Volume 54, Issue 1 pp. 237-249
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Sell the rumour, buy the fact?

Ben R. Marshall

Ben R. Marshall

School of Economics and Finance, Massey University, Wellington, New Zealand

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Nuttawat Visaltanachoti

Nuttawat Visaltanachoti

School of Economics and Finance, Massey University, Wellington, New Zealand

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Genevieve Cooper

Genevieve Cooper

School of Economics and Finance, Massey University, Wellington, New Zealand

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First published: 21 August 2012
Citations: 12

We thank conference participants at the 2010 FMA Annual Meeting in New York and the 2010 New Zealand Finance Colloquium and Veljko Fotak (our FMA discussant), Hamish Anderson, Henk Berkman, Ben Jacobsen, Chris Malone, Nick Nguyen, Kuntara Pukthuanthong, Jeff Wongchoti and the editor, Robert Faff for valuable comments. All errors are our own.

Abstract

We document a high-profile instance of mispricing that is puzzling given the gradual information diffusion hypothesis and the lack of obvious limits to arbitrage. An internet search in 2008 led to a story about United Airlines’ 2002 bankruptcy being re-released as ‘news’. This resulted in United Airlines losing 73 per cent of its value and caused a $4.2 billion decline in the value of airline stocks and United Airlines suppliers. The incorrect bankruptcy ‘news’ was quickly retracted, which led to a rebound in other airline and supplier firms, but the stock price of United Airlines was adversely affected for 4 days.

1. Introduction

We show how a false rumour led to inefficient pricing that persisted for 4 days. On 8 September 2008, an internet search retrieved a 2002 story detailing the bankruptcy of United Airlines, leading to the incorrect conclusion that United Airlines was filing for bankruptcy again. This bankruptcy ‘rumour’ spread through the market, resulting in United Airlines’ market value plunging by 73 per cent (over $1.1 billion). Other airline stocks and United Airline suppliers were also affected, with total value reductions of $3.1 billion. Our paper adds to the media coverage and stock returns literature (see Huberman and Regev, 2001; Tetlock, 2007; and Fang and Peress, 2009).

Our main contribution is related to what we suggest is the most puzzling aspect of the United Airlines (UA) episode – what happened after the rumour was clearly identified as being false. While the prices, volumes and bid–ask spreads of other airline stocks and UA supplier firms quickly returned to prerumour levels, the price of UA did not. Its price did begin to rebound when it was clear the rumour was false; however, it did not return to its prerumour level until 5 days later, despite there being no obvious impediment preventing this inefficient pricing being removed by arbitrageurs. The event we study is quite unique in this respect. The investors trading the stocks considered by earlier papers (see Huberman and Regev, 2001) in the hours and days following the release of the stale news would likely have been unaware that the news was not new. In contrast, investors in our setting were left under no illusions as to the false nature of the bankruptcy rumour with UA issuing the following statement within 20 min of the rumour affecting prices:

‘United Airlines today said reports that the company filed for bankruptcy are completely untrue and were caused by the irresponsible posting of a 6-year-old Chicago Tribune article by the Florida Sun Sentinel newspaper website with the date changed. The story was related to United’s 2002 bankruptcy filing, and United has demanded a retraction from the Sun Sentinel and is launching an investigation. United exited bankruptcy in February 2006. United continues to execute its previously announced business plan to successfully navigate through an environment marked by volatile fuel prices and continues to have strong liquidity’.

Trading in UA stock was halted while the market was informed, and the news media gave extensive coverage to the false rumour and the impact it had on the stock price of United Airlines and related firms. The event therefore neatly satisfies the Cohen and Frazzini (2008) test for true episodes of investor inattention and mispricing. They state (p. 1978) ‘(i) any information thought to be overlooked by investors needs to be available to the investing public before prices evolve, and (ii) the information needs to be salient information that investors should be reasonably expected to gather’.

Our results lead to at least two possible conclusions. Firstly, there may be other impediments to arbitrage that have thus far not been discussed in the literature. Secondly, it is possible that the irrational investor sentiment is responsible for the delayed reaction of the UA stock price, although it is not clear why this did not prevail beyond 4 days.

