Pacific-Basin Finance Journal 40 (2016) 323–334
Contents lists available at ScienceDirect
Pacific-Basin Finance Journal
journal homepage: www.elsevier.com/locate/pacfin
Detecting the great short squeeze on Volkswagen
Keith R.L. Godfrey
The University of Western Australia Business School, 35 Stirling Highway, Nedlands 6009, Australia
a r t i c l e
i n f o
Article history:
Received 25 November 2015
Received in revised form 31 January 2016
Accepted 15 February 2016
Available online 18 February 2016
JEL classifications:
G12
G17
D43
D81
a b s t r a c t
On 28 October 2008 a short squeeze on Volkswagen stock propelled this car maker to become
the world's most valuable company for a day. I study the market behavior empirically and investigate whether the timing of the price spike could have been anticipated from earlier trading. I utilize price information from regional stock exchanges in parallel with the primary
electronic trading platform Xetra. Although the trading volume on the seven regional exchanges is small, the geographical variation in traded prices shows anomalies when the law
of supply and demand begins to overrule the law of one price, and this is observed more
than 24 h ahead of the price peak. I find that the coefficient of variation in the prices at the
regional exchanges is a leading indicator of the Volkswagen price spike.
© 2016 Elsevier B.V. All rights reserved.
Keywords:
Short squeeze
Volkswagen
Porsche
Regional variation
Law of one price
Limits to arbitrage
1. Introduction
Financial events are notoriously difficult to predict. Investors and traders seek competitive advantages by analyzing information
such as news releases, accounting reports, industry forecasts, technical trends, and quantitative trading behavior. While individual
approaches may be as diverse as the market participants, their goal remains the same — to provide useful trading signals ahead of
anticipated price movements.
In this paper I study the information surrounding the extraordinary event in Volkswagen stock that occurred on Tuesday 28
October 2008. On this day, while most stock prices were battered by a global financial credit crisis, the price of Volkswagen
stock jumped from around €200 to €1000. The cause was insufficient stock available for purchase by traders needing to cover
short positions, and for a few hours this German automaker became the most valuable company in the world by market capitalization. While the short sellers who managed to hold on throughout the short squeeze could eventually feel vindicated with
Volkswagen trading under € 100 a year later, this is no comfort to those who were forcibly closed out on 28 October. Their losses
were massive — estimated to be around six billion euros (Economist, 2008b).
In hindsight it seems irrational that the short interest was so high. More than 12% of the stock had been short sold by October
2008 with an underlying value of around €10 billion. The short-selling of Volkswagen had become a crowded strategy. Several
news articles and analyst reports advised of the dangers, and the challenge for traders is to turn such analysis into profits.
E-mail address: keith.godfrey@uwa.edu.au.
http://dx.doi.org/10.1016/j.pacfin.2016.02.001
0927-538X/© 2016 Elsevier B.V. All rights reserved.
324
K.R.L. Godfrey / Pacific-Basin Finance Journal 40 (2016) 323–334
While a trader aware of a potential short squeeze can avoid losses by choosing not to go short, an even better strategy would be
to turn the same knowledge into a profitable trade. One possibility is to enter a long position, but that carries uncertainty of when
or if the squeeze will eventuate while in the meantime it risks losses from the downward price pressure of short sellers taking the
opposite position. The profitability of such a trade depends on the timing of the entry and the exit.
Recognizing the conditions for a short squeeze is one thing. Picking its timing is another. Although fundamental and technical
analyses are useful in identifying the forces that may move a price, they are less useful at forecasting the timing. Price movements
result from the active trading of market participants rather than their long-term predictions. A statistical approach, quantitative
analysis, may be better at identifying the times when market conditions start to change.
Quantitative analysis has intuitive appeal for detecting market shifts because it focuses on the trading empirically. In this study
of Volkswagen, I show that a change in trading conditions can be identified on Monday 27 October 2008 a full day ahead of the
price spike. Achieving this requires more than the traditional analysis of trade price and volume. The quantitative characteristics of
the price and volume show nothing unusual during the squeeze besides the abnormally high price, by which time any trading
opportunity has already passed. To gain predictive power I combine trading information from the seven regional stock exchanges
around Germany – specifically the price variation among them – information which is more commonly ignored.
Nearly all the trading in Volkswagen stock in Germany – more than 98% of trading volume –takes place on the electronic exchange
Xetra. The remaining trading occurs at regional stock exchanges in the cities of Berlin, Frankfurt, Düsseldorf, Hamburg, Hanover,
Munich, and Stuttgart. Although the volume of trading at these seven regional bourses may seem statistically insignificant (and indeed
the location of trade can be ignored for most purposes) I use this information to build an indicator of deteriorating market health. The
idea comes from the “law of one price” — the proposition that identical goods should trade at the same price. Under normal circumstances, the price of Volkswagen shares should be the same in each city, and indeed for most of the time this is confirmed empirically.
This rule however can break down when limits to arbitrage arise such as reduced stock availability in the extreme market conditions
of a short squeeze. During these times, the law of supply and demand can overrule the law of one price.
By measuring the coefficient of variation in Volkswagen stock prices between the seven exchanges in 15-minute intervals, I
find that abnormal trading conditions can be detected by 10 am on the day before the price spike. This warning could give traders
a significant time advantage. Those with short positions may be able to exit while the Volkswagen was trading at €350, perhaps
saving them from being closed out the next day as the price headed towards €1000. Speculators could profit by purchasing outof-the-money call options, which means paying a relatively low premium for a chance of a much larger payoff. Compared with
fundamental and technical analysis, this quantitative analysis is fast and can put traders ahead of others who need time to process
news and fundamentals. It may even be possible to profit by trading on the abnormal conditions in a stock without knowing what
has triggered them.
The following sections review the conditions for the Volkswagen short squeeze, examine warnings from news and technical
analysis, then develop a quantitative measure of price variation which can identify the onset of the squeeze empirically.
2. The Volkswagen Short Squeeze
A short squeeze occurs when short sellers race to repurchase a stock to close their positions, and their buying pressure in turn
triggers more short sellers to close out. In manipulated markets a short squeeze can arise in many ways (Merrick et al., 2005) but
the risk with Volkswagen may have seemed low because of the firm's large size and high liquidity (Elfakhani, 2000). In reality the
event on Volkswagen in 2008 was a “perfect” or “infinite” squeeze because there was less stock in free float than needed to close
out all the short seller's obligations. The short sellers could not have repurchased at any price.
