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The sample period in this study ranges from 01/1971 to 12/2006. However, the actual

period included in this study is from 01/1971 to 01/2007 because the subsequent realized

monthly returns are used in this dissertation as the proxy of the expected returns.

I retrieve the data of the sample firms from the COMPUSTAT and the CRSP

databases. Firms missing the following information are excluded from the sample: debt in

one year (DATA34) or long-term debt (DATA9) from the COMPUSTAT, price

information, shares outstanding or monthly returns from the CRSP database.

The following data are extracted from the COMPUSTAT North America annual file:

• Common equity (DATA60), which is used to measure book value (BV);

• Debt in current liabilities (DATA34)

• Long-Term Debt (DATA9)

• Long-term debt issuance (COMPUSTAT # 111)

• Change in current debt (COMPUSTAT # 301)

• Capital expenditure (COMPUSTAT # 128)

The financial information above has the report-delay problem. More specifically,

the COMPUSTAT database extracts its financial information disclosed by publicly traded

companies mainly from Forms 10-K and 10-Q, which are the annual and the quarterly

reports required by the SEC. The current deadlines for filing periodic reports are

implemented on Nov. 15th, 2002. These deadlines are reported in Table III (See

Appendix B, Table III for detail).

Prior to the change, a domestic reporting company must file a quarterly report no

later than 45 calendar days after the end of each of its first three fiscal quarters, and an

annual report no later than 90 calendar days after the end of its fiscal year. In the new

ruling, the filers are grouped into three groups - large accelerated filers, accelerated filers

and non-accelerated filers. The deadlines for the non-accelerated filers have not changed.

The deadlines of the 10-Q for the accelerated filers are shorten from 45 to 40 days. The

deadline of the 10-K for the large accelerated filers is reduced to 60 days and for the

accelerated filers to 75 days.

Since there can be a delay of up to 90 days for the 10-K form, I use the annual

financial information at year t four months after its reporting calendar date to calculate

the distance-to-default measure to make sure that all information is available to investors

when the default measure is calculated. For example, the 2005 fiscal year-end data from

the COMPUSTAT database will be used to match the CRSP data from May 1st, 2006 to

value used is from the annual financial information at year t six months after its reporting

calendar date.

The CRSP monthly file is used for the following variables:

• Monthly price

• Holding period returns (including dividend)

• Shares outstanding

• Delisting price

• Delisting returns (dividend included)

• Delisting date

• Shares outstanding when de-listed.

Monthly equity returns used in portfolio and regression analysis are from the CRSP

monthly file, which also contains delisting information.

As the returns of the distressed stocks are directly related to the delisting returns, the

empirical study needs to carefully consider the delisting of stocks. In many cases, the

CRSP monthly file reports delisting dates and delisting returns. This study has 15,937

delisting returns available in the sample, including delisting due to performance-related

reasons (The CRSP delisting code between 400 and 599) and those due to the other

reasons, including mergers and change of exchanges. In the case of the delisting stocks

without the available return information in the CRSP, the last available full-month returns

were used.

The following data are from the CRSP daily file:

• Daily equity price (dividend adjusted)

The price and shares outstanding used to calculate DLI is mostly from the CRSP daily

file. In addition, this study adjusted the delisting returns according to the delisting date

and return information from the CRSP monthly file. The annual equity volatility (σ_E) is

calculated using the adjusted daily historical data from the CRSP database. More

specifically, the following procedures are used.

Assuming the number of observations is n+1; P_E,iV_{E i,} is the stock price at the end of

the ith interval, with i=0,1,…, n+1

And let ) ln( 1 , , − = i E i E i P P r for i=1,2,…,n+1.

The estimation of daily volatility of r is given by _i

∑

= − = n i i r r n s 1 2 ) ( 1

The volatility per annum can be calculated from the volatility per trading day using

the following formula:

Volatility per annuam Volatility per trading day Number of trading datys per annum s 252

= ×

= ×

Market value (MV) is defined as the product of price at time t and the corresponding

shares outstanding; book-to-market ratio (BM) is defined as book value (BV) divided by

market value (MV). Firms with negative book values are excluded from the sample.

Monthly observations of the one-year Treasury bill rate obtained from the Federal

The historical data of Fama-French three risk factors, including the excess return,

SMB, and HML are from Kenneth French’s website24.

The aggregate default likelihood measure (ADLI) at time t is defined as a simple

average of the default likelihood indicators of all firms in a portfolio.

Table IV summarizes the descriptive statistics of ADLI, size and BM. The table also

includes the summary statistics of the Fama and French factors (HML and SMB). Panel

A reported the summary statistics of the time series. Panel B is the correlation matrix

among the aggregated variables and Fama and French factors. To calculate the values in

Table IV, this thesis first calculates ADLI, size and BM measure each month as the

simple average of all firms in that month to get the time series of these variables. The

time series are then compared with the Fama and French factors (See Appendix B, Table

IV for detail).

The relationships between ADLI, size and BM are quite interesting. The correlation

table shows a significant positive correlation (0.098) between ADLI and BM and a

significant negative correlation (-0.548) between ADLI and size, which are consistent

with our intuition. However, there was a positive correlation (0.211) between the market

value and BM, which is in conflict with my expectation of a negative relationship

because cēterīs paribus, the increase of market value would decrease BM. The significant

positive concurrent correlation between size and BM suggests that the book value may

increase/decrease more than the increase/decrease of the market value. This increasing

book value can be seen as an increasing safety cushion of higher market risks due to high

stock prices. Furthermore, there is no significant correlation between ADLI and the Fama

French factors, which suggests that ADLI may incorporate different information from

24

HML and SMB. The two Fama French factors are significant and negatively correlated

with each other (-0.227), which is what I expected because larger book-to-market ratio

CHAPTER V

In document UNIVERSIDAD DE SONORA DIVISIÓN DE INGENIERÍA T E S I S (página 67-80)