Description
The purpose of this paper is to determine if the US Treasury’s at-the-market sales of
5.27 billion Citigroup shares in 2010 drove down the banks’ share price. It attempts to use the evidence
of Citigroup’s stock returns to accept or reject competing hypotheses of larger stock sales.
Journal of Financial Economic Policy
Stock demand curves and TARP returns
Linus Wilson
Article information:
To cite this document:
Linus Wilson, (2011),"Stock demand curves and TARP returns", J ournal of Financial Economic Policy, Vol.
3 Iss 3 pp. 229 - 242
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Stock demand curves
and TARP returns
Linus Wilson
Department of Economics and Finance, B.I. Moody III College of Business,
University of Louisiana at Lafayette, Lafayette, Louisiana, USA
Abstract
Purpose – The purpose of this paper is to determine if the US Treasury’s at-the-market sales of
5.27 billion Citigroup shares in 2010 drove down the banks’ share price. It attempts to use the evidence
of Citigroup’s stock returns to accept or reject competing hypotheses of larger stock sales.
Design/methodology/approach – The paper uses a geometric Brownian motion model to test if
there were abnormal returns at various points in the US Treasury’s highly publicized stock sale that
lasted from 26 April to 6 December 2010.
Findings – There was a weakly signi?cant drop in the stock price at the announcement of the sale
and a weakly signi?cant rise in the stock price just after it ended. This is evidence that the demand
curve for the stock had a negative slope.
Practical implications – The evidence from this study will in?uence policy makers and investors
in the upcoming privatizations of large bailed-out ?rms such as American International Group,
Ally Financial, Chrysler, and General Motors. The evidence indicates that slow at-the-market sales
may temporarily depress stock prices more than quicker, underwritten secondary offerings. Patient
investors may experience modest abnormal returns from providing liquidity to the US Treasury as it
privatizes its holdings.
Originality/value – This is the only paper to study the stock price impacts of the US Treasury’s
liquidation of its 27 percent stake in Citigroup in 2010. Because the stock sales were delegated to a
third party and highly publicized, unlike most other large stock sales, the Citigroup privatization is an
unprecedented opportunity to test if the demand curve for common stocks is perfectly elastic.
Keywords United States of America, Fiscal policy, Bailout, Geometric Brownian motion, Citigroup,
Demand curves, Secondary offerings, TARP
Paper type Research paper
1. Introduction
The US Treasury began pre-announced, at-the-market sales of Citigroup shares on
26 April 2010, and concluded those sales on 6 December 2010. The US Treasury
acquired a common stock stake in July 2009 when it converted $25 billion par value of
preferred shares into approximately 7.7 billion common shares. At one point, the US
Treasury owned 34 percent of the company’s common stock. That number declined to
27 percent after a seasoned equity offering in December 2009 diluted its holdings.
Through the course of 130 trading days in 2010, the US Treasury sold nearly 5.3 billion
shares or about 7.0 percent of the daily volume on those days at an average price
of $4.04 per share. On the evening of 6 December 2010, the US Treasury sold
The current issue and full text archive of this journal is available at
www.emeraldinsight.com/1757-6385.htm
JEL classi?cation – G01, G13, G21, G28, G32
This is not investment advice. The author makes no warranties about the data or estimates in
this paper. The author was not compensated by any ?rm, trade association, or the federal
government to do this analysis.
Stock demand
curves and
TARP returns
229
Journal of Financial Economic Policy
Vol. 3 No. 3, 2011
pp. 229-242
qEmerald Group Publishing Limited
1757-6385
DOI 10.1108/17576381111152218
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the remainder of their stake in an underwritten secondary offering, which raised
$10.5 billion (Smith et al., 2010).
Such large and widely disclosed share sales are unprecedented. The US Treasury
primarily bought preferred stock from bailed-out banks as part of the Troubled Asset
Relief Program (TARP). At the time of writing, this was the only instance where the
US Treasury has sold its common shares to private investors in at-the-market trades.
Following the advice of Verret (2010), the US Treasury delegated its sales to its
selling agent according to a preset trading plan[1]. Policy makers and investors would
no doubt be interested in whether those sales are driving the price of Citigroup’s stock.
Further, these share sales give us a new natural experiment to test whether the demand
curve for stocks slopes downward. Further, the commencement of these sales coincided
with a negative one-day return that was weakly signi?cant, assuming the stock returns
adhered to a geometric Brownian motion model. The conclusion of these sales was also
followed immediately by a positive abnormal return. These returns are consistent with
a mild version of the price pressure hypothesis (PPH) ?rst advanced by Scholes (1972).
Unlike Scholes (1972), who studied the price impacts of underwritten secondary
offerings, we ?nd evidence that the price decline was temporary. Thus, this evidence
indicates that the US Treasury, unlike private sellers in Scholes (1972) and Kraus and
Stoll (1972), was not perceived to be acting on an informational advantage. Thus, these
returns are not consistent with the information hypothesis (IH), which would predict
that large stock sales would have a one-time abnormal decline in the stock price
because the sellers had non-public adverse information about the stock.
The literature exploring whether the price of stocks are subject to the whims of
supply and demand like the markets for goods and services has focused on event
studies on index inclusions and exclusions. Harris and Gurel (1986), Shleifer (1986), Jain
(1987), Dhillon and Johnson (1991), Beneish and Whaley (1996), Lynch and Mendenhall
(1997) and Wurgler and Zhuravskaya (2002) all conclude that stocks added to the S&P
500 stock index earn positive abnormal returns. Biktimirov et al. (2004) ?nd that stocks
listed on the Toronto Stock Exchange, which were dropped from the popular index,
experienced an abnormal decline in value. In addition, Biktimirov et al. (2004) discover
that stocks added to the Russell 2000 small-cap US stock index experience positive
abnormal returns upon inclusion and negative abnormal returns upon exclusion from
the index. These studies generally conclude or assume that there are no announcement
effects in inclusion. Instead, they generally argue that portfolio managers replicating a
particular index have to buy stocks at or close to the inclusion date and sell stocks close
to the exclusion date. Yet, Dennis et al. (2002) argue that there are many more positive
analyst reports released around the time of an S&P 500 index inclusion and many more
negative analyst reports around an index exclusion. Thus, it is not clear that an index
inclusion or exclusion is “information free,” according to Dennis et al. (2002).
Lin and Yung (2006)’s study of Real Estate Investment Trusts (REITS) also casts
doubt on the hypothesis that the demand curve for securities is downward sloping. Lin
and Yung (2006) ?nd that the prices of REITS are not affected by capital ?ows in and
out of REITS. They argue that this favors the argument that the demand curve for
REITS is perfectly elastic or ?at, supporting the substitution hypothesis (SH)
developed by Scholes (1972).
This paper is a part of a growing body of literature in the US Treasury’s
investments into banks under the $700 billion TARP. Many papers have addressed
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the question of whether the capital injections encouraged banks to lend. Examples of
this literature are Bebchuk and Goldstein (2009), Philippon and Schnabl (2009), Wilson
(2009), Taliaferro (2009), Li (2010) and Wilson and Wu (2010). Many studies have
addressed which banks receive or accept capital injections such as Bayazitova and
Shivdasani (2009), Duchin and Sosyura (2009), Taliaferro (2009), Cadman et al. (2010),
Li (2010), Jordan et al. (2010) and Ng et al. (2010). In contrast to the TARP entry
literature, Wilson and Wu (2011) look at the characteristics of the banks that exit the
program early. Veronesi and Zingales (2010) and Kim and Stock (2010) conduct event
studies testing the securities returns surrounding the ?rst capital injections. Kim (2010)
measures the stock returns before and after the announcement of new executive
compensation restrictions on TARP recipients. Wilson (2010) discusses the tight
deadlines that the US Treasury has for its Citigroup share sale, and simulates the US
Treasury’s chances of success. Unlike Wilson (2010), which is a forward looking
assessment of the wisdom of the at-the-market sales, the present study looks at how the
share sales affect the short-term returns of Citigroup’s stock price before, during, and
after the US Treasury’s selling period. The present study ?nds a signi?cant negative
abnormal decline in the stock price at the start of the selling period and a signi?cant
abnormal rise in the stock price right after the end of the selling period.