Carvalho et al. (2011) also document the events surrounding the incorrect UA bankruptcy news, although, as expected given the independent nature of the papers, there are important differences between our work and theirs. We show, using data for 1-min intervals, the microstructure dynamics (returns, volumes, bid–ask spreads and volatility) of UA and all firms in the airline and airline-related industries. Based on these results, we conclude other airline companies quickly reacted to the news that the UA bankruptcy rumour was false and were trading above their pre-UA rumour levels within two hours. On the other hand, UA remained substantially below its prerumour level for an extended period (4 days). We interpret these results to indicate that negative sentiment towards the airline industry in general is not driving the slow UA response. Carvalho et al. (2011) find, based on data for four airlines and counterfactual analysis around a three-factor asset pricing model, that other airline companies take a similar period as UA to return to ‘normal’ levels. We also consider the decline and the quick rebound in price of UA supplier firms following the corrected story and the implications of this for the gradual information diffusion hypothesis. Another paper that uses the same event is Lei and Li’s (2009). Their focus is quite different from ours. These authors show that investors exploit short-lived information using ‘intermarket sweep orders’.

2. Rumour timeline

United Airlines (UAL) Corporation, the parent company of United Airlines, filed for Chapter 11 bankruptcy protection on 9 December 2002. This was documented by the Chicago Tribune on this day, and this article was subsequently included in the company’s online database, which includes archives of stories published by the Chicago Tribune and The South Florida Sun-Sentinel newspapers. The archived article was visited by a member of the public around 1:00 a.m. EDT, Sunday, 7 September 2008, via the Sun-Sentinel website. Owing to low internet traffic volumes at this time, it is thought that this single visit caused the article to later become listed under ‘Popular Stories Business: Most Viewed’ section of the Sun-Sentinel’s web page. On the same day, the Google WebCrawler visited the website at 1:36:57 a.m. EDT and crawled the story, which had the headline ‘UAL Files for Bankruptcy’. The story did not have a standard newspaper article dateline so it was indexed as being new and subsequently included on Google News. The first referral to The Sun-Sentinel website via Google News was made at 1:39:57 a.m. EDT, and traffic increased during the course of the day.

An employee of a third-party news agency, Income Securities Advisor, conducted a routine Google Internet search and retrieved the 6-year-old article with the current date. The headline ‘United Airlines: Files for Ch. 11, to cut costs by 20 per cent’ was subsequently posted on Bloomberg news soon after 10:53 a.m. EDT. A sell-off of United Airlines’ stock ensued, and at 11:00:10 a.m. EDT, UA shares traded at $3.25, a 73 per cent decline from their opening trade price of $12.18. A trading halt on UA stock was imposed by the NASDAQ at 11:06:57 a.m. EDT following denials of the bankruptcy claims by United Airlines at 11:06 a.m. EDT. The bankruptcy headline was then removed by Bloomberg and a correction was issued. At around midday, United Airlines issued a formal statement denying the bankruptcy rumours, which very clearly explained the sequence of events that led to the old story being re-released as new. Trading on UA’s stock resumed at 12:30:00 p.m. EDT. Its price trended downwards during the afternoon’s trading session to a close of $10.92.

3. Data and analysis

Daily price, volume and shares outstanding data are obtained from the CRSP database, and intraday tick quote, trade price and volume data are obtained from Thompson Reuters Tick History (TRTH) via the Securities Industry Research Centre of Asia Pacific (SIRCA) for the 3–5 September 2008 period. Data are obtained for UA and the other 14 companies which share the SIC code of 4512 (Air Transportation, Scheduled) with UA and the 17 companies which have an SIC code of 45XX (Air Transportation, Scheduled, Air Courier Services, Air Transportation, Nonscheduled, and Airports, Flying Fields, and Airport Terminal Services). We include all companies which have these SIC codes and have the required data. We also obtain data for the SPDR S&P 500 index fund.

