Value investing in credit markets

Beaver et al. (2012) combine the bankruptcy database from Beaver et al. (2005), which was derived from multiple sources including CRSP, Compustat, Bankruptcy.com, Capital Changes Reporter, and a list provided by Shumway with a list of bankruptcy firms provided by Chava and Jarrow and used in Chava and Jarrow (2004).

To ensure that prediction is made out of sample and to avoid a potential bias of ex post over-fitting the data, we estimate coefficients using an expanding window approach. In particular, to estimate the probability of default for calendar year 2011 (January 2011 to December 2011), we combine all the available accounting and market data from January 1980 to December 2009, use it to predict bankruptcy outcomes for January 1981 to December 2010, retain the coefficients, and use them to estimate the probability of default for 2011. To obtain an estimate of the probability of default for the period from February 2011 to January 2012, we include one more month in the estimation. In particular, we combine all the available accounting and market data from January 1980 to January 2010, use it to predict bankruptcy outcomes for January 1981 to January 2011, and apply the estimated coefficients to accounting and market data available at January 2011.

We compare the ability of the default prediction models in correctly predicting bankruptcies based on the area under the receiver operating curves (ROC). Based on this comparison, we find that the areas under the ROC for the models that we use in our main analysis are significantly larger. The finding that market-based models that we use for our main analysis perform better than pure accounting-based models is consistent with Hillegeist et al. (2004).

We use Moody’s/KMV EDF score directly as a measure of probability of default. The EDF score is empirically mapped by Moody’s/KMV to their default database, using a more flexible empirical transformation.

Our return calculation is imprecise as it misses some aspects of accrued interest for bonds and the impact of “roll” over the course of the month (Lok and Richardson 2011). While these are second order effects, we have re-estimated all of our returns-based tests using total returns inclusive of accrued interest and roll as per Merrill Lynch’s total return computations. Our results are virtually identical between using our pseudo return measure or total bond returns. We have chosen to present the results based on the return approximation, as this allows greater comparability with the CDS market data.

Campbell et al. (2008) find that a reduced form specification that includes accounting and market variables has higher predictive power for bankruptcy than a measure of distance to default estimated using the approach outlined by Hillegeist et al. (2004). However, they do not use Moody’s/KMV measure, EDF, in their analysis, and therefore their results are not necessarily inconsistent with ours.

The option adjusted spread is the difference between a bond’s yield and the yield of a duration matched treasury issue, adjusted for the portion of that difference that is due to embedded options.

In untabulated analysis we find that the predictive power of the EDF measure for bankruptcy and with respect to credit market returns is higher after 2002, the year in which Moody´s acquired KMV. It is possible that EDF data became more widely ‘known’ to the market at this time. The positive relation we document between EDF based measures of credit relative value and future credit returns suggests that the market continues to fail to incorporate value relevant information in a timely manner.

Our results are robust to the inclusion of bond returns for month t + k − 1 as an additional explanatory variable to control for bond market momentum.

The Sharpe ratio for the Bharath and Shumway (2008) model is the highest among all four. This result is explained by the fact that this model includes equity returns and therefore captures information spillover effects from the equity market to the credit market. Note that the characteristic regressions reported in Table 6 document a lower relative predictive ability for the Bharath and Shumway measure as evidenced by the lower test statistics for its coefficient when the equity return characteristics (e.g., MOMS and MOML) are directly controlled for.

The average cumulative long/short returns over the next 3 (6) months for CDS instruments are 87 (139) bps. CDS contracts are usually more liquid than bonds. Moreover, the cost of buying CDS protection is in general substantially lower than the cost of shorting bonds. For these reasons, long/short CDS returns should be sufficient to cover transaction costs.