In Section 2, we discuss two competing hypotheses of the effect on the share price of
large sales. In Section 3, we introduce the Brownian motion model and use it to test if
the stock returns experienced around these share sales can be considered abnormal.
In Section 4, we conclude our discussion.
2. Competing hypotheses
Scholes’s (1972) analysis of block trades kicked off a long line of literature attempting
to determine if the demand curve for stocks is perfectly elastic. That study identi?ed
competing views. The ?rst hypothesis is the SH. The SH says that regardless the size
of the block of shares being sold at any given moment or on any given day, the price
that it will trade is the fundamental value of the stock at any given moment. Thus,
rational traders have an in?nite demand for the stock at a price at or below its
fundamental value. At the other extreme, the PPH says that, when you increase the
supply of the stock at any given time, you push down its price. These are different
views about the nature of the demand curve for stocks are shown in Figure 1.
In panel A, the demand curve is ?at, signifying that investors will buy as many as
all the shares outstanding at any given moment. In contrast to the SH, the PPH says
that the demand for the security slopes down. Thus, a shift in supply, in panel B,
Figure 1.
Competing theories of
large share sales
D
D
S(1)
S(2)
S(1)
S(2)
P(1) = P(2)
P(1)
P(2)
Q(1) Q(2)
Price
Panel A: Substitution
Hypothesis (SH)
Panel B: Price Pressure
Hypothesis (PPH)
Price
Quantity Quantity
Q(1) Q(2)
Stock demand
curves and
TARP returns
231
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causes a fall in the price of the stock. The US Treasury’s share sale offers a good
natural experiment to test which view is correct.
The SH can be de?ned as the following:
1. Substitution hypothesis
H
0.
The share price is unaffected by announcement, initiation, pauses, or cessation
of the share purchases.
H
1.
There are signi?cant abnormal share price returns at the announcement,
initiation, pauses, and/or cessation of the share purchases.
Departing from Scholes’s (1972) classi?cations somewhat. There are really two forms
of the PPH, the extreme and mild form, which are de?ned below:
2a. Extreme PPH
H
0.
The stock will drop abnormally every day of share sales and will rise
abnormally at each pause of share sales.
H
1.
The stock does not drop abnormally for each day of share sales or it does not
rise abnormally during share sale pauses.
2b. Mild PPH
H
0.
The stock price will drop at the announcement and initiation of the share sales
and it will rise at the announcement and act of their cessation.
H
1.
The stock price will not drop at the announcement and initiation of the share
sales or it will not rise at the announcement and act of their cessation.
The initiation of the Citigroup share sale was announced on 26 April 2010, and it began
that day. The cessation of share sales was announced after trading halted on
6 December 2010, and share sales ceased that night with an after-hours underwritten
secondary offering of 2.42 billion shares, which was the remainder of the US
Treasury’s stake.
Scholes (1972) introduces a third hypothesis, the IH. This hypothesis says that
sellers of large numbers of shares have better information about adverse events than
other market participants. The US Treasury delegated the sales and very publicly
disclosed their sales to help dispute the fact that they had adverse information about
the Citigroup stock. Nevertheless, market participants may not have been convinced by
these efforts.
The IH’s prediction is summarized in the null and alternative hypothesis below:
3. Information hypothesis
H
0
. There will be a drop in the stock price at the announcement of the sale, and the
share price will not rise abnormally after the cessation of share sales.
H
1
. There is no drop in the stock price at the announcement of the sale or the drop
is temporary and the stock price rises after the cessation of stock sales.
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3. Price movements
We established in the previous section that the supply of shares sold increased
signi?cantly during the US Treasury’s selling period. Yet, did this increase in supply
lead to signi?cantly lower share prices? We use the geometric Brownian motion model
to test the hypotheses developed in Section 2. The analysis here ?nds that the only
signi?cant drop in the share price occurred at the start of share sales. Further, this drop
was temporary and was mostly reversed by an abnormal rise at the share sale’s
conclusion.
The geometric Brownian motion model of the stock price predicts that the stock
moves with a random walk plus a drift. The drift component, r, for the stock is its
expected return or cost of capital. The random walk is determined by the stock’s
volatility, s, or standard deviation and the random draw, 1. Let dt stand for a small
interval of time, t. In that case, the stock price evolves according to the following
differential equation:
dt ¼ rSdt þsS1
????
dt
p
ð1Þ
If the value of the stock at any given time is S(t), then the initial value of the stock is
S(0). The terminal value of the stock is S(T), where T is the time to that date in years.
In the Appendix, it is shown that the exact formula for the terminal value of the stock is
the following:
SðTÞ ¼ Sð0Þexp r 2
s
2
2
T þs1
????
T
p
ð2Þ
For our purposes, we want to invert this equation so that we can ?nd the likelihood of a
particular stock price realization, 1:
1 ¼
lnðSðTÞ=Sð0ÞÞ 2ðr 2ðs
2
=2ÞÞT
s
????
T
p ð3Þ
1 is the Z score in a standard normal distribution. The higher the absolute value of 1,
the more abnormal is the return. If 1 . 0, then the return is unexpectedly positive, and,
if 1 , 0, then the return is unexpectedly low. The two-tailed signi?cance level implied
by the error in equation (3) is 2
*
min{Nð1Þ; ð1 2Nð1ÞÞ}, where N() denotes the
standard normal distribution.
All the inputs on the right-hand side of equation (3) can be observed or easily
estimated. Time in years is measured by dividing the number of trading days that pass
by 252, the typical number of trading days in a given year. The stock prices can be
taken from a variety of sources. Here, we use closing stock prices from Yahoo! Finance.
The volatility of the stock is estimated from the vega-weighted average of Black and
Scholes (1973) implied volatilities of Citigroup’s options. These implied volatilities and
vegas were obtained from IVolatility.com. The implied volatilities used were from
options traded at time 0 with expiration dates just before time T and just after time T.
Vega is the marginal sensitivity of an option’s price to a change in the expected
volatility of the stock. This weighting favors heavily traded options that have exercise
prices close to the current stock prices. Simple averages produced very similar implied
volatility estimates. The expected return on the stock is estimated according to the
market model of Sharpe (1964) and Lintner (1965). Wilson (2010) estimated the capital
Stock demand
curves and
TARP returns
233
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asset pricing model beta of the Citigroup stock just prior to the start of the US
Treasury’s share sale at 2.771.