The Volkswagen short squeeze of 2008 arose after rival car manufacturer Porsche had built an interest of 74.1% in the company including an undisclosed holding of 31.5% in cash-settled options. Porsche had earlier declared a milestone holding of 30% as
required by German takeover law, and the next update was not required until reaching 50%. Meanwhile the option position did
not require disclosure at all under German law because settlement by cash would not provide stock and therefore not provide
control of the company. Delaying the disclosure of insider trades tends to increase the profit opportunity of such trades
(Etebari et al., 2004) and this was no doubt part of the Porsche's strategy. Nonetheless, although Porsche could build its holding
quietly, the options purchases would still cause observable upward pressure on the stock price because Porsche's counterparties
would need to hedge their written positions by buying the underlying stock.
Porsche's counterparties found they could reduce their hedging costs by lending their Volkswagen shares for short-sale. They
could earn a lending fee each time they lent out a share, and meanwhile the same share could be repurchased on the market by
themselves or another counterparty, or perhaps even by Porsche. They were incentivized to encourage short selling and they had
plenty of stock to lend, inverting the more common situation where demand for short selling outstrips supply (Asquith et al.,
2005). Without disclosing their intent to repurchase the stock, this action would have biased the market for short selling (the typical market for borrowing stock is described by D'Avolio (2002)). It introduced a cycle where the same share could be purchased
then be lent for short sale again as if it were untainted (Murphy, 2008), and this enabled Porsche's counterparties to acquire their
stake in Volkswagen more cheaply and quickly than otherwise possible.
Porsche declared its interests on Sunday 26 October 2008 in a voluntary news release. By that time, there was perhaps only
5.7% in free float due to Porsche's holding of 42.6%, Porsche's counterparties' hedge of up to 31.5%, and a 20.2% protective
stake held by the State of Lower Saxony (Ehrhardt, 2007). At the same time, the short interest in Volkswagen had grown to
around 12.9% of the stock (de la Merced and Dougherty, 2008). The short-sellers were in an infinite squeeze.
K.R.L. Godfrey / Pacific-Basin Finance Journal 40 (2016) 323–334
325
The stock price reaction to Porsche's news was surprisingly slow. Price discovery evolved over two days. On Monday 27
October 2008 Volkswagen stock opened at 350 euros, which was up 67% on its previous Friday close, but not too alarming as
it had been trading at that level just two weeks earlier. The price rose that day to 635 euros before closing at 520 euros, both
of which were new records. On Tuesday 28 October 2008 it opened at 500 euros and traded as high as 1005 euros before closing
at 945 euros. By this stage Volkswagen was distorting the DAX index, having grown to about 27% of the uncapped index, and the
plight of the short sellers was making news. Schmidhammer et al. (2014) study the consequences on the DAX index and several
exchange traded funds (ETFs) and show that the DAX index futures–cash arbitrage relationship broke down with the index level
exceeding the discounted value of the DAX futures by about 4% at 10 am.
It was Porsche that offered a solution to the impasse. It announced it would settle options on around 5% of Volkswagen so its
counterparties could release enough stock for the short sellers to meet their obligations. With the price at short squeeze heights,
Porsche earned a windfall profit. The Economist (2008b) estimates that Porsche made 6–12 billion euros from this maneuver, in
cash, on top of paper gains on its stock holding of 30–40 billion. Porsche itself (2008) had earlier declared that its financial activities had contributed 6.8 billion euros or around 80% of its 8.6 billion euros pre-tax profit on 31 July 2008. The car-maker had
transformed itself into a successful banking house with car-making division on the side (Dalan, 2008).
Fig. 1 shows the Volkswagen share price from six years before the short squeeze to three years after. Volkswagen's price
returned to the 200-euro level soon after the short squeeze, and Porsche continued buying, making a compulsory announcement
in January 2009 when it controlled more than 50% of the stock. At that time Porsche seemed to be on course for its goal, but the
path started to become more difficult. The protective stake held by Lower Saxony prevented an outright takeover, and fallout from
the global financial crisis made it hard for Porsche to continue raising funds. In the end, the roles of bidder and target became
reversed, and it was Volkswagen that acquired Porsche.
The Volkswagen squeeze has a huge economic significance. Lamb et al. (2008) estimate hedge funds could have lost as much
as 30 billion euros when their strategy to short-sell Volkswagen stock backfired. Dougherty (2009) names a couple of hedge funds
with large exposures and describes how the world's 94th richest man at that time, German billionaire Adolf Merckle, ended his
own life after his empire lost several hundred million euros on the Volkswagen short trade. Despite their sufferings, short sellers
garner little sympathy (Pattison, 2010), and rumors about which banks were exposed hit their respective shares prices hard.
Bloomberg (2008b) reports that Morgan Stanley's share price fell as much as 26% on 28 October, and Goldman Sachs 11.5%,
amid speculation that the Volkswagen share surge may have saddled these banks with losses.
Volkswagen's wild ride also distorted the German DAX market index. Hetzner (2008) reports the drop in Volkswagen share
price by 45% on 29 October (the day after the price spike) had the consequence of shaving nearly 600 points off the DAX
index. Without Volkswagen, the rest of the index closed up 12% in line with Wall Street's second best one-day gain on record.
The index disruption forced Deutsche Bourse to alter the stock inclusion rules of its three main indices. Volkswagen's weighting
in the DAX reduced from 27 to a maximum of 10%, with a possibility of being dropped altogether if its capitalization exceeded
10% or its volatility exceeded 250% (Deutsche Welle, 2008). This took pressure off the index-tracker funds attempting to mimic
the index portfolio, and in turn reduced any further impact on the index from their transactions.
The daily share prices and market capitalization of Volkswagen common stock are listed in euros in Table 1 for the two days of
the short squeeze and the day on either side. With around 295 million shares on issue, Volkswagen's capitalization jumped by
nearly 240 billion euros ($300 billion) then dropped by 150 billion euros ($195 billion). These are extraordinary moves for a
Fig. 1. Milestones in Porsche's maneuvers and the trade prices of Volkswagen stock on Xetra. Porsche began buying quietly in March 2005 and made compulsory
announcements in March 2007 and January 2009. The short squeeze took place on 27–28 October 2008 following a voluntary news release by Porsche on Sunday
26 October 2008. Porsche stated it had built an interest in 42.6% of Volkswagen and had also purchased cash-settled options on a further 31.5% of the stock, which
left insufficient stock in free float for the short sellers to repurchase. The short squeeze was released on 29 October 2008 when Porsche agreed to cash-settle sufficient options for the short sellers to close out their positions.
