment grade bonds have a -.100 return. We found statistical significance in T-Test Model (p=0.000). Therefore, data shows that junk bond return is significantly higher than investment grade bonds on average. Table 6. T-test Model Results CONCLUSIONThis paper conducts an empirical study and develops an ANOVA model to test if financial theory on risk and return holds true for corporate bonds. Evidences show that it in fact does not hold true, when tested, as BB rated bonds outperform all other ratings of bonds. Not only are these bonds non-investment grade, but also the risk associated with them has no significant difference to investment grade bonds. Further studies on this subject can investigate the causes for this occurrence in bond returns. Also, the effect of studies with consistent findings such as this one’s effect on the bond market. This research provides the corporate bond market literature with empirical evidence of which bond rating is optimal in terms of return. Evidence suggests that bond investors can achieve profitable outcomes through incorporating BB rated bonds into their portfolio. REFERENCESAltman, E. I. (1989), Measuring Corporate Bond Mortality and Performance.?The Journal of Finance, Vol. 44, No. 4, pp. 909-922.Altman, E., Gonzalez-Heres, J., Chen, P., & Shin, S. (2014), The Return/Volatility Trade-Off of Distressed Corporate Debt Portfolios.?The Journal of Portfolio Management,?Winter 2014, Vol. 40, No. 2, pp. 69-85.Cici, G and Gibson, S., (2012), The Performance of Corporate Bond Mutual Funds: Evidence Based on Security-Level Holdings.?journal of financial and quantitative analysis, Vol. 47, No. 1, pp. 159-178.Cornel, B. and Green, K. 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