The expected log return is:
r ¼ lnð1 þEðR
T
ÞÞ; where EðR
T
Þ ¼ r
f
þ2:771
*
{RðSPY; TÞ 2r
f
}: ð4Þ
r
f
is the risk-free rate or the return on T-bills over that time horizon. For the time
periods studied, the 28- and 91-day T-bill rates were between 0.14 and 0.16 percent. Yet,
over time horizons of 1-48, days r
f
was equal to 0.00-0.02 percent. SPY is the
exchange-traded fund that attempts to replicate the returns of the S&P 500. We use the
SPY security returns as a proxy for the returns on the market as a whole. R(SPY, T) is
the expected arithmetic return over the period de?ned as the difference in the
beginning, SPY
0
, and ending, SPY
T
, prices over the period and the sum of any
dividends paid over that interval, DIV:
RðSPY; TÞ ¼
SPY
T
2SPY
0
þDIV
SPY
0
ð5Þ
In Figure 2, we plot the timeline of the US Treasury’s share sales. On average, the US
Treasury made up 7.0 percent of the trading volume over the selling periods. Using
monthly disclosures of the US Treasury, the government’s share sales ranged from
6.8 to 9.7 percent of the average number of shares sold per day.
Figure 2.
US Treasury’s cumulative
share sales and a
percentage of average
trading volume
Billions of shares sold, or percent of average share volume
Total shares sold
Date
% of average volume
0
2
4
6
8
10
4
/
2
6
/
1
0
5
/
2
6
/
1
0
6
/
2
6
/
1
0
7
/
2
6
/
1
0
8
/
2
6
/
1
0
9
/
2
6
/
1
0
1
0
/
2
6
/
1
0
1
1
/
2
6
/
1
0
Notes: From 26 April 2010 to 6 December 2010, the US Treasury sold
shares of Citigroup at market prices through its broker Morgan Stanley
in a series of four preset trading plans; the US Treasury disclosed the
progress of their sales though press releases, SEC filings, and monthly
reports on the TARP; share volumes are obtained from Yahoo! Finance;
in total, the US Treasury sold 5.27 billion shares by this method; on
7 December, the US Treasury sold 2.42 billion shares using an
underwritten secondary offering for $4.35 per share; the mostly flat line
is the percent of average trading volume that the US Treasury’s share sales
represented; the upward sloping line is the total number of at-the-market
sales by the US Treasury in billions; there were two periods just prior to
earnings announcements where share sales were halted; those periods were
1-22 July 2010, and 1-18 October
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There were “blackout periods,” days before and after earnings announcements where
the US Treasury promised not to sell shares. These blackout periods were
pre-announced. The blackout periods, or selling pauses, were from 1 to 22 July 2010,
around second quarter earnings and 1-18 October 2010, for third quarter earnings.
There is only information on the progress of the US Treasury’s sales on a roughly
monthly basis. Thus, the percent of average volumes are ?at until a new disclosure at
the end of the month, the end of a preset trading plan, or the start of an earnings
blackout period. The upward sloping line is the number of shares sold. This line is ?at
during the pauses around earnings. On 6 December 2010, the US Treasury sold the
remainder of its stake 2.42 billion shares overnight by means of an underwritten
secondary offering at a price of $4.35 per share or at about a 2.2 percent discount from
the previous day’s closing price (Smith et al., 2010).
In Table I, we have examined 14 different time horizons where we would suspect
that Citgroup’s stock price may have signi?cant excess returns.
In the ?rst test, Table I, we have the closing stock price on 23 April 2010, just prior
to the announcement of the details of the dribble-out sale plan and its beginning
and the closing stock price on the day of the announcement on Monday, 26 April
2010. That was the only period that had signi?cant negative returns. Since investors
expected the share sales to commence as early as 16 March 2010, the announcement
may have surprised some investors about the US Treasury’s lack of progress[2]. That
close-to-close return was abnormally negative with greater than 90 percent con?dence.
Thus, it appears that the announcement of the ?rst trading plan on 26 April 2010, was
badly received by investors.
Interestingly, the stock return, test 13, at the announcement of and the completion of
the US Treasury’s share sales from 6 to 7 December 2010, was also signi?cantly
positive with greater than 90 percent con?dence. These two returns, tests 1 and 13,
are consistent with the mild PPH (MPPH). Since the MPPH is inconsistent with the SH,
we can reject that latter theory with 90 percent con?dence. Moreover, since the drop in
the share price from 23 to 26 April 2010, was not permanent and was reversed at the
end of share sales, we can discard the IH.
There is little support for the extreme PPH (EPPH). That hypothesis would predict
abnormal price declines whenever the US Treasury sold its stake. That hypothesis
would predict negative abnormal returns for the tests 1, 2, 5, 6, 7, 10, 11, and 12.
Yet, only test 1 has an abnormally negative return on the day the sale was begun. The
EPPH would predict that there would be positive returns for tests 3, 4, 8, 9, 13, and 14.
Yet, only test 8, at the start of the third quarter earnings selling pause, and test 13 at the
completion of the share sale experienced positive abnormal returns.
Interestingly, both these positive excess returns also coincided with unexpected
underwritten offerings of the US Treasury’s stakes in Citigroup. On 30 September
2010, Citigroup repurchased the US Treasury’s $2.2 billion of trust preferred shares
obtained from a then-cancelled $301 billion asset guarantee. Citigroup re?nanced the
US Treasury’s preferred stake by selling similar shares to private investors
(Thiruvengadam and Rieker, 2010). On 6 December 2010, after trading hours, the US
Treasury sold 2.42 billion shares in an underwritten secondary offering[3]. One
interpretation is that investors cheered faster than expected sales of the US Treasury’s
stake. Part of the disappointment of investors on 26 April 2010, in test 1, may have
Stock demand
curves and
TARP returns
235
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Table I.
Geometric Brownian
motion model of
Citigroup’s realized stock
returns over various time
periods of interest
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been that investors expected a faster means to exit the Citigroup stake than the US
Treasury’s plan to sell just a small fraction of the stake every day.
4. Conclusion
The US Treasury’s share sales made up about 7 percent of the daily volume of
Citigroup’s shares traded from26 April to 6 December 2010, with two pauses around Q2
and Q3 2010 earnings announcements. This paper used a geometric Brownian motion
model to test for abnormal price reactions to the US Treasury’s at-the-market sales.
This study ?nds that the US Treasury’s share sales led to abnormally negative returns
in the Citigroup share price on the ?rst day of the at-the-market share sale. Moreover,
the share price rose signi?cantly the day after the close of share sales, 7 December 2010.
This evidence is consistent with the theory that the slope of the demand curve for
Citigroup’s stock slopes downward in the short term, but any declines due to large
share sales are transitory. This evidence is consistent with the mild form of the PPH.
We can reject the hypothesis that investors believed that the US Treasury sold out of
superior information because most of the price decline was reversed after the share
sales ended. Moreover, we can reject the SH because there appeared to be abnormal
price reactions at the beginning and the ends of Citgroup share sale. The initial price
decline was 5.1 percent when the sale began and 3.8 percent when the sale ended. Yet,
there is no evidence that the share sales led to negative abnormal price reactions during
selling periods besides the ?rst day. Thus, more extreme forms of the PPH, which
would expect abnormal returns during the whole selling period, cannot be supported.
An underwritten secondary offering of shares typically is sold at a 2-3 percent
discount of the prevailing price, according to Dunbar et al. (2004). Taxpayers accepted
a 2.2 percent discount from the closing price when the balance of the Citigroup stake
was sold on the evening of 6 December 2010. Thus, it seems that this slow
privatization’s 5 percent initial price drop was worse than what could have been
expected, had most of the stake been sold on 26 April 2010, by an underwritten
secondary offering of the shares. Moreover, the average share price of the at-the-market
sales of the 5.27 billion shares was $4.04. The closing price on 23 April 2010 was $4.86.