326
K.R.L. Godfrey / Pacific-Basin Finance Journal 40 (2016) 323–334
Table 1
The daily trading price range of Volkswagen common stock on Xetra from 24 to 29 October 2008. These dates center on the two-day short squeeze with a trading day on
either side. The daily high (low) market capitalization of the Volkswagen group is the product of the high (low) stock price and the number of ordinary shares outstanding, being approximately 295 million shares.
Volkswagen stock price daily (euros)
Market cap (euros)
Date
Open
High
Low
Close
Daily range
Fri 24 Oct 2008
Mon 27 Oct 2008
Tue 28 Oct 2008
Wed 29 Oct 2008
217.90
350.00
500.00
510.00
219.80
635.00
1005.01
607.11
201.02
324.99
471.00
491.00
210.85
520.00
945.00
517.00
59 to 65 billion
96 to187 billion
139 to 296 billion
145 to 179 billion
high-cap company. Market capitalization is calculated by multiplying the stock price by the number of shares outstanding, and
although this represents a price from marginal trading rather than the total value of a company when all its shares are for
sale, it is widely used as a proxy because of its ease of calculation.
The swings in Volkswagen's share price caused corresponding distortions in capitalization rankings. During most of October
2008 the company with highest market capitalization was Exxon Mobil, while Volkswagen Group ranked several hundred places
lower with around one-fifth the capitalization. The short squeeze propelled Volkswagen into first place on 28 October 2008 and
pushed Exxon Mobil into second place for the day. Fig. 2 shows the market capitalizations of Volkswagen and Exxon Mobil on a
daily basis in the second half of 2008.
Could this event have been predicted? We begin with an overview of the fundamental and technical environment, then move
into quantitative analysis.
3. Traditional Warnings
Short sellers need superior information in order to overcome the additional costs of borrowing the shares to short. There is evidence
that short sellers are not always right (Clunie, 2010) and not especially well informed (Best et al., 2008) besides sniffing out insurance
losses (Blau et al., 2008) and accounting downgrades (Christophe et al., 2004). With Volkswagen there was no special exposure to
business risks and no suggestion of accounting irregularities.
The unusually high demand for short selling of Volkswagen in 2008 was based on speculation that a takeover attempt by
Porsche would temporarily elevate the share price. Although this is the primary explanation, there can be many motives for
short sales. One fundamental reason is an apparent deviation from accounting valuation. Dechow et al. (2001) show that short
sellers take positions in stocks with low fundamental-to-price ratios, and Volkwagen's price was rising without a corresponding
increase in its intrinsic value. The higher the price became, without a corresponding change in company performance, the greater
would be the incentive to sell short. Traders following that strategy might however have been surprised by the unwavering rise in
Volkswagen's price, and want to look for an explanation.
Fig. 2. Market capitalizations of Volkswagen and Exxon Mobil around the Volkswagen short squeeze of 2008. The daily ranges of market capitalization are calculated
from the highest and lowest daily trade prices of VOW (on Xetra) and XOM (on NYSE), with euros converted to US dollars using daily mid-range exchange rates, and
multiplied respectively by 295 million and 5.09 billion shares outstanding. Exxon Mobil is the most highly valued company by market capitalization for most of 2008,
with Volkswagen typically around one fifth the size. The short squeeze on Volkswagen on 27–28 October 2008 caused Volkswagen's market capitalization to overtake
that of Exxon Mobil on 28 October 2008.
K.R.L. Godfrey / Pacific-Basin Finance Journal 40 (2016) 323–334
327
Another source of short-selling comes from traders conducting relative value or pairs trading, a market-neutral strategy based
on the law of one price. Trading on relative value can be conducted without knowledge of the fundamentals or the takeover
maneuvers. As the Volkswagen price increased relative to its peers such as BMW and Daimler, these traders would have been
motivated to short-sell Volkswagen while simultaneously purchasing its peers. Do et al. (2012) study this trading in the
Australian market and find that the operation of the law of one price, or the relative value rule, can remain strong even in adverse
trading conditions such as the presence of a short-sale ban. This means that purchasers of automotive stocks could unwittingly
maintain the long-run price ratios by choosing to purchase the seemingly cheaper BMW and Daimler rather than the overpriced
Volkswagen, and those wishing to sell could offload Volkswagen first. The lack of a corresponding rise in BMW and Daimler
compared with Volkswagen however could warn such traders of the unusual situation evolving with Volkswagen.
International short sales offer another potential explanation for the short-selling interest on Volkswagen stock. While some
foreigners can short-sell Volkswagen on the German exchanges directly (Wang and Lee (2015) document foreigners accounting
for 88% of short sales in Korea where such transactions are traceable) they also had a separate opportunity to short-sell in the
USA through an international cross-listing. Bris et al. (2007) show that there is often an active market for shorting international
listings even when there are restrictions on short sales in the home market, and international short sales help to transfer price
information to the home market. Volkswagen ordinary shares are cross-listed in the USA with American Depositary Receipts
(ADRs) trading over-the-counter (OTC) under ticker VLKAY. This ADR has a ratio of 5:1 which means each depositary receipt
corresponds to one-fifth of an underlying share. It would be interesting to know whether Porsche's options counterparties
were able to help offer ADRs for short sale in the USA while they grew their Volkswagen stock holdings in Germany. Conditions
for a short squeeze could have existed in the ADR market in parallel with the German home market, although trading in a different time
zone. The shape of the VKLAY price closely follows that of the underlying VOW shares after taking into account the foreign exchange
and 1/5 ADR ratio, with the price rising from around USD 50.00 at the start of 2008 to a sharp peak of USD 232.30 on 28 October
2008. Traders in this OTC or “pink sheet” market should nonetheless have been aware its relative opaqueness and thin trading
compared with exchange-listed securities, and therefore should not have been surprised to see wide spreads and irregular price
movements.
Bolton and Oehmke (2013) compare the naked shorting of Volkswagen stock with the naked shorting of credit default swaps
(CDSs) occurring around the same time and which contributed to the global financial crisis of 2007–09. They point out that naked
shorting CDS securities is less risky than naked shorting a stock because there is no equivalent short squeeze risk, but as a result
the consequences of a blow up are even greater. This was demonstrated with the global financial crisis where the naked CDS
exposure had grown to many times that of the naked Volkswagen shorts. As the global crisis had begun a year earlier, the opportunities and consequences of shorting any security should have been fresh in traders' minds.
