DOI: 10.5817/FAI2015-2-2 No. 2/2015
21
Cross Sectional Analysis of Short Sale
Determinants on U.S. Blue Chips
Dagmar Linnertová
Masaryk University
Faculty of Economics and Administration, Department of Finance
Lipová 41, 602 00 Brno, Czech Republic
E-mail: Dagmar.Linnertova@mail.muni.cz
Abstract: Short sale is a market practice that allows participle in overpricing
markets. The fundamental goal of short sale is to sell borrowed securities,
repurchase them back after their prices decrease and then return them to a
lender. The aim of this paper is to investigate determinants of the short sale
(measured by short sale ratio or SIR) activity. Based on the previous studies the
short sale determinants are represented by market specific variables and
fundamental-to-price ratios and correspond with hypotheses that explain investor
motivations of going short. A panel regression with fixed effect is applied to
determine these variables. The trend of short sale is analyzed by splitting the full
sample period in three sub periods. There are identified factors such as abnormal
rate of return, volume of trade, volatility, market capitalization and beta
coefficient that are stable long term and influence the level of short sale. The
results of fundamentals-to price ratio is not unambiguous and these variables do
not considerably influence the level of short sale.
Keywords: short sale, determinants, panel regression, S&P 500, hypotheses of
going short
JEL codes: G10, G14
Introduction
The short sale is a market mechanism that allows the potential to capitalize
overpricing of securities or to participate in a decreasing market. A short sale is a
sale of a stock that a subject does not own in the time of a transaction, but has
borrowed it from a lender that may be represented by a large institutional
investor, brokerage house or a broker-dealer. A short seller opens his position by
selling borrowed securities and closes his position by purchasing securities back
and returning them to a lender. The whole transaction is backed by collateral. The
mechanism of short selling is demonstrated in Figure 1. The first part of Figure 1
represents the process of shorting, while the second part notes the closing of a
position.
Financial Assets and Investing
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Figure 1 Short Sale Mechanism
Source: Author’
s
The profit-loss profile of a short seller is described in Figure 2. The maximum gain
of the short seller is the sale price (S0) of the stock at the time t = 0 if the stock
price falls at zero at the time t = 1. The loss is unlimited if the stock price rises.
The transaction costs are not taken into account in this scheme. The standard
stock-lending practice is that the loan must be repaid on the demand. The specific
risk calling a short squeeze emerges because of this practice. While term basis
loans exist, they are more expensive and rare.
Figure 2 Profit and Loss Profile of a Short Seller
Source: Author's
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Because of the high risk associated with short selling it is also an activity that is
heavily regulated. In the U.S. short sale was made more difficult because of the
adoption of so called tge uptick rule that went into effect in 1938 and was
removed in 2007. In 2009, the reintroduction of the uptick rule was widely
debated, and proposals for a form of its reintroduction by the SEC. A modified
form of the rule was adopted in 2010.
1 Related Literature on Short Interest
The motivations of the investor for short selling are summarized in four
hypotheses. Trend Hypothesis (1) (also known as Following the Trend
Hypothesis) states that short sellers close their positions if the stock prices have
been increasing in the past short term. Jagadeesh & Titman (1993) demonstrate
that the stocks with high (low) rate of returns at the horizon from 3 to 12 months
are repeating this high (low) rate of return at the horizon of next 3 to 12 months.
The overpricing hypothesis (2) expects that investors have inside information and
if they expect that the stock is overpriced the short selling is a way to capitalize
it. Diamond and Verreichia (1987) point out that short sale is an expensive
transaction and short sellers trade only if they expect that the price will
significantly decrease as compensation for this cost and risk. Dechow et al.
(2001) emphasize the relationship between the low fundamental factors and the
level of short selling. The arbitrage hypothesis (3) argues that short sellers
participate in overpricing between a stock and convertible security. High
correlation between an instrument and instrument that is going short is
demanded. And the taxation hypothesis (4) has only limited impact on short
interest nowadays because of elimination of the opportunity to defer capital gain
tax by shorting the investor’s securities. (Arnold et al., 2005)
The aim of this paper is to analyze short sale determinants in the period 2000–
2014 and particular sub periods. Based on previous literature reviews the
determinants of short sale are represented by two categories – market specific
and fundamentals-to-price. The analyzed periods reflect different economical and
financial conditions. The period 2000–2006 is the term of economic growth that
came out with the bankrupcy of Lehman Brothers. The first years of the 2000s
were weak because of uncertainty following the September 2001 crisis and fraud
cases of corporation but the economy of the U.S. improved during 2003 and was
generally stable till the end of this sub period. The interval 2007–2009
represents financial market uncertainty, a real estate bubble and the epoch of a
sub-prime crisis that passed into to world financial crisis. The last period 2010–
2014 represents the first years of the world economy recovery.
Financial Assets and Investing
24
Brent et al. (1990) analyzed the motivation for short selling based on the three
above-mentioned hypotheses. They found that short interest follows a seasonal
pattern that is weakly consistent with the tax hypothesis. Further stocks with high
betas and the existence of convertible securities or options tend to have a higher
level of short interest. This supports the arbitrage motivation for short sale. The
list of analyzed determinants is summarized in Table 1.