Even with a three percent discount, taxpayers likely could have sold most of their stake
for $4.71 per share. With the bene?t of hindsight, taxpayers could have generated
$3.53 billion more, before underwriting fees, if those 5.27 billion shares had been sold in
an underwritten secondary offering on 26 April 2010.
The US Treasury sold a large portion of its stake in a November 2010 initial public
offering (IPO) of General Motors after it emerged from bankruptcy. Yet, taxpayers
retain a 33 percent stake or about 0.5 billion shares in General Motors at the time of
writing. The US Treasury will be able to begin selling these shares in May 2010
( Jones, 2010; Mitchell, 2010). The evidence from the Citigroup share sale indicates that
the negative price reaction from a slow at-the-market sale may be larger than an
underwritten secondary offering. Nevertheless, the US Treasury is likely to favor a slow
at-the-market sale because such a sale gives the GM shares a greater chance of edging
closer to the US Treasury’s politically important breakeven price of over $50 per share.
The GM shares were trading at between $33 and $35 per share at the time of writing.
According to US Treasury (2010), taxpayers will have a 93 percent stake in
American International Group which will receive nearly $70 billion from the TARP in
addition to many billions more from Federal Reserve loans. Moreover, taxpayers have
Stock demand
curves and
TARP returns
237
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a 56 percent common stock stake in the privately held Ally Financial (formerly GMAC),
which received $17 billion from the TARP. Finally, taxpayers retain a 9.9 percent
common stock stake in Chrysler Motors, which has emerged from bankruptcy and is
currently privately held. The lessons from this paper may help policy makers better
choose between:
.
selling more of their shares in the IPO and/or underwritten secondary offerings;
and
.
attempting lengthy at-the-market sales as were conducted in the case of
Citigroup.
The lesson of Citigroup is that a gradual exit leads to a price drop comparable or
greater than large underwritten secondary offerings. This evidence should cause
conscientious policy makers to reconsider the wisdom of slow dribble out sales similar
to the 2010 Citigroup share sale.
Notes
1. Verret (2010) worries about the government using inside information in its dispositions of
assets. Yet, The Assistant US Treasury Secretary for Financial Stability Herb Allison
testi?ed before the Congressional Oversight Panel hearing on Citigroup on 4 March 2010,
saying that US Treasury of?cials in charge of Citigroup share sales only looked at publically
available information.
To assuage fears that the US Treasury may use access to non-public information, the US
Treasury delegated its sales to a third party, Morgan Stanley. The selling instructions were
not disclosed, but the number of shares available to be sold and the duration of the selling
periods were disclosed. See the 8-K and prospectus’ ?led on 26 April 2010, available at
web sites: www.sec.gov/Archives/edgar/data/831001/000114420410022189/v182217_8k.htm
and www.sec.gov/Archives/edgar/data/831001/000095012310037908/y83942e424b2.htm.
The US Treasury disclosed its sales in monthly reports and at the beginning and end of
each of four different selling periods, which authorized Morgan Stanley and its af?liated
brokers to sell up to 1.5 billion shares.
2. See Exhibit 99.1 of the SEC form 8-K dated 14 December 2009, accessed online on 12 July
2010 at: www.sec.gov/Archives/edgar/data/831001/000095012309070361/y80976exv99w1.
htm and Citigroup, “Press Release: Citi Prices $17 Billion Common Stock Offering and
$3.5 Billion of Tangible Equity Units, Prices Largest US Public Equity Offering in History,
Citi to Repay $20 Billion of TARP Trust Preferred Securities, Terminate Loss-Sharing
Agreement, US Treasury Extends Lock-Up to 90 Days,” 16 December 2009, exhibit 99.1 in
SEC form 8-K dated 17 December 2009, accessed online on 12 July 2010 at: www.sec.gov/
Archives/edgar/data/831001/000095012309071395/y81063exv99w1.htm.
On 29 March 2010, the treasury disclosed their intention to use a prearranged trading plan
( Jacobs, 2010; Lawder and Eder, 2010).
3. The US Treasury had promised a year earlier to exit it stake in Citigroup by 14 December
2010. Yet, it backed away from the commitment in the fall of 2010 (Guerra, 2010; Miller, 2010;
Wilson, 2010).
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Journal of Business, Vol. 75, pp. 583-608.
Further reading
Biktimirov, E.N. (2004), “The effect of demand on stock prices: evidence from index fund
rebalancing”, Financial Review, Vol. 39, pp. 455-72.
Wilson, L. (2010), “Treasury’s policy of silence could come back to haunt US”,
Financial Times, October 5, available at: www.ft.com/cms/s/0/ccc970e4-d017-11df-bb9e-
00144feab49a,s01¼1.html (accessed 25 December 2010).
Appendix. Derivation of S(T)
To solve for the terminal value of the stock following a geometric Brownian motion path, we
must transform equation (1), using Ito’s Lemma ?rst developed in Ito (1951). Hull (2003, pp. 226-8,
232-3, 410-13) also has a good discussion of the derivation below. First, we need to ?nd the
change in the log stock return, dln S. Ito’s Lemma says the function f¼f(S, t). Can be expanded
using a Taylor expansion:
df ¼ d ln S ¼
df
dS
dS þ
df
dt
dt þ
1
2
d
2
f
dS
2
dS
2
þ
d
2
f
dSdt
dSdt þ
1
2
d
2
f
dt
2
dt
2
. . . ðA1Þ
We will solve for equation (A1) in pieces. Some of the partial derivatives of f¼f(S, t) are as
follows:
df
dS
¼
1
S
;
d
2
f
dS
2
¼ 2
1
S
2
;
df
dt
¼ 0: ðA2Þ
Squaring equation (1):
dS
2
¼ m
2
S
2
dt
2
þ2smS
2
dt
????
dt
p
þs
2
S
2
dt ¼ s
2
S
2
dt; when dt !0: ðA3Þ
The ?rst and second terms on the right-hand side of equation (A3) are zero because dt
y
¼0, when
both y . 1, and dt ! 0. For this same reason, the dt
2
term in equation (A1) is also zero in this
case. It is also clear that the dSdt term below is zero for the same reason:
dSdt ¼ rSdt
2
þsS1dt
????
dt
p
¼ 0; when dt !0: ðA4Þ
The higher order terms in equation (A1) are also eliminated because the dt is taken to a power
y . 1. Inserting equations (1), (A2), (A3), and (A4) into equation (A1), the differential equation
simpli?es to:
df ¼ d ln S ¼ r 2
s
2
2
dt þs1
????
dt
p
: ðA5Þ
Stock demand
curves and
TARP returns
241
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Equation (A5) can be rewritten:
ln Sðt þdtÞ 2ln SðtÞ ¼ r 2
s
2
2
dt þs1
????
dt
p
: ðA6Þ
If we add ln S(t) to both sides of equation (A6) and take the exponential of both sides, we obtain
the following expression:
Sðt þdtÞ ¼ SðtÞexp r 2
s
2
2
dt þs1
????
dt
p
ðA7Þ
When t¼0 and dt¼T, then equation (A7) is identical to equation (2). This is what we wanted to
derive.