Speculative short selling carries high risk, especially when facing strong players with private agendas. Why would intelligent
fund managers take positions against Porsche? Lynn (2006) cautioned nearly two years before the short squeeze: “There are only
three hard and fast rules in the motor industry if you want to make money: never build an orange car; steer clear of Formula 1;
and never bet against Porsche.” Many fundamental and technical warnings became visible in the months prior to the short
squeeze including news articles of Porsche's takeover intentions, unusually high short interest, and a high short ratio.
3.1. News and Fundamentals
It should have been possible to foresee the types of financial instruments Porsche could use in its takeover maneuvers. Security types
involving cash-settlement were known to elude the German disclosure laws, indeed the review by Noack (2007) indicates that the
German disclosure laws had several ongoing flaws despite reforms. Burger (2008) cites derivatives being used silently in two previous
German takeovers that would have required disclosure in the United Kingdom. Haines et al. (2008) examine the decision by the German
Federal Financial Supervisory Authority (BaFin) concerning cash-settled total-return equity swaps used by Schaeffler in its takeover of
Continental, and argue that this implies disclosure by Porsche would not be required for cash-settled options.
Although the market reaction to Porsche's announcement on 26 Oct 2008 looks like a surprise, the information was not entirely
new. Richter (2008) quotes Porsche's Chief Financial Officer Holger Haerter three months earlier saying Porsche had secured the
purchase price for additional shares in Volkswagen through financial instruments. Porsche itself (2007) had declared a profit of
3.5 billion euros on its Volkswagen holding in its annual report of 2006–07, and disclosed its use of “cash-compensated hedges”.
Porsche's dabbling in options was public knowledge. The Economist (2008a) reports two months before the squeeze that Porsche
had earned 4.5 billion euros from its Volkswagen options in the 18 months to 31 January 2008. A fortnight before the squeeze,
Bredoux (2008) noted it was common knowledge Porsche held options and warned that as the expiry date approached the banks
would need to make sure they own the underlying shares.
Media discussion of a possible short squeeze began many weeks beforehand. Bloomberg (2008a) reported Volkswagen had
become a crowded short play, noting unusually high short interest with about 15% of Volkswagen shares shorted. It also became
apparent that Lehman Brothers had lent Volkswagen shares for short sale and the bank's bankruptcy could cause these shares to
be recalled. With the fall of a prime-brokering lender potentially triggering a wave of repurchases in one of the most shorted
stocks in Europe, the conditions seemed ripe for a short squeeze.
Ten days before the price spike, Murphy (2008) applauded a report by Sanford Bernstein's analyst Max Warburton that explained
the extraordinary rise in the Volkswagen stock price. The “VW fruit machine” as Warburton called it could enable Porsche to profit
iteratively by lending the share inventory to short sellers, buying additional stock on market from these short sellers, and meanwhile
328
K.R.L. Godfrey / Pacific-Basin Finance Journal 40 (2016) 323–334
writing puts. The warning signs were there, and Sanford Bernstein was not alone. The Economist (2008b) cites Morgan Stanley as
warning its clients on 8 October 2008 of the danger of playing billionaire's poker.
A numerical indicator of over-shorting is the short ratio, or short interest ratio, which is the number of short-sold shares
divided by the average daily trading volume. Intuitively this is the number of trading days it would take for the short sellers to
repurchase the shares if they bought all the average daily trading volume. In the case of Volkswagen with 12.9–15% of shares
shorted and around 600,000 shares trading each day (about 0.2% of the 295 million shares outstanding) the short ratio was
between 65 and 75 days. In the same way that it had taken several months for the large short position to have built up, it
could be expected to take similarly a few months for this situation to unwind in a gentle way. This is an uncomfortably long
time. Even a week might feel a long time for short sellers to unwind their positions. If the situation were to unwind rapidly,
the price could be expected to rise rather than fall.
3.2. Technical Analysis
Technical analysis aims to infer trading direction from price charts without needing to know the fundamental reasons behind the
movements. There are several approaches that could have helped predict the Volkswagen price peak. One observation of Porsche's
stake-building activities is that Volkswagen's price rose from around 100 euros in March 2007 to 200 euros in September 2008
while Porsche's stake increased from 30 to 35%. If this trend were to continue while Porsche increased its stake from 35 to its stated
50%, the price could be predicted to increase a further eight fold. This simple calculation suggests Volkswagen stock could end up
between 800 and 1600 euros – perhaps an extreme estimate – but it could also warn that entering a short position at 200 euros
was unwise.
The classic strategy of trend-following suggested buying Volkswagen rather than shorting the stock, because the stock price
had been rising. Correlation with local industry competitors such as Daimler and BMW shows the Volkswagen share price was
moving in the opposite direction to the industry trend, so a market-neutral strategy could involve buying Volkswagen and
shorting its competitors. The technical signals all point to buying Volkswagen rather than shorting it.
Analysts who combine technical and fundamental approaches may have observed the rising price trend in the months prior to
the squeeze was unusual compared with patterns from other short-selling environments. The typical consequence of short selling
is to drive prices down. Aitken et al. (1998) find that significant negative abnormal returns occur almost instantly when the
reporting of short selling is transparent. Angel et al. (2003) find that days of high short selling tend to be followed by days of unusually low returns. Diether et al. (2009)find that short sellers correctly predict negative abnormal returns and tend to increase
their trading following positive returns, but with a median contract length of 11 days which is much shorter than the steady
rise of Volkswagen. Blau and Wade (2013) predict that the negative price effect from the short-sellers should be approximately
four times that of alternative approaches such as buying put options. Boehmer and Wu (2013) study the impact of short sellers on
the price discovery process. In light of all this evidence, why would the Volkswagen price keep rising as the short interest ratio
increases to abnormally high levels? Surely it warns of even greater forces affecting the share price.
Bloomberg (2008a) describes the situation as an unprecedented short squeeze, yet the market response to all this information
seems surprisingly slow. Why did the short sellers hang on for so long when the tide was moving against them? Perhaps they
remained focused on the long-term anticipated drop in price rather than the risk of being squeezed in the meantime. Their
long-term view would eventually prove correct but this was too late for those closed out by stop losses on 27 or 28 October 2008.