Figure 1a shows the reaction of UA, firms with the identical SIC code (4512 – Air Transportation, Scheduled), firms with the same broader SIC code (45XX) and the SPDR S&P 500 ETF to the United Airlines bankruptcy rumour. The 4512 and 45XX indices we create are value weighted, which means that more weight is given to other commercial passenger airlines that are most closely related to UA. These indices and the SPDR are given a starting value equal to that of UA to aid comparison. All results are generated using end of 1-min interval quote mid-prices to avoid bid–ask bounce issues. Figure 1a shows the price of UA that started to decline around the time Bloomberg reported the bankruptcy rumour at 10.53 a.m. EDT. UA traded at its intraday low of $3.25, which represents a decline of 73 per cent from its opening trade price, during the interval beginning at 11.00 a.m. The last mid-price in this interval, as shown in Figure 1a, is $3.89. Companies in the same industry were affected by the UA rumour. The average loss of firms with the same SIC code as UA (4512) was 12 per cent in the 11.00 a.m. interval, which is when its low point for the day occurred. In contrast, the broader market (including 45XX firms) was down just 1.7 per cent from its opening at this point. The price of UA increased prior to the 11:06:57 a.m. trading halt, as United Airlines discredited the bankruptcy story, and increased further when trading resumed at 12.30 p.m.

Details are in the caption following the image

(a) UA, Airline Industry and Market Prices on Event Day – Part 1. Price movements of United Airlines, airline companies with an SIC code of 4512 (excluding UA), airline companies with an SIC code of 45XX (exluding UA and 4512 companies) and the SPDR S&P 500 index fund on 8 September 2008. Value-weighted indices are created and indexed to the UA opening price. End of 1-min interval quote mid-prices are used. UA trading was halted at 11:06:57 a.m and resumed at 12:30:00 p.m. (b) UA Cumulative Abnormal Excess Returns. Cumulative abnormal excess returns are calculated for UA using SIC code 4512 industry returns (excluding UA), industry 45XX (exluding 4512 companies) and the SPDR S&P 500 index fund as the benchmark. Daily close prices and value weights are used in each instance.

While the initial reaction of UA and other airline stocks to the bankruptcy rumour is not expected in a world of full information, it is not surprising given the way investors obtain news in reality. In what Huang and Liu (2007) suggest is a rational approach, investors typically source company ‘news’ from trusted financial news sources rather than official company sources. Moreover, the initial reaction is predicted by LeRoy (2004) whose reasoning implies it is rational for investors who identified the bankruptcy story as a false rumour to sell UA stock on the basis that many investors would learn of the rumour and sell.

However, lack of a rebound in the UA stock price to prerumour levels is a puzzle. Investors certainly reacted as expected with regard to other airline stocks. Their prices rebounded rapidly when it became evident that the United Airlines bankruptcy story was not true. For instance, both 4512 and 45XX firms traded above their opening price levels, at 12.54 p.m., just two hours after the UA rumour began affecting prices. The general market did trend down slightly during the afternoon with the SPDR closing down 0.7 per cent from its opening levels and appears to have affected stocks in industry 4512, which were down 1.9 per cent from the opening. However, stocks in industry 45XX were up 1.5 per cent. In contrast, UA closed the day over 11 per cent lower than its opening price.

While the impact of the UA rumour is most visible on an intraday basis, it also stands out when daily data are used. UA’s closing price on the event day was 11.90 per cent lower than the previous day’s closing price, while 4512 firms were 1.29 per cent lower, on average. A daily UA excess return of 10.61 per cent (11.90–1.29 per cent) is atypical. An excess return of this magnitude is above the 97th percentile of excess returns over the prior 250 trading days. We plot the cumulative abnormal returns of UA using three different benchmarks, average 4512 industry returns (excluding UA), average 45XX industry returns (excluding both UA and 4512) and market (S&P 500 Index Fund – SPDR) returns in Figure 1b. The UA cumulative abnormal returns reflect the fact that neither the 4512 or 45XX industry nor the market (SPDR) declined dramatically over this period.

We present granger causality results in Table 1 to measure how much of the 4512 and 45XX returns are captured by lagged UA returns. These are based on the null hypothesis that UA price movements do not granger cause the price movement in 4512 and 45XX stocks. All results are generated using the Granger causality F-test based on a 1-min intraday quote midpoint return. We are able to strongly reject the null hypothesis that UA returns do not granger cause the movements in other airline stock prices in the 4512 and 45XX industries on the event day prior to the trading halt. The results presented in Table 1 show the F-statistic is 93.71 for the null hypothesis involving 4512 returns and 16.08 for the null hypothesis involving 45XX returns. UA returns do not, in general, granger cause 4512 returns prior to the event day or following the event day based on 5 per cent statistical significance levels. These results are consistent with those documented in Figure 1a,b.