About the author
Linus Wilson is an Assistant Professor of Finance at the University of Louisiana at Lafayette,
and is the Charles and Vicky Milam Board of Regents Support Fund Professor of Business
Administration there. He received his Doctor of Philosophy in Financial Economics at Oxford
University in England. He has written over 30 academic papers on bank privatizations,
bankruptcy, CEO pay, entrepreneurship, market entry decisions, Ponzi schemes, stock warrants,
government plans to buy toxic assets, and bank recapitalization programs. He has written over
a dozen academic papers on the Troubled Asset Relief Program (TARP). Dr Wilson has been
a source for hundreds of news stories on the bank rescues in news outlets such as the Wall Street
Journal, the NewYork Times, Bloomberg BusinessWeek, and National Public Radio. Linus Wilson
can be contacted at: [email protected]
JFEP
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242
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doc_657630588.pdf
The purpose of this paper is to determine if the US Treasury’s at-the-market sales of
5.27 billion Citigroup shares in 2010 drove down the banks’ share price. It attempts to use the evidence
of Citigroup’s stock returns to accept or reject competing hypotheses of larger stock sales.
Journal of Financial Economic Policy
Stock demand curves and TARP returns
Linus Wilson
Article information:
To cite this document:
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3 Iss 3 pp. 229 - 242
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Stock demand curves
and TARP returns
Linus Wilson
Department of Economics and Finance, B.I. Moody III College of Business,
University of Louisiana at Lafayette, Lafayette, Louisiana, USA
Abstract
Purpose – The purpose of this paper is to determine if the US Treasury’s at-the-market sales of
5.27 billion Citigroup shares in 2010 drove down the banks’ share price. It attempts to use the evidence
of Citigroup’s stock returns to accept or reject competing hypotheses of larger stock sales.
Design/methodology/approach – The paper uses a geometric Brownian motion model to test if
there were abnormal returns at various points in the US Treasury’s highly publicized stock sale that
lasted from 26 April to 6 December 2010.
Findings – There was a weakly signi?cant drop in the stock price at the announcement of the sale
and a weakly signi?cant rise in the stock price just after it ended. This is evidence that the demand
curve for the stock had a negative slope.
Practical implications – The evidence from this study will in?uence policy makers and investors
in the upcoming privatizations of large bailed-out ?rms such as American International Group,
Ally Financial, Chrysler, and General Motors. The evidence indicates that slow at-the-market sales
may temporarily depress stock prices more than quicker, underwritten secondary offerings. Patient
investors may experience modest abnormal returns from providing liquidity to the US Treasury as it
privatizes its holdings.
Originality/value – This is the only paper to study the stock price impacts of the US Treasury’s
liquidation of its 27 percent stake in Citigroup in 2010. Because the stock sales were delegated to a
third party and highly publicized, unlike most other large stock sales, the Citigroup privatization is an
unprecedented opportunity to test if the demand curve for common stocks is perfectly elastic.
Keywords United States of America, Fiscal policy, Bailout, Geometric Brownian motion, Citigroup,
Demand curves, Secondary offerings, TARP
Paper type Research paper
1. Introduction
The US Treasury began pre-announced, at-the-market sales of Citigroup shares on
26 April 2010, and concluded those sales on 6 December 2010. The US Treasury
acquired a common stock stake in July 2009 when it converted $25 billion par value of
preferred shares into approximately 7.7 billion common shares. At one point, the US
Treasury owned 34 percent of the company’s common stock. That number declined to
27 percent after a seasoned equity offering in December 2009 diluted its holdings.
Through the course of 130 trading days in 2010, the US Treasury sold nearly 5.3 billion
shares or about 7.0 percent of the daily volume on those days at an average price
of $4.04 per share. On the evening of 6 December 2010, the US Treasury sold
The current issue and full text archive of this journal is available at
www.emeraldinsight.com/1757-6385.htm
JEL classi?cation – G01, G13, G21, G28, G32
This is not investment advice. The author makes no warranties about the data or estimates in
this paper. The author was not compensated by any ?rm, trade association, or the federal
government to do this analysis.
Stock demand
curves and
TARP returns
229
Journal of Financial Economic Policy
Vol. 3 No. 3, 2011
pp. 229-242
qEmerald Group Publishing Limited
1757-6385
DOI 10.1108/17576381111152218
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the remainder of their stake in an underwritten secondary offering, which raised
$10.5 billion (Smith et al., 2010).
Such large and widely disclosed share sales are unprecedented. The US Treasury
primarily bought preferred stock from bailed-out banks as part of the Troubled Asset
Relief Program (TARP). At the time of writing, this was the only instance where the
US Treasury has sold its common shares to private investors in at-the-market trades.
Following the advice of Verret (2010), the US Treasury delegated its sales to its
selling agent according to a preset trading plan[1]. Policy makers and investors would
no doubt be interested in whether those sales are driving the price of Citigroup’s stock.
Further, these share sales give us a new natural experiment to test whether the demand
curve for stocks slopes downward. Further, the commencement of these sales coincided
with a negative one-day return that was weakly signi?cant, assuming the stock returns
adhered to a geometric Brownian motion model. The conclusion of these sales was also
followed immediately by a positive abnormal return. These returns are consistent with
a mild version of the price pressure hypothesis (PPH) ?rst advanced by Scholes (1972).
Unlike Scholes (1972), who studied the price impacts of underwritten secondary
offerings, we ?nd evidence that the price decline was temporary. Thus, this evidence
indicates that the US Treasury, unlike private sellers in Scholes (1972) and Kraus and
Stoll (1972), was not perceived to be acting on an informational advantage. Thus, these
returns are not consistent with the information hypothesis (IH), which would predict
that large stock sales would have a one-time abnormal decline in the stock price
because the sellers had non-public adverse information about the stock.
The literature exploring whether the price of stocks are subject to the whims of
supply and demand like the markets for goods and services has focused on event
studies on index inclusions and exclusions. Harris and Gurel (1986), Shleifer (1986), Jain
(1987), Dhillon and Johnson (1991), Beneish and Whaley (1996), Lynch and Mendenhall
(1997) and Wurgler and Zhuravskaya (2002) all conclude that stocks added to the S&P
500 stock index earn positive abnormal returns. Biktimirov et al. (2004) ?nd that stocks
listed on the Toronto Stock Exchange, which were dropped from the popular index,
experienced an abnormal decline in value. In addition, Biktimirov et al. (2004) discover
that stocks added to the Russell 2000 small-cap US stock index experience positive
abnormal returns upon inclusion and negative abnormal returns upon exclusion from
the index. These studies generally conclude or assume that there are no announcement
effects in inclusion. Instead, they generally argue that portfolio managers replicating a
particular index have to buy stocks at or close to the inclusion date and sell stocks close
to the exclusion date. Yet, Dennis et al. (2002) argue that there are many more positive
analyst reports released around the time of an S&P 500 index inclusion and many more
negative analyst reports around an index exclusion. Thus, it is not clear that an index
inclusion or exclusion is “information free,” according to Dennis et al. (2002).
Lin and Yung (2006)’s study of Real Estate Investment Trusts (REITS) also casts
doubt on the hypothesis that the demand curve for securities is downward sloping. Lin
and Yung (2006) ?nd that the prices of REITS are not affected by capital ?ows in and
out of REITS. They argue that this favors the argument that the demand curve for
REITS is perfectly elastic or ?at, supporting the substitution hypothesis (SH)
developed by Scholes (1972).