The biggest challenge for traders would have been to identify when the trend was changing from a gradual price rise to the
onset of the conditions for the price spike. The infinite short squeeze became public knowledge when Porsche declared its interests on 26 October 2008, but this was a Sunday — the markets were closed and most traders would not have been watching the
news feeds. Market participants inevitably take different times to observe and respond to news, even with news as significant as
Porsche's option interest in Volkswagen. Nonetheless it should be sufficient for a few alert traders to start a reaction on Monday
27 October 2008 after the markets reopen. We want to be able to identify the abnormal conditions at that time, in the first hour
of trading, without needing to be aware of Porsche's announcement.
3.3. Quantitative Analysis
Quantitative analysis looks at the trading empirically — the trade prices, trade volumes, and the order book of bids and asks. It
can be relatively fast compared with fundamental and technical analysis, and it can enable quick and seemingly perceptive
decisions because it can react to and follow the fastest traders. One of the surprising features of the trading in Volkswagen
stock on 27 and 28 October 2008 is that its quantitative behavior looks typical apart from the share price rising much higher
than usual. The share volume traded, the intraday timing of the trades, and the relative price ranges each day are all remarkably
unremarkable. This means any indicators based on the traditional concepts of price and volume may be of little value, either
because they cannot detect abnormal behavior early enough, or because they produce false positives on ordinary trading days.
Fig. 3 shows the share volume, the intraday timing, and the relative price ranges of Volkswagen trading around October 2008.
Panel (a) shows the daily volume of trades over time from 2003 to 2008 inclusive. While the trading volumes on 27 and 28
October 2008 are above their long-term average, they are well within the daily range of the past six years. Panel (b) shows
the intraday timing of trades for each day from 20 to 31 October 2008, plotted as the cumulative trading volume between
9:00 and 17:30 central European time and normalized to the total volume of each day. While the trading on 27 and 28 October
looks slightly busier in the opening hours between 10:00 and 12:00 this loses significance when all the days are compared. Panel
K.R.L. Godfrey / Pacific-Basin Finance Journal 40 (2016) 323–334
329
Fig. 3. Volume and price behavior of Volkswagen trading around the short squeeze. Panel (a) shows the daily volume of trades from 2003 to 2008 plotted on a log scale
with 27 and 28 October 2008 highlighted. Panel (b) shows the intraday cumulative volume trading pattern each day from 20th to 31st October 2008 inclusive, normalized
between 09:00 and 17:30 each day. Panel (c) shows box plots of the prices traded each day in October 2008, collated in 5-second trading intervals and scaled so each plot
has the same vertical range. Overall the quantitative characteristics of Volkswagen trading during the short squeeze appear similar to other days — the volume fits within
the typical range, the intraday timing is ordinary, and the normalized pricing shows nothing special. It would be difficult for conventional quantitative analysis of price and
volume to detect the onset of the price spike, aside from observing the spike itself.
(c) shows the statistics of each day's trading with the price scale removed. When the trading data from each day from 3 to 31
October is normalized relative to the price range of that day and presented as a box plot showing the quartiles and the outliers
beyond 1.5 times the interquartile range, the plots for these 20 days show that there is nothing extraordinary in the normalized
price behavior on either 27 or 28 October 2008.
Overall the “ordinariness” of the trading volume and price behavior (aside from the absolute price spike) mean it would be
difficult to use either volume or price as an early indicator of the short squeeze. The price spike could be detected when it crosses
above a price threshold, but there is little value in detecting a price spike after the event. We need a different approach.
4. Regional Price Variation
The law of one price suggests that identical securities should trade at the same price. Although this “law” lacks a rigorous
scientific proof, its argument is intuitive and powerful. Arbitrage opportunities exist whenever two or more identical securities
trade at different prices, provided they can be traded without substantial cost. Rational traders will exploit these opportunities,
and this process keeps the prices in check.
It is foreseeable that the prices of identical securities may differ when there are impediments to arbitrage such as the lack of
stock being available for one or both directions of the trade (Shleiffer and Vishny (1997) discuss such limits). I make use of this
insight to identify the change in the market conditions of Volkswagen stock without needing to know the reason why the
arbitrage process is failing (in this case an infinite short squeeze).
330
K.R.L. Godfrey / Pacific-Basin Finance Journal 40 (2016) 323–334
4.1. Trading in Volkswagen
Volkswagen stock traded in 2008 on eight exchanges around its home country Germany — an electronic exchange Xetra and
regional bourses in Berlin, Frankfurt, Düsseldorf, Hamburg, Hanover, Munich, and Stuttgart. It also traded in euros on European
exchanges such as Euronext Amsterdam and the Italian Exchange, in Swiss francs on the Swiss Exchange, and in US dollars via
American depositary receipts (ADRs) on Pink Sheets. In this article it is sufficient to consider just the German exchanges.
The majority of trading in Germany takes place on the electronic exchange Xetra, which in 2008 handled around 98.5% of the
Volkswagen trades. The remaining 1.5% of trades occurred on the seven regional exchanges, predominantly Frankfurt and Stuttgart.
Table 2 shows the percentage volume of trading in Volkswagen on each of the German exchanges from 2003 to 2009.
Given the dominance of Xetra it is interesting to consider whether the regional exchanges add any information of value to a trader.
Most traders will focus on the price information coming from Xetra because of its greater liquidity and speed. Perhaps arbitrageurs
will look at the regional exchanges to exploit any price disparity and thereby maintain the law of one price, but any high frequency
trading strategy is likely to be implemented using Xetra data. It would be easy for quantitative analysts to overlook the possible uses
for the data coming from the tiny amount of regional trading. It turns out that this data can be useful in determining whether the law
of one price is operating normally, an insight into the health of the market.
4.2. Measuring Price Variation
The variation in the price distribution between the regional locations of trade can be measured by the coefficient of variation
of prices in any time interval. The coefficient of variation is defined as the ratio of the standard deviation to the mean:
Coefficient of variation CV ¼
σ Standard Deviation
¼
:
μ
Mean
ð1Þ
Normalizing with respect to the mean allows the coefficient of variation to be independent of the absolute value of the mean,
in this case the price of Volkswagen stock in the time interval.