Table 1. Granger causality of UA and airline industry
Day Period UA does not Granger cause 4512 UA does not Granger cause 45XX
F-statistic P-value F-statistic P-value
−3 Full day 1.85 0.10 4.09 0.00
−2 Full day 1.06 0.38 1.60 0.16
−1 Full day 1.94 0.09 1.87 0.10
0 Before halt 93.71 0.00 16.08 0.00
0 After halt 1.87 0.10 3.08 0.01
1 Full day 1.53 0.18 2.05 0.07
2 Full day 1.27 0.28 5.79 0.00
3 Full day 3.10 0.01 4.16 0.00
4 Full day 1.44 0.21 1.37 0.24
5 Full day 1.25 0.28 0.62 0.69
  • Granger causality test results for the null hypothesis that United Airline returns do not granger cause industry 4512 returns and industry 45XX returns. Granger causality F-statistics test the hypothesis that all coefficients of lagged UA returns are jointly equal to zero.

There are many examples of companies remaining overvalued for no apparent fundamental reason (Lamont and Thaler, 2003), but it is typically found that there are impediments to rational arbitrageurs removing this ‘inefficiency’, such as short sales constraints. In our setting, there is no apparent factor preventing prices returning to normal levels. Any market participant could have simply purchased undervalued UA stock, which leaves open the possibility that irrational negative investor sentiment towards UA was pervasive.

This delayed reaction coupled with the rapid adjustment of other airline stocks is interesting from a gradual information diffusion perspective. Hong et al. (2007, p. 371) articulate this theory as: ‘Intuitively, investors in market k rationally condition on all information associated with market k. As a result, the price is efficient with respect to own asset information. Hence, the own serial correlation is zero. However, investors in asset market Y ignore or cannot process the information from X, including past returns’. Hong et al. (2007) show how gradual information diffusion results in some industries leading the broader market. The evidence we provide is inconsistent with this and is therefore somewhat of a puzzle. Companies in the identical (4512) and related (45XX) industries as UA returned to more normal levels soon after the rumour regarding UA was clarified, yet the stock price of UA took 4 days to return to its prerumour levels.

We suggest the quick rebound of other airline stocks following United Airlines’ statement which clearly outlined it was not re-entering bankruptcy, coupled with the fact that the S&P 500 was <1 per cent below its pre-event levels during the 4 days UA remained depressed, is the evidence that general investor fear regarding the equity market is not driving our results. Nonetheless, we investigate CBOE S&P 500 market volatility index (VIX), which is commonly referred to as the ‘investor fear gauge’. We source these data from Global Financial Data. We find (in results that are not reported but are available upon request) that the VIX was at levels close to its prior 10-year average on 8 September 2008 and the four following days, as UA remained below its prestale-news-release level. This further reinforces that general investor fear does not seem a likely explanation for the delayed response of UA.

In Figure 2a,b, we present the bid–ask spreads and volume of UA on 8 September 2008. Our results are based on end of 1-min interval bid–ask quotes and total volume over 1-min intervals. From Figure 2a, it is clear that spreads and volume are elevated as trading opens for the day. Both spreads and volumes decline during the morning before surging around the time that the UA bankruptcy rumour was publicized by Bloomberg around 10.53 a.m. The spread of UA ended the 1-min interval commencing 11.00:00 a.m. at 4.62 per cent, some 55 times larger than its spread at 10.50:00 a.m. UA volume surged to a level 44 times larger during this same period. Figure 2b shows that spreads and volume were elevated when trading commenced following the trading halt, which is not unexpected, but quickly declined and returned to prerumour levels for the remainder of the day.

Details are in the caption following the image

(a) UA Bid–Ask Spread and Volume on Event Day Prior to Halt. Volume and bid–ask spreads for United Airlines on 8 September 2008 prior to the trading halt at 11:06:57 a.m. End of 1-min interval bid and ask quotes are used for the spread. Volume is the total volume over 1-min intervals. (b) UA Bid–Ask Spread and Volume on Event Day Following Halt. Volume and bid–ask spreads for United Airlines on 8 September 2008 following the resumption of trading at 12:30:00 p.m. End of 1-min interval bid and ask quotes are used for the spread. Volume is the total volume over 1-min intervals.