This paper is a part of a growing body of literature in the US Treasury’s
investments into banks under the $700 billion TARP. Many papers have addressed
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the question of whether the capital injections encouraged banks to lend. Examples of
this literature are Bebchuk and Goldstein (2009), Philippon and Schnabl (2009), Wilson
(2009), Taliaferro (2009), Li (2010) and Wilson and Wu (2010). Many studies have
addressed which banks receive or accept capital injections such as Bayazitova and
Shivdasani (2009), Duchin and Sosyura (2009), Taliaferro (2009), Cadman et al. (2010),
Li (2010), Jordan et al. (2010) and Ng et al. (2010). In contrast to the TARP entry
literature, Wilson and Wu (2011) look at the characteristics of the banks that exit the
program early. Veronesi and Zingales (2010) and Kim and Stock (2010) conduct event
studies testing the securities returns surrounding the ?rst capital injections. Kim (2010)
measures the stock returns before and after the announcement of new executive
compensation restrictions on TARP recipients. Wilson (2010) discusses the tight
deadlines that the US Treasury has for its Citigroup share sale, and simulates the US
Treasury’s chances of success. Unlike Wilson (2010), which is a forward looking
assessment of the wisdom of the at-the-market sales, the present study looks at how the
share sales affect the short-term returns of Citigroup’s stock price before, during, and
after the US Treasury’s selling period. The present study ?nds a signi?cant negative
abnormal decline in the stock price at the start of the selling period and a signi?cant
abnormal rise in the stock price right after the end of the selling period.
In Section 2, we discuss two competing hypotheses of the effect on the share price of
large sales. In Section 3, we introduce the Brownian motion model and use it to test if
the stock returns experienced around these share sales can be considered abnormal.
In Section 4, we conclude our discussion.
2. Competing hypotheses
Scholes’s (1972) analysis of block trades kicked off a long line of literature attempting
to determine if the demand curve for stocks is perfectly elastic. That study identi?ed
competing views. The ?rst hypothesis is the SH. The SH says that regardless the size
of the block of shares being sold at any given moment or on any given day, the price
that it will trade is the fundamental value of the stock at any given moment. Thus,
rational traders have an in?nite demand for the stock at a price at or below its
fundamental value. At the other extreme, the PPH says that, when you increase the
supply of the stock at any given time, you push down its price. These are different
views about the nature of the demand curve for stocks are shown in Figure 1.
In panel A, the demand curve is ?at, signifying that investors will buy as many as
all the shares outstanding at any given moment. In contrast to the SH, the PPH says
that the demand for the security slopes down. Thus, a shift in supply, in panel B,
Figure 1.
Competing theories of
large share sales
D
D
S(1)
S(2)
S(1)
S(2)
P(1) = P(2)
P(1)
P(2)
Q(1) Q(2)
Price
Panel A: Substitution
Hypothesis (SH)
Panel B: Price Pressure
Hypothesis (PPH)
Price
Quantity Quantity
Q(1) Q(2)
Stock demand
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causes a fall in the price of the stock. The US Treasury’s share sale offers a good
natural experiment to test which view is correct.
The SH can be de?ned as the following:
1. Substitution hypothesis
H
0.
The share price is unaffected by announcement, initiation, pauses, or cessation
of the share purchases.
H
1.
There are signi?cant abnormal share price returns at the announcement,
initiation, pauses, and/or cessation of the share purchases.
Departing from Scholes’s (1972) classi?cations somewhat. There are really two forms
of the PPH, the extreme and mild form, which are de?ned below:
2a. Extreme PPH
H
0.
The stock will drop abnormally every day of share sales and will rise
abnormally at each pause of share sales.
H
1.
The stock does not drop abnormally for each day of share sales or it does not
rise abnormally during share sale pauses.
2b. Mild PPH
H
0.
The stock price will drop at the announcement and initiation of the share sales
and it will rise at the announcement and act of their cessation.
H
1.
The stock price will not drop at the announcement and initiation of the share
sales or it will not rise at the announcement and act of their cessation.
The initiation of the Citigroup share sale was announced on 26 April 2010, and it began
that day. The cessation of share sales was announced after trading halted on
6 December 2010, and share sales ceased that night with an after-hours underwritten
secondary offering of 2.42 billion shares, which was the remainder of the US
Treasury’s stake.
Scholes (1972) introduces a third hypothesis, the IH. This hypothesis says that
sellers of large numbers of shares have better information about adverse events than
other market participants. The US Treasury delegated the sales and very publicly
disclosed their sales to help dispute the fact that they had adverse information about
the Citigroup stock. Nevertheless, market participants may not have been convinced by
these efforts.
The IH’s prediction is summarized in the null and alternative hypothesis below:
3. Information hypothesis
H
0
. There will be a drop in the stock price at the announcement of the sale, and the
share price will not rise abnormally after the cessation of share sales.
H
1
. There is no drop in the stock price at the announcement of the sale or the drop
is temporary and the stock price rises after the cessation of stock sales.
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3. Price movements
We established in the previous section that the supply of shares sold increased
signi?cantly during the US Treasury’s selling period. Yet, did this increase in supply
lead to signi?cantly lower share prices? We use the geometric Brownian motion model
to test the hypotheses developed in Section 2. The analysis here ?nds that the only
signi?cant drop in the share price occurred at the start of share sales. Further, this drop
was temporary and was mostly reversed by an abnormal rise at the share sale’s
conclusion.
The geometric Brownian motion model of the stock price predicts that the stock
moves with a random walk plus a drift. The drift component, r, for the stock is its
expected return or cost of capital. The random walk is determined by the stock’s
volatility, s, or standard deviation and the random draw, 1. Let dt stand for a small
interval of time, t. In that case, the stock price evolves according to the following
differential equation:
dt ¼ rSdt þsS1
????
dt
p
ð1Þ
If the value of the stock at any given time is S(t), then the initial value of the stock is
S(0). The terminal value of the stock is S(T), where T is the time to that date in years.
In the Appendix, it is shown that the exact formula for the terminal value of the stock is
the following:
SðTÞ ¼ Sð0Þexp r 2
s
2
2
T þs1
????
T
p
ð2Þ
For our purposes, we want to invert this equation so that we can ?nd the likelihood of a
particular stock price realization, 1:
1 ¼
lnðSðTÞ=Sð0ÞÞ 2ðr 2ðs
2
=2ÞÞT
s
????
T
p ð3Þ
1 is the Z score in a standard normal distribution. The higher the absolute value of 1,
the more abnormal is the return. If 1 . 0, then the return is unexpectedly positive, and,
if 1 , 0, then the return is unexpectedly low. The two-tailed signi?cance level implied
by the error in equation (3) is 2
*
min{Nð1Þ; ð1 2Nð1ÞÞ}, where N() denotes the
standard normal distribution.
All the inputs on the right-hand side of equation (3) can be observed or easily
estimated. Time in years is measured by dividing the number of trading days that pass
by 252, the typical number of trading days in a given year. The stock prices can be
taken from a variety of sources. Here, we use closing stock prices from Yahoo! Finance.
The volatility of the stock is estimated from the vega-weighted average of Black and
Scholes (1973) implied volatilities of Citigroup’s options. These implied volatilities and
vegas were obtained from IVolatility.com. The implied volatilities used were from
options traded at time 0 with expiration dates just before time T and just after time T.
Vega is the marginal sensitivity of an option’s price to a change in the expected
volatility of the stock. This weighting favors heavily traded options that have exercise
prices close to the current stock prices. Simple averages produced very similar implied
volatility estimates. The expected return on the stock is estimated according to the
market model of Sharpe (1964) and Lintner (1965). Wilson (2010) estimated the capital
Stock demand
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asset pricing model beta of the Citigroup stock just prior to the start of the US
Treasury’s share sale at 2.771.