For the seven regional exchanges, the price used here is the volume-weighted average price (VWAP) of the trades in each time
interval at each exchange. There is a single parameter to be selected – the time interval – which could be daily, hourly, 15 min, or
so forth. Once that is chosen, the procedure for calculating the CV for the t-th time interval is to determine the VWAP at each
exchange where the stock traded during the time interval, then to calculate the CV from those VWAPs. If the stock trades at Nt
exchanges during the t-th time interval, and the VWAP at the n-th such exchange is denoted VWAPn,t then
t
1 X
V WAP n;t
Nt n¼1
N
μt ¼
ð2Þ
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
u
Nt 2
u1 X
V WAP n;t −μ t
σt ¼ t
Nt n¼1
CV t ¼
ð3Þ
σt
:
μt
ð4Þ
Fig. 4 shows the coefficient of variation in the VWAP of Volkswagen trades across the seven regional exchanges during 2008
calculated on a daily basis. There is a significant spike on 27 October 2008 which is the first day of the two-day short squeeze.
There is no significant variation on 28 October 2008 which is the day of the extraordinary price spike. Although daily computation
Table 2
Percentage of Volkswagen trading volume on each German exchange in each year from 2003 to 2009. Nearly all trades, more than 98%, were placed on the electronic
trading system Xetra. In 2008 the regional exchanges handled less than 1.5% of Volkswagen trades, and their share appears to be decreasing over time.
Exchange
Xetra
Frankfurt
Stuttgart
Hamburg
Munich
Düsseldorf
Berlin
Hanover
DE
F
SG
H
MU
D
BE
HA
2003
2004
2005
2006
2007
2008
2009
96.775
2.329
0.577
0.125
0.094
0.030
0.026
0.045
97.317
1.648
0.748
0.095
0.114
0.026
0.018
0.034
97.099
1.641
0.928
0.097
0.151
0.032
0.017
0.035
97.720
1.289
0.701
0.087
0.135
0.031
0.013
0.025
97.942
1.287
0.502
0.082
0.116
0.031
0.015
0.025
98.503
0.871
0.418
0.081
0.078
0.019
0.018
0.013
98.609
0.754
0.468
0.056
0.056
0.037
0.012
0.008
K.R.L. Godfrey / Pacific-Basin Finance Journal 40 (2016) 323–334
331
Fig. 4. The coefficient of variation (CV) in the daily volume-weighted average prices (VWAPs) of Volkswagen trades across the seven German regional exchanges
during 2008. The strong and isolated peak occurring on Monday 27 October 2008 marks the first day of the infinite short squeeze after Porsche disclosed its position in cash-settled call options. Accordingly the CV of regional VWAPs shows potential to be a leading indicator of the price spike. The following day, 28 October
2008, shows nothing unusual in the daily CV despite the price spiking on that day.
is coarse and has little use as a leading indicator because it is computed only at the end of each trading day, it is sufficient to show
this technique offers the potential to identify the unusual trading conditions in the day ahead of the price spike.
A daily time interval is also too long for the VWAP computations because the heaviest trading at each exchange may occur at
substantially different times in any given day. This can skew the volume-weighted prices, meaning the VWAPs could represent
trading concentrated at different times of day. The law of one price cannot be expected to hold if the assumption about simultaneous trading is ignored. The solution is to select a shorter time interval and compute the VWAPs more frequently.
4.3. Parameterization and Filtering
The single parameter in this algorithm is the time interval on which the volume-weighted average prices (VWAPs) and their
coefficient of variation are calculated. The choice of interval size is a compromise between speed, accuracy, and precision. Shorter
time intervals and higher frequency calculations have the advantages that the signal is available sooner and the volume-weighting
Fig. 5. The coefficient of variation (CV) of the 15-minute volume-weighted average prices (VWAPs) of Volkswagen trades at each of the seven German regional
exchanges, median-filtered to remove outliers. The variation is unusually high during the two days of the short squeeze, 27 and 28 October 2008. This metric highlights the period of unusual trading activity and importantly it becomes strong at the start of each day, within the first hour of trading each day. The high signal in
the first hour of trading on 27 October 2008 occurred more than 24 h before the price spike.
332
K.R.L. Godfrey / Pacific-Basin Finance Journal 40 (2016) 323–334
occurs at closer times. The disadvantage is there may be fewer exchanges reporting trades in the shorter intervals, which risks
increased noise and reduced precision. As calculation of a standard deviation requires at least three VWAPs, there is also a practical minimum size for the time interval because it needs to capture trades from at least three exchanges. If the interval selected is
too short, there will be many intervals in which the coefficient of variation cannot be calculated.
It is possible to reduce the noise from isolated trades that are unusually high or low during the interval so they do not distort
the coefficient of variation calculation. These outliers can be discarded through the use of median filtering, where a median filter
of size M returns the middle of an ordered set of M consecutive time-series values. The smallest median filter, size three, can eliminate single-period outliers while maintaining the main statistical features of the signal. The median filter is applied only after the
computation of the coefficient of variation so as not to weaken the inputs to the calculation.
Filtered CV t ¼ medianðCV t ; CV t−1 ; CV t−2 Þ
ð5Þ
Fig. 5 shows the results for the coefficient of variation of Volkswagen stock at the seven regional exchanges, computed in 15-minute
intervals during the four weeks surrounding the short squeeze, with median filtering of size three and the removal of intervals in which
fewer than three exchanges reported trades.
There is a strong variation on 27 and 28 October 2008 compared with the other days in Fig. 5. Besides the higher resolution
compared with the daily computation in Fig. 4, this also shows better detection of the abnormal market conditions throughout the
two days of the short squeeze. The median-filtered 15-minute signal appears to meet the requirements of a short squeeze detector
— it is quantitative; its calculation is independent of the absolute price level; and it is active throughout the period of the short squeeze
while apparently not at other times. It starts strongly at the beginning of each day in the short squeeze and not on other days.
4.4. Robustness Testing
One of the risks in quantitative research is “data mining” because it is often possible to look through data after an event to find
patterns that appear to have predicted the event. This article does not promise a universally applicable algorithm. Infinite short
squeezes are rare events and it is possible the findings here may be unique to Volkswagen. Nonetheless we can gain reassurance
by testing the way the approach performs with Volkswagen and similar stocks over a longer time period. A good indicator should
detect the short squeeze on Volkswagen while not giving false positives on Volkswagen or other stocks despite the events of the
global credit crisis occurring at around the same time.
Fig. 6 shows the median-filtered 15-minute coefficient of variation applied to three German automakers Volkswagen, Daimler,
and BMW after the first hour of trading on every trading day from 1 June to 30 November 2008. The idea in studying only the
first hour of each day is to test whether the median-filtered 15-minute signal can be a reliable leading indicator by 10:00 am
for the trading during the rest of the day. The results show significant peaks for Volkswagen on 27 and 28 October 2008, the
two days of the short squeeze, and nothing of significance for Daimler or BMW on those days. Furthermore there are no exceptional
peaks on any of these stocks on any of the other days. The indications for all three stocks are raised slightly during the credit crisis, but
not to the extent of Volkswagen during the infinite short squeeze.