We now turn our attention to the question of determining what is driving the marked increase in spread in the 20 min preceding the trading halt. We are unable to apply any of the traditional spread decomposition methods in the literature as these require a much longer time period so we are left to infer the major driver of the spread change using other means. Hasbrouck and Sofianos (1993) find adjustment lags in inventory levels can take months so it seems unlikely that changes in inventory risk explain the sharp increase in spread. Lin et al. (1995) note that order costs tend to be fixed for a particular transaction so ‘the average order processing cost per share should decrease as trade size increases’ (p. 1154). We observe an increase in the average trade size in the minutes leading up to the trading halt, so we conclude a change in order processing costs does not account for the sharp increase in spread. This implies the spread increase following the UA bankruptcy rumour is because of an increase in the adverse selection spread component. Dealers were clearly concerned they might be trading with informed investors, so they increased their spreads accordingly. Spreads then return to more normal levels following the trading halt. We also generate equivalent results to those in Figure 2a,b for UA volatility and Airline industry volume and bid–ask spreads. These results, which are available on request, show similar patterns to those documented for UA spread and volume.

In Table 2, we present the average 1-min volume of UA, airline companies and the SPDR S&P 500 index fund on 8 September 2008 (day 0), the 3 days prior and the 5 days following the rumour. The reaction of UA to the bankruptcy rumour is very strong, with average volume approximately four times higher than that on surrounding days. Authors, such as Harris and Raviv (1993), have pointed out that volume is a proxy for differences in investors’ opinion. If there is more divergent opinion regarding the value of a stock and its future price path, then volume is likely to increase. UA volume declines dramatically on days +1 to +5 to levels that are lower than those on days −3 to −1. This decline is even more striking when considered in conjunction with volume in related industry indices and the SPDR as all three of these had higher volume in [+1, +5] than [−3, −1]. This UA volume pattern appears to indicate that investors in general did not believe UA to be undervalued following the retraction of the false bankruptcy rumour.

Table 2. Volume around event day
[−3, −1] 0 [+1, +5] Post- and Predifference P-value
UA 18,511 65,365 15,714 −2798 0.00
4512 3668 6755 3789 121 0.32
45XX 2463 3378 3722 1259 0.00
SPDR 705,415 866,623 839,205 133,790 0.00
  • Average 1-min interval volume of United Airlines, airline companies with an SIC code of 4512 (exclusing UA), airline companies with an SIC code of 45XX (exluding UA and 4512) and the SPDR S&P 500 index fund around the UA rumour event day of 8 September 2009.

This adds to the puzzle as most theoretical models (De Long et al., 1990) assume that noise traders operate within financial markets. This introduces risk as De Long et al. (1990, p. 705) note: ‘If noise traders today are pessimistic about an asset and have driven down its price, an arbitrageur buying this asset must recognize that in the near future noise traders might become even more pessimistic and drive the price down even further. If the arbitrageur has to liquidate before the price recovers, he suffers a loss. Fear of this loss should limit his original arbitrage position’. However, if there were many noise traders selling UA stock in days [+1, +5] and this selling pressure was offsetting the buying of more rational investors who identified the UA rumour was false, one would expect a marked increase in volume. The fact this did not occur implies investors in general did not perceive UA to be undervalued following the correction of the bankruptcy rumour despite it trading at up to 10 per cent below its prerumour levels.

Cohen and Frazzini (2008) document predictability across economically linked firms. Company-specific news appears to be quickly incorporated into stock prices, but the stock prices of supplier firms are slow to react to important customer firm news. We find no Regulation SFAS 131 disclosures for firms deriving 10 per cent or more of their yearly sales or profits from UA. Airline supplier firms appear to have a diverse customer base. We then search the websites of all Airline supplier industry firms (SIC codes 3720, 3721, 3724 and 3728) for mention of UA being an important customer. It is clear that these firms will have a weaker supplier link to UA than the customer – supplier links considered by Cohen and Frazzini (2008). However, it is possible that these companies will still react to the UA rumour given investors will be aware of their relationship with UA. We find three companies (AAR Corporation, Genesis Lease Limited and Rockwell Collins Incorporated) with clear mentions of UA as an important customer.