The expected log return is:
r ¼ lnð1 þEðR
T
ÞÞ; where EðR
T
Þ ¼ r
f
þ2:771
*
{RðSPY; TÞ 2r
f
}: ð4Þ
r
f
is the risk-free rate or the return on T-bills over that time horizon. For the time
periods studied, the 28- and 91-day T-bill rates were between 0.14 and 0.16 percent. Yet,
over time horizons of 1-48, days r
f
was equal to 0.00-0.02 percent. SPY is the
exchange-traded fund that attempts to replicate the returns of the S&P 500. We use the
SPY security returns as a proxy for the returns on the market as a whole. R(SPY, T) is
the expected arithmetic return over the period de?ned as the difference in the
beginning, SPY
0
, and ending, SPY
T
, prices over the period and the sum of any
dividends paid over that interval, DIV:
RðSPY; TÞ ¼
SPY
T
2SPY
0
þDIV
SPY
0
ð5Þ
In Figure 2, we plot the timeline of the US Treasury’s share sales. On average, the US
Treasury made up 7.0 percent of the trading volume over the selling periods. Using
monthly disclosures of the US Treasury, the government’s share sales ranged from
6.8 to 9.7 percent of the average number of shares sold per day.
Figure 2.
US Treasury’s cumulative
share sales and a
percentage of average
trading volume
Billions of shares sold, or percent of average share volume
Total shares sold
Date
% of average volume
0
2
4
6
8
10
4
/
2
6
/
1
0
5
/
2
6
/
1
0
6
/
2
6
/
1
0
7
/
2
6
/
1
0
8
/
2
6
/
1
0
9
/
2
6
/
1
0
1
0
/
2
6
/
1
0
1
1
/
2
6
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1
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Notes: From 26 April 2010 to 6 December 2010, the US Treasury sold
shares of Citigroup at market prices through its broker Morgan Stanley
in a series of four preset trading plans; the US Treasury disclosed the
progress of their sales though press releases, SEC filings, and monthly
reports on the TARP; share volumes are obtained from Yahoo! Finance;
in total, the US Treasury sold 5.27 billion shares by this method; on
7 December, the US Treasury sold 2.42 billion shares using an
underwritten secondary offering for $4.35 per share; the mostly flat line
is the percent of average trading volume that the US Treasury’s share sales
represented; the upward sloping line is the total number of at-the-market
sales by the US Treasury in billions; there were two periods just prior to
earnings announcements where share sales were halted; those periods were
1-22 July 2010, and 1-18 October
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There were “blackout periods,” days before and after earnings announcements where
the US Treasury promised not to sell shares. These blackout periods were
pre-announced. The blackout periods, or selling pauses, were from 1 to 22 July 2010,
around second quarter earnings and 1-18 October 2010, for third quarter earnings.
There is only information on the progress of the US Treasury’s sales on a roughly
monthly basis. Thus, the percent of average volumes are ?at until a new disclosure at
the end of the month, the end of a preset trading plan, or the start of an earnings
blackout period. The upward sloping line is the number of shares sold. This line is ?at
during the pauses around earnings. On 6 December 2010, the US Treasury sold the
remainder of its stake 2.42 billion shares overnight by means of an underwritten
secondary offering at a price of $4.35 per share or at about a 2.2 percent discount from
the previous day’s closing price (Smith et al., 2010).
In Table I, we have examined 14 different time horizons where we would suspect
that Citgroup’s stock price may have signi?cant excess returns.
In the ?rst test, Table I, we have the closing stock price on 23 April 2010, just prior
to the announcement of the details of the dribble-out sale plan and its beginning
and the closing stock price on the day of the announcement on Monday, 26 April
2010. That was the only period that had signi?cant negative returns. Since investors
expected the share sales to commence as early as 16 March 2010, the announcement
may have surprised some investors about the US Treasury’s lack of progress[2]. That
close-to-close return was abnormally negative with greater than 90 percent con?dence.
Thus, it appears that the announcement of the ?rst trading plan on 26 April 2010, was
badly received by investors.
Interestingly, the stock return, test 13, at the announcement of and the completion of
the US Treasury’s share sales from 6 to 7 December 2010, was also signi?cantly
positive with greater than 90 percent con?dence. These two returns, tests 1 and 13,
are consistent with the mild PPH (MPPH). Since the MPPH is inconsistent with the SH,
we can reject that latter theory with 90 percent con?dence. Moreover, since the drop in
the share price from 23 to 26 April 2010, was not permanent and was reversed at the
end of share sales, we can discard the IH.
There is little support for the extreme PPH (EPPH). That hypothesis would predict
abnormal price declines whenever the US Treasury sold its stake. That hypothesis
would predict negative abnormal returns for the tests 1, 2, 5, 6, 7, 10, 11, and 12.
Yet, only test 1 has an abnormally negative return on the day the sale was begun. The
EPPH would predict that there would be positive returns for tests 3, 4, 8, 9, 13, and 14.
Yet, only test 8, at the start of the third quarter earnings selling pause, and test 13 at the
completion of the share sale experienced positive abnormal returns.
Interestingly, both these positive excess returns also coincided with unexpected
underwritten offerings of the US Treasury’s stakes in Citigroup. On 30 September
2010, Citigroup repurchased the US Treasury’s $2.2 billion of trust preferred shares
obtained from a then-cancelled $301 billion asset guarantee. Citigroup re?nanced the
US Treasury’s preferred stake by selling similar shares to private investors
(Thiruvengadam and Rieker, 2010). On 6 December 2010, after trading hours, the US
Treasury sold 2.42 billion shares in an underwritten secondary offering[3]. One
interpretation is that investors cheered faster than expected sales of the US Treasury’s
stake. Part of the disappointment of investors on 26 April 2010, in test 1, may have
Stock demand
curves and
TARP returns
235
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Geometric Brownian
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been that investors expected a faster means to exit the Citigroup stake than the US
Treasury’s plan to sell just a small fraction of the stake every day.
4. Conclusion
The US Treasury’s share sales made up about 7 percent of the daily volume of
Citigroup’s shares traded from26 April to 6 December 2010, with two pauses around Q2
and Q3 2010 earnings announcements. This paper used a geometric Brownian motion
model to test for abnormal price reactions to the US Treasury’s at-the-market sales.
This study ?nds that the US Treasury’s share sales led to abnormally negative returns
in the Citigroup share price on the ?rst day of the at-the-market share sale. Moreover,
the share price rose signi?cantly the day after the close of share sales, 7 December 2010.
This evidence is consistent with the theory that the slope of the demand curve for
Citigroup’s stock slopes downward in the short term, but any declines due to large
share sales are transitory. This evidence is consistent with the mild form of the PPH.
We can reject the hypothesis that investors believed that the US Treasury sold out of
superior information because most of the price decline was reversed after the share
sales ended. Moreover, we can reject the SH because there appeared to be abnormal
price reactions at the beginning and the ends of Citgroup share sale. The initial price
decline was 5.1 percent when the sale began and 3.8 percent when the sale ended. Yet,
there is no evidence that the share sales led to negative abnormal price reactions during
selling periods besides the ?rst day. Thus, more extreme forms of the PPH, which
would expect abnormal returns during the whole selling period, cannot be supported.
An underwritten secondary offering of shares typically is sold at a 2-3 percent
discount of the prevailing price, according to Dunbar et al. (2004). Taxpayers accepted
a 2.2 percent discount from the closing price when the balance of the Citigroup stake
was sold on the evening of 6 December 2010. Thus, it seems that this slow
privatization’s 5 percent initial price drop was worse than what could have been
expected, had most of the stake been sold on 26 April 2010, by an underwritten
secondary offering of the shares. Moreover, the average share price of the at-the-market
sales of the 5.27 billion shares was $4.04. The closing price on 23 April 2010 was $4.86.