Fig. 6. The coefficient of variation of the 15-minute volume-weighted average prices (VWAPs) of BMW, Daimler, and Volkswagen at the seven German exchanges,
median-filtered at 10:00 am each day. The filtered signal is calculated as the median value from the three intervals 9:15 to 9:30, 9:30 to 9:45, and 9:45 to 10:00
CET each morning so it can be calculated at 10:00 am each day. The signal for Volkswagen is unusually high on 27 and 28 October 2008, while the other car
makers show nothing unusual, confirming the signal is responding to company-specific conditions rather than industry-wide or market-systematic factors. The
two significant points for Volkswagen stand out compared with the signals from all three car makers on everyday throughout this seven year period from
2003 to 2010.
K.R.L. Godfrey / Pacific-Basin Finance Journal 40 (2016) 323–334
333
5. Discussion
The indicator developed here – the median filtered coefficient of variation in regional pricing –demonstrates an ability to
detect the unusual trading behavior in the first hour of trading after Porsche announced its call option position on
Volkswagen, a full day before the peak of the price spike. This quantitative signal has the potential to alert traders to the
anomalous market conditions even if they had not yet seen or digested Porsche's announcement. They could have started
looking for the news and monitoring the price closely, and short-sellers could perhaps have closed out their positions before
others, before matters got worse. The signal could be a warning for traders to hold off from entering the market, or a trigger
for opportunistic derivatives traders to open a long straddle or short butterfly with options that benefit from a large move in
either direction. Overall the approach is quantitative and can be automated without reliance on any fundamental
information.
It is one thing to be able to detect unusual trading conditions and another to be able to act in a timely and cost-effective way.
The use of this signal – or any signal – by short-sellers does not guarantee their position can be exited profitably, or closed at all.
The short sellers who were fortunate to have read Porsche's announcement on Sunday 26 October 2008 had the choice of whether to
repurchase stock on 27 October 2008 or whether to hold on, and they would have been in the same predicament if they had used the
metric described here. Their actions of repurchasing the stock would inevitably drive up the price and squeeze other short-sellers into
repurchasing, as is the nature of a short squeeze.
Constructing this indicator in real-time requires trading data to be available from several exchanges, and trading must occur at
three or more exchanges for the coefficient of variation to be meaningful. Besides the application to the German market, this
approach can be applied in other markets having multiple exchanges such as European and American markets, but not in markets
such as Australia where the securities are traded either on a single exchange or at most two exchanges.
There are many opportunities for further research. The idea of regional price variation increasing during anomalous market
conditions can be tested during other significant events that introduce limits to arbitrage, provided there are multiple exchanges
involved. It would be interesting to explore how far the concept holds. There are also opportunities for deeper research into the
Volkswagen squeeze, for example to study whether alternative contract types such as call options were available at the start of
the squeeze at prices, and whether they could have reduced financial risk.
6. Conclusions
The Volkswagen short squeeze on 27–28 October 2008 was unprecedented in propelling a car maker to become the world's most
valuable company by market capitalization. The squeeze was triggered by a news release from Porsche the day before, on Sunday 26
October 2008. The research question here was whether a change in market behavior could be detected empirically on the morning of
27 October 2008 without knowledge of the earlier announcement.
Traditional fundamental and technical analysis predicted the possibility of a rising price, but could not have predicted its
timing or speed. On the other hand, traditional quantitative analysis of trading price and volume shows nothing unusual on
27 or 28 October 2008. To detect the onset of the abnormal market behavior with quantitative analysis, we need more
information.
Additional trading data is available from the location of trade — the seven regional exchanges around Germany and the Xetra
electronic exchange. While the regional exchanges handled less than 1.5% of the Volkswagen share trading volume in 2008, the
price variation among them can be used as an indicator of deteriorating market health. The law of one price suggests that
Volkswagen stock should normally trade at the same price across all exchanges under normal trading conditions, but empirical
analysis shows that the price variation is significantly wider throughout the two days of the short squeeze. This is consistent
with barriers to arbitrage arising from the lack of available stock.
To detect the abnormal behavior early, an indicator is constructed by median-filtering the 15-minute coefficient of variation of
the volume weighted average prices (VWAPs) of trades at each regional exchange. This metric produces a strong alert throughout
the two days of the Volkswagen short squeeze. It becomes significant in the first hour of trading during each day of the short
squeeze, and importantly it is significant a full day ahead of the price spike. It produces no false positives on Volkswagen throughout the rest of 2008 despite the high volatility from the global financial credit crisis, and it does not trigger at all on the stocks of
competing automakers BMW and Daimler.
While there is no guarantee an algorithm such as this can predict future short squeezes, this approach has a compelling intuition that
regional price variation can arise from the breakdown of the law of one price. It makes sense that the law of supply and demand can
override the law of one price during a short squeeze. With the overload of fundamental information released each day, a quantitative
algorithm such as this may be helpful in computer-assisted trading to focus human attention towards stocks that are exhibiting the
most unusual behavior. Traders who respond quickly in such conditions can perhaps reduce their losses or enter speculative trades
before the price moves further.
The case of Volkswagen is interesting for researchers because of its high economic significance coupled with the availability of high frequency trading data. The limitation of this example is its uniqueness – the unprecedented nature of the
event – as no other company has been propelled in the same way in the history of computerized recording. The trading
data from Volkswagen in 2008 may be the best opportunity for researchers to study an infinite short squeeze for many
years to come.
334
K.R.L. Godfrey / Pacific-Basin Finance Journal 40 (2016) 323–334
Acknowledgments
This research has been funded by The University of Western Australia, with security trading data provided by SIRCA. I am grateful
for feedback and discussions with Philip Brown, Raymond Da Silva Rosa, Darryl Duffie, Robert Durand, Robert Faff, Andrew Karolyi,
Vikas Mehrotra, Natalie Packham, Ying Yu, an anonymous reviewer and participants at FCCCE, AFFI, and FIF conferences.
References
Aitken, M.J., Frino, A., McCorry, M.S., Swan, P.L., 1998. Short sales are almost instantaneously bad news: evidence from the australian stock exchange. J. Financ. 53,
2205–2223.
Angel, J.J., Christophe, S.E., Ferri, M.G., 2003. A close look at short selling on Nasdaq. Financ. Anal. J. 59 (6), 66–74.
