Measuring abnormal returns

I use a buy-and-hold abnormal return (BHAR) strategy to make inferences about my sample firms’ stock return pattern before, during and after their Chapter 11 date. Barber and Lyon (1997) show that the alternative cumulative abnormal returns (CARs) do not accurately capture the magnitude of investing in an average sample firm relative to an appropriate benchmark over the horizon of interest, which is precisely the objective of long-run event studies of stock returns. Accordingly, the authors favour the BHAR strategy since it “correctly reflects the actual investors’ experience”. Moreover, Barber and Lyon (1997) show that CARs are biased predictors of BHARs, which can lead to an incorrect inference about medium- and long-term stock price performance.

Fama (1998), however, criticizes the use of BHARs and favours CARs because of their desirable statistical properties, which allow cleaner tests of mispricing. Fortunately, Barber and Lyon (1997) and Kothari and Warner (1997) show that the statistical problems uncovered by Fama (1998) with the use of BHARs usually arise over the 3- to 5-year time horizon whereas I restrict my analysis to a one-year period. This is for two reasons. First, filing for bankruptcy often leads to firm delisting, and thus extending the period for computing abnormal returns is problematic due to the loss of many sample cases (e.g., Morse and Shaw, 1988). Secondly, my typical sample firm spends an average (median) of 24.4 (18.1) months in bankruptcy.30 _{Ending the} abnormal return calculation period twelve months before minimizes the impact of this important event on my results. Buy-and-hold abnormal returns are computed as follows:

(

)

2

(

)

2

( )

1 1 1

,

2

1

,

1

, i i t i t t t

BHAR

r

E r

τ τ τ τ

τ τ

= =

⎡

⎤

=Π

+

−Π_⎣

+

_⎦

(3.1)

where

BHAR

_i

(τ τ

₁

,

₂

)

is the buy-and-hold return for firm

i

from time

τ

₁ to

τ

₂,

r

_{i t,} is the raw return for firm

i

at time

t

and

E r( )

_{i t,} is the expected return for firm

i

at time

t

.31 In order to produce meaningful results, individual BHARs are averaged cross-sectionaly as follows (e.g., Barber and Lyon, 1997; Campbell, Lo and MacKinlay, 1997):

(

1 2

)

(

1 2

)

1

1

,

,

n i i

BHAR

BHAR

n

τ τ

τ τ

=

=

∑

(3.2)

where

BHAR

_i

(τ τ

₁

,

₂

)

is defined as above and

n

is the number of firms with a valid BHAR for

time

τ

₁ to

τ

₂. As suggested by equation (3.2), I use equally weighted rather than value- weighted returns since this is more appropriate in the context I address. In fact, strategies that give the same weight to all firms in the investment portfolio allow maximum diversification of each company’s idiosyncratic risk, a critical aspect when dealing with failed firms (e.g., Gilson,

30 _{Altman (1993) and Eberhart, Altman and Aggarwal (1999) report similar statistics for the average/median time spent} in Chapter 11 bankruptcy reorganizations.

31 _{CRSP reports simple returns (both on its daily and monthly file). For more information see the data description} section on WRDS about variable RET.

1995; Platt, 1999, p. 110).32 _{Additionally, previous research has shown that equally weighting} captures the extent of underperformance better than value-weighting (Brav, Geczy and Gompers, 2000; Kadiyala and Rau, 2004). Loughran and Ritter (2000) also argue that value- weighted portfolio returns reduce the power of the tests to detect any potential behavioural bias.

Unless otherwise stated, daily returns collected from CRSP are employed in the calculation of abnormal returns, where

t=0

is the bankruptcy announcement date.33 As argued by Kothari

and Warner (2007, p. 8), the use of daily rather than monthly security return data permits a more precise measurement of abnormal returns and more informative studies of announcement effects. I define a year as twelve 21-trading day intervals, an approach consistent with previous research (e.g, Michaely, Thaler and Womack, 1995; Loughran and Ritter 1995; Ikenberry and Ramnath, 2002). Importantly, in all tests based on daily data, event day +1 is included in the bankruptcy announcement window. Dawkins, Bhattacharya and Bamber (2007) point out that US stock markets close at 4:00 p.m. Eastern Standard Time (EST) while US Courts do not close until 5:00 p.m. local time, making it possible for firms to file their bankruptcy petition after the market closes on event day zero (i.e., after 4:00 p.m. EST). In such cases, investors cannot trade on the information disclosed at the event date until the next trading day.

Some of my sample firms are delisted in the 12-month period subsequent to their Chapter 11 date.34 _{Drawing on Shumway (1997) and Shumway and Warther (1999), I include the delisting} return in the calculation of the abnormal returns, a procedure also used by Campbell, Hilscher and Szilayi (2007). CRSP provides delisting returns for 165 cases, with an average value of - 19.21 percent. Following Ogneva and Subramanyam (2007), for the remaining 30 cases with no data available on CRSP, I substitute the missing delisting return with the average delisting

32 _{In a recent paper, Klein, Rosenfeld and Tucker (2006) examine the long-term stock performance of firms following} reverse stock splits. Similarly to my own case, this paper deals with event firms that are small and trade at very low prices. In order to deal with this issue when analysing the market reaction to the announcement of reverse stock splits, Klein, Rosenfeld and Tucker (2006) also compute equally weighted returns in lieu of value-weighted returns.

33 _{All data sources mentioned in section 3.1 provide the bankruptcy date for each firm they cover. The only exception is} COMPUSTAT. Factiva is used to determine the bankruptcy date for COMPUSTAT cases.

return in the entire CRSP database for the similar type of delisting (as identified by CRSP 3-digit delisting code). The average delisting return after considering this correction for all 195 cases is -20.16 percent.35

In line with Barber and Lyon (1997) and Lyon, Barber and Tsai (1999), when a company is delisted, I assume proceeds from the delisting payment are re-invested in a portfolio of stocks comprising the same size decile of the delisted firm for the remaining of the compounding period. As the authors explain, the sample’s mean long-run abnormal returns calculated with truncation does not represent the average return an investor could earn from investing in an executable strategy since his use of the proceeds from the investment in a delisted firm is left unresolved.

In document Market reaction to bad news: The case of bankruptcy filings. Luis Coelho (Page 59-62)