Table 1 Short Selling Determinants Analyzed by Brent et al.
Analyzed determinant
Expected impact
on short sale interest
Motivation /
Hypothesis
Average market value of
shares during year proxy
for firm size
Unknown Transactions costs
Average coefficient of
variation of analyst
forecast of the next
annual earnings during
year
Unknown Speculation
Systematic risk (beta) Positive
Arbitrage and hedging
hypothesis
Prior year’s average
monthly return
Unknown Speculation
Dummy for convertible
security existence
Positive
Arbitrage and hedging
hypothesis
Dummy for option
existence
Positive if arbitrage
reasons or negative if
substitute to short sale
Arbitrage or Speculation
Source: Author’s summary of Brent et al. (1990)
Dechow et al. (2001) document that short sellers open positions in stock of firms
with low ratios of fundamentals (like earnings or book value) to market value and
close their positions at the ratios mean-revert. They also point out the importance
of transactions costs in the decision making process of short sellers. Angel et al.
(2003) examine the frequency of short selling in stocks listed in NASDAQ and
analyzed stock characteristics. They get that short sale is more common among
stocks with high returns than stocks with weaker performance and further
actively traded stocks are more shorted. Short selling also depends directly and
positively on stock price volatility. Desai et al. (2002) examines the relationship
between the level of short interest and stock return on the NASDAQ. They find
out that heavily shorted stocks experience significant negative abnormal returns
with respect to the market, size, book-to-market and momentum factors. The
higher level of short interest is a stronger bearish signal. Kot (2007) finds that
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short-selling activity is positively related to arbitrage opportunities and hedging
demand, and negatively related to previous short-term returns.
Based on previous studies the characteristics affecting the level of short sale
measured by short interest ratio in the period 2000–2014 are summarized in
Table 2.
Table 2 Variable Characteristics
Variable Abbrev. Definition
Expected
effect
Motivation
Short interest
ratio SIR
Average number of
days for closing all
open short sale
positions
- -
Market
Capitalization
(logarithm)
LOGCAP
Proxy for company
size. Dollar market
value of all shares
outstanding.
Positive/
Negative
Transactions
costs/
Overpricing
hypothesis
Volume of
trade
(logarithm)
LOGVOLUME
The total quantity of
shares bought and
sold during a
particular period.
Positive/
Negative
Transactions
costs/
Overpricing
hypothesis
Volatility VOL
A measure of the risk
of price moves for
security calculated
from the standard
deviation
Positive
Overpricing
hypothesis
Beta
coefficient BETA The systematic risk Positive
Arbitrage and
Hedging
Hypothesis
Price-to-BookValue
PBV
A ratio used to
compare a stock's
market value to its
book value.
Low value might
indicate
undervaluation
of a stock.
Negative
Overpricing
hypothesis
Price-toEarnings
PE
A valuation ratio of a
company's current
share price compared
to its per-share
earnings.
Negative
Overpricing
hypothesis
Price-to-Sales PS
A valuation ratio that
compares a
company’s stock price
to its revenues.
Negative
Overpricing
hypothesis
Financial Assets and Investing
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Variable Abbrev. Definition
Expected
effect
Motivation
Price-to-FreeCash-Flow
PFCF
A valuation metric
that compares a
company's market
price to its level of
annual free cash flow.
Negative
Overpricing
hypothesis
Abnormal rate
of return AB
A measure of the
difference between
the return on the
stock and the risk free
security represented
by T-Bonds
Negative
Overpricing
hypothesis
Dividend yield YIELD
A financial ratio that
shows how much a
company pays out in
dividends each year
relative to its share
price
Negative
Overpricing
hypothesis
Source: Author’s
Short interest ratio is defined as the short interest (number of stocks shorted)
divided by the average daily trading volume. It represents the dependant variable
in the panel.
Volume of trade indicates that short sellers prefer stocks with larger trading
volumes that are more liquid. Volume of trade is measured as a monthly traded
average number of securities. The expected impact of the volume of trade on
short interest ratio is positive and it is based on problems with transactions costs.
On the other hand advocates of overpricing hypothesis expected negative impact
because less liquid stocks are more likely overpriced.
Market capitalization is included in the analyses because smaller firms are
associated with more overreaction and smaller market capitalization firms may be
more sensitive to mispricing because they have a smaller investor following Cox &
Peterson (1994). If transactions costs are taken into account firms with large
market capitalization are cheaper for short selling because their liquidity. Thus
the effect of market capitalization on short interest may be positive.
Abnormal return as one analyzed determinant corresponds with the findings of
Angel et al. (2003) that short sellers choose a stock of firms that have
experienced significant price run-ups. This is due to the fact that the investor
expects a potential correction in response to the market’s previous overreaction.
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Beta coefficient measures the systematic risk, McDonald and Baron (1973)
suggest that short interest is positively correlated with beta. That is an
assumption of a successful arbitrage or hedging activity.