Asquith, P., Pathak, P.A., Ritter, J., 2005. Short interest, institutional ownership, and stock returns. J. Financ. Econ. 78, 243–276.
Best, R.J., Best, R.W., Mercado-Mendez, J., 2008. Do short sellers anticipate large stock price changes? Acad. Account. Financ. Stud. J. 12 (3), 71–84.
Blau, B.M., Wade, C., 2013. Comparing the information in short sales and put options. Rev. Quant. Finan. Acc. 41, 567–583.
Blau, B.M., Van Ness, R.A., Wade, C., 2008. Capitalizing on catastrophe: short selling insurance stocks around hurricanes Katrina and Rita. J. Risk Insur. 75, 967–996.
Bloomberg, 2008a. VW overtakes Toyota — thanks to Lehman. The Sydney Morning Herald Business Day (7 October 2008).
Bloomberg, 2008b. Banks spin over Volkswagen's surge. The Sydney Morning Herald Business Day (29 October 2008).
Boehmer, E., Wu, J., 2013. Short selling and the price discovery process. Rev. Financ. Stud. 26, 287–322.
Bolton, P., Oehmke, M., 2013. Strategic conduct in credit derivative markets. Int. J. Ind. Organ. 31, 652–658.
Bredoux, L., 2008. VW defies stock market panic to hit record highs. Agence France Presse (Reprinted in Asia One Motoring 14 October 2008).
Bris, A., Goetzmann, W.N., Zhu, N., 2007. Efficiency and the bear: short sales and markets around the world. J. Financ. 62, 1029–1079.
Burger, L., 2008. German finance ministry to reassess disclosure rules for stake building. Thomson Reuters (28 August 2008).
Christophe, S.E., Ferri, M.G., Angel, J.J., 2004. Short-selling prior to earnings announcements. J. Financ. 59, 1845–1875.
Clunie, J., 2010. The hidden risks of short selling: the crowds aren't always wise when trading from the short side. Active Trader Magazine, pp. 40–44 (May 2010).
Dalan, M., 2008. Ein banker mit nebenjob (a banker with a side job). Die Welt Online (23 November 2008).
D'Avolio, G., 2002. The market for borrowing stock. J. Financ. Econ. 66, 271–306.
de la Merced, M.J., Dougherty, C., 2008. Panicked traders take VW shares on a wild ride. International Herald Tribune (29 October 2008).
Dechow, P.M., Hutton, A.P., Meulbroek, L., Sloan, R.G., 2001. Short-sellers, fundamental analysis, and stock returns. J. Financ. Econ. 61, 77–106.
Deutsche Welle, 2008. Frankfurt stock exchange changes DAX rules after VW jump. Available at: http://www.dw.de/frankfurt-stock-exchange-changes-dax-rulesafter-vw-jump/a-3756993.
Diether, K., Lee, K., Werner, I.M., 2009. Short sale strategies and return predictability. Rev. Financ. Stud. 22, 575–607.
Do, B., Do, V., Chai, D., 2012. Does the 2008 short sale ban affect the enforcement of the Law of One Price? Evidence from Australia. Account. Finance 52, 117–144.
Dougherty, C., 2009. Facing losses billionaire takes his own life. International Herald Tribune (6 January 2009).
Economist, 2008a. In the driving seat. The Economist 8570, 72-72 available at http://www.economist.com/node/10808857, (Mar 6th 2008).
Economist, 2008b. Squeezy money: how Porsche fleeced hedge funds and roiled the world's financial markets. The Economist 8604, 85-85 available at http://www.
economist.com/node/12523898, (Oct 30th 2008).
Ehrhardt, S., 2007. Lower Saxony buys VW shares to keep 20 percent stake. Thomson Reuters (29 May 2007).
Elfakhani, S., 2000. Short positions, size effect, and the liquidity hypothesis: implications for stock performance. Appl. Financ. Econ. 10, 105–116.
Etebari, A., Tourani-Rad, A., Gilbert, A., 2004. Disclosure regulation and the profitability of insider trading: Evidence from New Zealand. Pac. Basin Financ. J. 12, 479–502.
Haines, J., Holmes, N., von Jacobs, N., 2008. Porsche and VW: is this the final lap? Ashurst London corporate briefing. Available at: https://www.ashurst.com/doc.aspx?
id_Content=4030.
Hetzner, C., 2008. VW shares halve as Porsche eases short squeeze. Thomson Reuters (29 October 2008).
Lamb, P., Khanp, N., Silkin, L., 2008. Porsche–VW highlights inadequacies of German system. Hedge Funds Review (7 November 2008).
Lynn, M., 2006. Why Porsche would be mad to bid for Volkswagen. The Spectator (29 November 2006).
Merrick Jr., J.J., Naik, N.Y., Yadav, P.K., 2005. Strategic trading behaviour and price distortion in a manipulated market: anatomy of a squeeze. J. Financ. Econ. 77,
171–218.
Murphy, P., 2008. Porsche LLC? The VW fruit machine explained. The Financial Times (17 October 2008).
Noack, U., 2007. The 2007 reform of the German disclosure system for company data (DDie neue Unternehmenspublizität nach EHUG und TUG). SSRN and CBC-RPS
0027 (Available at: http://ssrn.com/abstract=980289).
Pattison, I., 2010. Caught short? Let the market decide. IPA Review, pp. 32–35 (Nov 2010).
Porsche Automobil Holding, 2007. Annual Report 2006/07. Available at: https://bib.kuleuven.be/files/ebib/jaarverslagen/PORSCHE_200607.pdf.
Porsche Automobil Holding, 2008. Porsche achieves new records in profit, turnover and sales. Available at: www.porsche-se.com/pho/en/press/newsarchive2008/?
pool=pho&id=2008-11-26.
Richter, F., 2008. Porsche to gradually increase Volkswagen stake in September — CFO. Finanz Nachrichten (28 July 2008).
Schmidhammer, C., Lobe, S., Röder, K., 2014. The real benchmark of DAX index products and the influence of information dissemination: a natural experiment. J. Asset
Manag. 15 (2), 129–149.
Shleiffer, A., Vishny, R.W., 1997. The limits of arbitrage. J. Financ. 52, 35–55.
Wang, S.-F., Lee, K.-H., 2015. Do foreign short-sellers predict stock returns? Evidence from daily short-selling in Korean stock market. Pac. Basin Financ. J. 32, 56–75.