Figure 3a,b show the reaction of a ‘supplier index’ of these three firms to the UA bankruptcy rumour.Cohen and Frazzini (2008) find a value-relevant event, such as an earnings downgrade, results in an immediate reaction in the stock price of the firm in question, but the stock price of economically linked supplier firms takes time to reflect this news. In Figure 3a, we see that UA suppliers quickly declined 3 per cent from opening levels as the market began to react to the UA bankruptcy rumour. We suggest it is not surprising that UA supplier firms reacted much quicker than the supplier firms considered in the Cohen and Frazzini (2008) study. The UA rumour received widespread coverage in popular financial news sources, so there would have been more widespread knowledge of it among investors in UA supplier firms than an event like a customer firm earnings downgrade. Figure 3b shows supplier companies rebounded once it was clear the rumour was false, closing the day <0.4 per cent lower, on average, than their opening levels. This compares to the UA decline of over 11%. While consistent with our industry results, this result is puzzling from a gradual information diffusion/investor inattention perspective. The news that the United Airlines bankruptcy rumour was false is certainly relevant for UA supplier firms given their reaction to the initial rumour, so it is not surprising they quickly rebounded and closed just 0.4 per cent down on the day, in line with the broader market. However, the lack of rebound by United Airlines is inconsistent with both the gradual information diffusion and investor inattention hypotheses, as both of these imply the firm most directly affected by news should react more quickly than less related firms.

Details are in the caption following the image

UA and UA Supplier Prices around Trading Halt. Price movements of United Airlines and United Airline supplier firms on 8 September 2008. An equal-weighted index is created for UA suppliers and indexed to an opening level of 100. End of one-minute interval quote mid-prices are used. (a) Part 1: UA trading was halted at 11:06:57 a.m. and resumed at 12:30:00 p.m. (b) Part 2: The data between 10:30:00 a.m. and 2:00:00 p.m. are cut to allow a more appropriate scale.

In unreported results, we find UA returns granger cause the returns of supplier firms on the event day prior to and following the trading halt. However, they do not granger cause returns on days following the halt. The UA bankruptcy rumour is clearly responsible for the price decline of supplier firms on the event day. Supplier firms then rebound while the price of UA remains depressed for 4 days.

4. Conclusions

An internet search in September 2008 led to an old story about the 2002 bankruptcy of United Airlines being released as new news. The stock price of United Airlines promptly fell 73 per cent, and over $4.1 billion was wiped of the market value of United Airlines, other airline stocks and United Airlines suppliers. To our knowledge, this episode is the first-documented instance of stale news affecting prices for an extended period in spite of the stale news release being retracted in a very public way.

The stock prices, volume and bid–ask spreads of airline industry companies and United Airline suppliers quickly rebounded once it was clear the 2008 bankruptcy story was stale news, but the price of United Airlines remained depressed for 4 days. This is puzzling on a number of fronts. Firstly, unlike many instance of ‘inefficient pricing’ in the literature, none of the well-documented limits to arbitrage seem to apply in our setting. Investors wishing to exploit the apparent mispricing in the stock price of United Airlines needed to simply purchase its stock. This raises the possibility that there are other impediments to arbitrage that have not been discussed in the literature. An alternative explanation is that irrational investor sentiment is responsible for the delayed reaction of the United Airlines stock price, although it is not clear why this did not prevail beyond 4 days. The United Airlines rumour episode is also puzzling from the perspective of the gradual information diffusion and investor inattention hypotheses. We find that the price of the firm the news relates to reacts slower than firms that the news is less relevant for, which is opposite to what these two theories predict.

Footnotes

  • 1 http://ir.united.com/phoenix.zhtml?c=83680&p=irol-newsArticle&ID=1194726&highlight
  • 2 http://www.forbes.com/2008/09/08/ual-tribune-bankruptcy-biz-media-cz_ja_0908ualstory2.html
  • 3 While there is a broad consensus on the timing of the key events, some articles do refer to slightly different times. Where there is a discrepancy, we provide times which reflect the consensus. All times in this section are stated as EDT to aid readability.
  • 4 http://googlenewsblog.blogspot.com/2008/09/update-on-united-airlines-story.html
  • 5 http://www.forbes.com/2008/09/08/ual-tribune-bankruptcy-biz-media-cz_ja_0908ualstory2.html
  • 6 http://247wallst.com/2008/09/08/ual-confusion-c/
  • 7 http://www.itworld.com/node/54925
  • 8 We calculate an equally weighted index to give a clearer presentation of the joint reaction as Rockwell Collins is 89 per cent of the total market capitalization of these firms.
    • The full text of this article hosted at iucr.org is unavailable due to technical difficulties.