Sample Selection

Unlike the extant empirical literature of EHH, Lyden & Saraniti (2000), and JMR, we do not have the objective of selecting only firms with simple capital structures and few bonds on issue. Instead we select firms with a broad range of maturities traded so that we obtain the most information possible across bonds and across the term structure. That tends to direct our sampling toward more frequently traded firms.

The NAIC database comprises all fixed interest trades by North American insurance companies including Treasury and corporate debt trades over the period commencing 1 January 1994 to 31 December 2000. Before combining bought and sold trades, the data comprises over 734,000 trades. For our purposes we require panel data from a smaller subset of corporate firms that exhibit relatively frequent trading, and have several outstanding bonds with remaining maturities that span a term structure, with a history of trading over an extended period of time. Unlike early empirical studies we do not restrict ourselves to firms with debt structures that approximate the zero-coupon Merton ideal (see for example JMR and EHH). This enables us to consider the broad population

of corporate issuers, tempered only by the limitations of data availability and accuracy. We exclude government entities (FISD industry code 04), banks (FISD industry code 20), and savings and loan institutions (FISD industry code 25). Deposit-taking institu- tions have a special role in the economy and bond pricing may be influenced by the implicit government guarantee arising from the moral hazard associated with their fail- ure. Since financial firms are a major source of bond issues, we have chosen to include them in the sample.

Where issuing firms are non-listed subsidiaries of a listed parent, the parent’s market capital and balance sheet data is used. Where there is more than one subsidiary within a corporate group with a unique CUSIP (for example, Ford Motor Company and Ford Motor Credit Company), only one subsidiary is included in the sample.

The second level of filtering removes issues that may be subject to embedded option features, or credit enhancements, not included in the theoretical models under consider- ation. From issue-level data sourced from FISD we:

1. exclude bonds that are convertible, or redeemable (via call, IPO clawback, main- tenance and replacement call or sinking fund), subject to puts, or are credit en- hanced, for example by financial guarantees; and,

2. include only fixed-interest coupon bonds, and corporate debentures with semi- annual compounding with 30/360 day convention, where there are no planned future variation in coupons.

Further issue-level filters are then applied to minimise potential data errors. To un- derstand what data errors may be present in the NAIC data we reviewed prior studies that have utilised schedule D submissions from insurance companies. Hong & Warga (2000) match the recorded bond prices between New York Stock Exchange’s Automated Bond System (ABS), and Schedule D sourced NAIC price data supplied by Capital Access Inc. (CAI), and compare with the closest-in-time bid quotes from Lehman Brothers as reported in the FID. They find that the transaction-based prices from the ABS and NAIC sources are broadly in agreement with each other and with the month-end dealer quotes given by Lehman Brothers dealers. A source of bias was identified in the recording practices of NAIC, in which total transaction costs were rounded upward to the nearest $1,000. Hong & Warga (2000) minimised the bias by restricting their sample to trades with costs of $500,000 or more.2 Bedendo, Cathcart & El-Jahel (1994) exclude bonds with transaction prices below $80 and above $135 as well as bonds with negative credit spreads.

2_{For example, a sale with the value of $1,500,900 would be reported as $1,501,000. To limit the potential}

upward bias in reported prices we adopt the same filter rule and exclude trades of less than $500,000 in total cost which limits the maximum percentage error in reported price to be no more than 0.20 percent of the total transaction cost.

Chakravarty & Sarkar (1999) use CAI sourced NAIC data to compare spreads be- tween government, corporate and municipal debt. In order to minimize incidences of data entry error, they remove all observations where the transaction price is outside the range $500,000 to $1,500,000. Some entries were observed on non-trading days and were removed, and trades occurring on June 30, 1995, June 30, 1996, and December 31, 1997 are removed. Anecdotal evidence suggests insurance companies may have used these dates for recording transactions that they had failed to report in a timely manner.

Consideration is made of the prior findings of errors in the NAIC data. We therefore exclude observations if:

1. there are missing or invalid trade dates;

2. the credit spread is negative (due to measurement error or estimation error for the matched Treasury rate);

3. the remaining maturity of the bond, at the time of the trade, is less than 12 months. We exclude very short-dated bonds due to their sensitivity to small measurement errors as suggested by Cooper & Davydenko (2004);

4. the remaining maturity is greater than 30 years because this is the maximum con- stant maturity Treasury (CMT) risk-free maturity available;

5. total cost of the trade is less than $500,000 in total cost as per Hong & Warga (2000); and,

6. trades occur on 30 June 1995, 30 June 1996 and 31 December 1997 as in Chakravarty & Sarkar (1999).

Where more than one trade occurs on a single day, we use a single representative obser- vation calculated as the weighted average price, where the relative total transaction costs form the weight. This removes duplicate records caused when insurance companies are on both sides of the same transaction.

After these adjustments the data set comprises 1,373 issuers, with 8,799 issues and 96,472 trades. We then apply issuer-level filters to select firms with patterns of trading suitable for robust panel estimation. We select firms with:

1. at least 3 bonds, where each averages at least 6 trades per annum, for a minimum period of 12 months;

2. a broad range of remaining terms to maturity; and,

3. a complete balance sheet history on COMPUSTAT and stock prices from CRSP over the sample period.This information is used for comparison with the firm’s observable solvency ratio, and for deriving initial parameter estimates for the EKF.

To reduce the dimension of the model estimation, no more than ten bonds are in- cluded per issuer. Where more than ten bonds have met the filter rules, the most fre- quently traded are chosen. Finally, the beginning, and end dates, of the issuer’s sample period are chosen as the earliest, and latest dates respectively, that a cross-section of maturities is evident. Consequently, the beginning and end dates of each issuer’s sam- ple vary slightly. Our selection criteria is intended to result in a sample of observations that are closely spaced in time and well represented across the dynamic term structure of the issuing firm. The overall density of the observations provides cross-sectional and time-series information best suited to fitting continuous-time structural credit models. Figure 3.1 shows an example of the trading density for Northrop Grumman Corporation (Northrop). Each point represents an observed trade from one of the four bonds in the sample. Each bond has a different maturity causing the distribution of trades into a pat- tern of distinct parallel lines. Two features in Figure 3.1 are noteworthy. Firstly, our selection criteria results in trades with a broad distribution across the term structure rep- resented by the vertical spacing of observations. Secondly, the horizontal axis shows the passage of time and an overall shortening of the remaining maturities. The final sample comprises 32 issuers, 200 bonds, and 8,953 trades. Table 3.1 shows the final sample of firms and numbers of bonds and observations per issuer. Table C.1 details each bond’s characteristics and descriptive statistics of the bond’s credit spreads. The relatively small sample size is due mainly to merger and acquisition activity causing incomplete COM- PUSTAT and CRSP histories, which are not strictly required for successful model fitting, but are necessary to compare implied solvency ratios with observed market leverage ra- tios.