Even with a three percent discount, taxpayers likely could have sold most of their stake
for $4.71 per share. With the bene?t of hindsight, taxpayers could have generated
$3.53 billion more, before underwriting fees, if those 5.27 billion shares had been sold in
an underwritten secondary offering on 26 April 2010.
The US Treasury sold a large portion of its stake in a November 2010 initial public
offering (IPO) of General Motors after it emerged from bankruptcy. Yet, taxpayers
retain a 33 percent stake or about 0.5 billion shares in General Motors at the time of
writing. The US Treasury will be able to begin selling these shares in May 2010
( Jones, 2010; Mitchell, 2010). The evidence from the Citigroup share sale indicates that
the negative price reaction from a slow at-the-market sale may be larger than an
underwritten secondary offering. Nevertheless, the US Treasury is likely to favor a slow
at-the-market sale because such a sale gives the GM shares a greater chance of edging
closer to the US Treasury’s politically important breakeven price of over $50 per share.
The GM shares were trading at between $33 and $35 per share at the time of writing.
According to US Treasury (2010), taxpayers will have a 93 percent stake in
American International Group which will receive nearly $70 billion from the TARP in
addition to many billions more from Federal Reserve loans. Moreover, taxpayers have
Stock demand
curves and
TARP returns
237
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a 56 percent common stock stake in the privately held Ally Financial (formerly GMAC),
which received $17 billion from the TARP. Finally, taxpayers retain a 9.9 percent
common stock stake in Chrysler Motors, which has emerged from bankruptcy and is
currently privately held. The lessons from this paper may help policy makers better
choose between:
.
selling more of their shares in the IPO and/or underwritten secondary offerings;
and
.
attempting lengthy at-the-market sales as were conducted in the case of
Citigroup.
The lesson of Citigroup is that a gradual exit leads to a price drop comparable or
greater than large underwritten secondary offerings. This evidence should cause
conscientious policy makers to reconsider the wisdom of slow dribble out sales similar
to the 2010 Citigroup share sale.
Notes
1. Verret (2010) worries about the government using inside information in its dispositions of
assets. Yet, The Assistant US Treasury Secretary for Financial Stability Herb Allison
testi?ed before the Congressional Oversight Panel hearing on Citigroup on 4 March 2010,
saying that US Treasury of?cials in charge of Citigroup share sales only looked at publically
available information.
To assuage fears that the US Treasury may use access to non-public information, the US
Treasury delegated its sales to a third party, Morgan Stanley. The selling instructions were
not disclosed, but the number of shares available to be sold and the duration of the selling
periods were disclosed. See the 8-K and prospectus’ ?led on 26 April 2010, available at
web sites: www.sec.gov/Archives/edgar/data/831001/000114420410022189/v182217_8k.htm
and www.sec.gov/Archives/edgar/data/831001/000095012310037908/y83942e424b2.htm.
The US Treasury disclosed its sales in monthly reports and at the beginning and end of
each of four different selling periods, which authorized Morgan Stanley and its af?liated
brokers to sell up to 1.5 billion shares.
2. See Exhibit 99.1 of the SEC form 8-K dated 14 December 2009, accessed online on 12 July
2010 at: www.sec.gov/Archives/edgar/data/831001/000095012309070361/y80976exv99w1.
htm and Citigroup, “Press Release: Citi Prices $17 Billion Common Stock Offering and
$3.5 Billion of Tangible Equity Units, Prices Largest US Public Equity Offering in History,
Citi to Repay $20 Billion of TARP Trust Preferred Securities, Terminate Loss-Sharing
Agreement, US Treasury Extends Lock-Up to 90 Days,” 16 December 2009, exhibit 99.1 in
SEC form 8-K dated 17 December 2009, accessed online on 12 July 2010 at: www.sec.gov/
Archives/edgar/data/831001/000095012309071395/y81063exv99w1.htm.
On 29 March 2010, the treasury disclosed their intention to use a prearranged trading plan
( Jacobs, 2010; Lawder and Eder, 2010).
3. The US Treasury had promised a year earlier to exit it stake in Citigroup by 14 December
2010. Yet, it backed away from the commitment in the fall of 2010 (Guerra, 2010; Miller, 2010;
Wilson, 2010).
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Appendix. Derivation of S(T)
To solve for the terminal value of the stock following a geometric Brownian motion path, we
must transform equation (1), using Ito’s Lemma ?rst developed in Ito (1951). Hull (2003, pp. 226-8,
232-3, 410-13) also has a good discussion of the derivation below. First, we need to ?nd the
change in the log stock return, dln S. Ito’s Lemma says the function f¼f(S, t). Can be expanded
using a Taylor expansion:
df ¼ d ln S ¼
df
dS
dS þ
df
dt
dt þ
1
2
d
2
f
dS
2
dS
2
þ
d
2
f
dSdt
dSdt þ
1
2
d
2
f
dt
2
dt
2
. . . ðA1Þ
We will solve for equation (A1) in pieces. Some of the partial derivatives of f¼f(S, t) are as
follows:
df
dS
¼
1
S
;
d
2
f
dS
2
¼ 2
1
S
2
;
df
dt
¼ 0: ðA2Þ
Squaring equation (1):
dS
2
¼ m
2
S
2
dt
2
þ2smS
2
dt
????
dt
p
þs
2
S
2
dt ¼ s
2
S
2
dt; when dt !0: ðA3Þ
The ?rst and second terms on the right-hand side of equation (A3) are zero because dt
y
¼0, when
both y . 1, and dt ! 0. For this same reason, the dt
2
term in equation (A1) is also zero in this
case. It is also clear that the dSdt term below is zero for the same reason:
dSdt ¼ rSdt
2
þsS1dt
????
dt
p
¼ 0; when dt !0: ðA4Þ
The higher order terms in equation (A1) are also eliminated because the dt is taken to a power
y . 1. Inserting equations (1), (A2), (A3), and (A4) into equation (A1), the differential equation
simpli?es to:
df ¼ d ln S ¼ r 2
s
2
2
dt þs1
????
dt
p
: ðA5Þ
Stock demand
curves and
TARP returns
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Equation (A5) can be rewritten:
ln Sðt þdtÞ 2ln SðtÞ ¼ r 2
s
2
2
dt þs1
????
dt
p
: ðA6Þ
If we add ln S(t) to both sides of equation (A6) and take the exponential of both sides, we obtain
the following expression:
Sðt þdtÞ ¼ SðtÞexp r 2
s
2
2
dt þs1
????
dt
p
ðA7Þ
When t¼0 and dt¼T, then equation (A7) is identical to equation (2). This is what we wanted to
derive.
About the author
Linus Wilson is an Assistant Professor of Finance at the University of Louisiana at Lafayette,
and is the Charles and Vicky Milam Board of Regents Support Fund Professor of Business
Administration there. He received his Doctor of Philosophy in Financial Economics at Oxford
University in England. He has written over 30 academic papers on bank privatizations,
bankruptcy, CEO pay, entrepreneurship, market entry decisions, Ponzi schemes, stock warrants,
government plans to buy toxic assets, and bank recapitalization programs. He has written over
a dozen academic papers on the Troubled Asset Relief Program (TARP). Dr Wilson has been
a source for hundreds of news stories on the bank rescues in news outlets such as the Wall Street
Journal, the NewYork Times, Bloomberg BusinessWeek, and National Public Radio. Linus Wilson
can be contacted at: [email protected]
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