Volatility as a short sale determinant corresponding with the overpricing
hypothesis and suggests that more volatile stocks may be a subject of mispricing,
Richards (1997). This also matches the findings of Angel et al. (2003) about
targeting more volatile stocks for short selling.
Dividends make short sale more expensive because all dividend payments must
be redistributed to a lender. Thus, short sellers may avoid stocks with higher
dividend yield.
The fundamentals-to-price ratios are represented by Price-To-Earnings, Priceto-Book
Value, Price-to-Free Cash Flow and Price-to Sales. According to Dechow
(2001) statistically significant concentration of short positions in firms with low
fundamentals-to-price ratios exists, but not all stocks with low fundamentals-toprice
ratios are heavily shorted. The reasons are transactions costs and existence
of additional information that a stock is not overprices.
The trend in short sale activity is investigated splitting up the examined period
into three sub periods.
2 Methodology and Data
The cross-sectional panel regression is carried out for 502 stock representing
Standard and Poor’s 500 Index in the period 2000–2014. The data was gathered
from the Bloomberg and the analysis is based on 73,752 monthly observations.
The development of short selling activity measures by short interest ratio
(statistical mean) is documented in the Figure 3. The full dataset is spit into three
sub periods representing different economics conditions for the comparison of
short sale determinants. Particular sub periods are following:
• Sub period 2000–2006 or pre crisis period
• Sub period 2007–2009 or crisis period
• Sub period 2010–2014 or post crisis period or period or the recovery
For the period 2000–2014 the highest level of SIR was 6 day and the lowest was
2.5 days on the average. In the sub period 2000–2006 the short sale reached its
peak in 2004 with SIR 5.5 days at the same period the minimum SIR was
represented by 3.5 day in 2001. In the crisis period (2007–2009) the SIR was
more volatile and it reached minimum of 2.5 days in 2007. In the subsequent
period SIR has been increasing toward a new maximum of 6 days in 2014.
Financial Assets and Investing
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Figure 3 Short Interest Ratio (SIR) in the period 2000–2014
Source: Author in Eviews
The summary statistics for the whole sample and sub periods is set in the Table 4
and Figure 4, respectively. The average SIR for analyzed period is 3.91 days. The
level of short sale was above average in the period 2000–2006 and lower in the
crisis and after the crisis period. But in the after crisis period some form of a
recovery could be identified.
Table 4 Sample statistics
Variable
Full
sample
2000–2006 2007–2009 2010–2014
Short interest ratio
3.91
(2.99)
4.25
(3.36)
3.57
(2.69)
3.74
(2.79)
Abnormal rate
of return
-0.02
(-0.02)
-0.03
(-0.03)
-0.04
(-0.03)
-0.01
(-0.01)
Beta coefficient
1.05
(0.98)
0.98
(0.86)
1.09
(1.01)
1.12
(1.04)
Market capitalization
(logarithm)
9.34
(9.25)
9.05
(8.99)
9.32
(9.19)
9.65
(9.50)
Volume of trade
(logarithm)
16.98
(16.92)
17.23
(17.19)
17.18
(17.13)
16.61
(16.57)
Price-to-Book Value
8.09
(2.69)
6.25
(2.91)
5.11
(2.44)
11.69
(2.59)
Price-to-Earnings
31.89
(17.97)
31.26
(19.65)
32.75
(16.23)
32.10
(17.25)
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Variable
Full
sample
2000–2006 2007–2009 2010–2014
Price-to-Sales
2.42
(1.61)
2.61
(1.57)
2.11
(1.38)
2.39
(1.74)
Price-to-Free Cash
Flow
95.19
(19.12)
137.89
(21.07)
66.90
(18.06)
137.89
(21.07)
Dividend yield
1.90
(1.26)
1.63
(1.05)
2.43
(1.36)
1.63
(1.05)
The numbers in the brackets are the medians.
Source: Author in Eviews
Figure 4 Volatility, Abnormal Rate of Return, Volume of Trade and SIR
in the period 2000–2014
Source: Author’s in Eviews
In the paper the cross-sectional panel regression is applied. Consider the multiple
linear regression model for individual i = 1,…, N that is observed at several time
period t =1, …., T.
Financial Assets and Investing
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= + ´ + ´ + + (1)
Where yit is the dependent variable, ´ is a K- dimensional row vector of timevarying
explanatory variables and ´ is a M-dimensional row vector of timeinvariant
explanatory variables excluding the constant, is the intercept, is a Kdimensional
column vector of parameters, is a M-dimensional columns of vector
of parameters, is a individual-specific effect and is an idiosyncratic error
term. We assume the balanced panel that each individual i is observed in all time
periods t. There are two basic models for the analysis of panel data, the fixed
effect model and the random effect model. For the fixed effects model, the
individual-specific effect is a random variable that is allowed to be correlated with
the explanatory variables, in the random effects model is random variable
uncorrelated with explanatory variables.
In a fixed effects model an individual-specific intercept is included in the model
(1). In this case, the model is written as
= + ´ + , 					 ~ (0, ) (2)
Where (i = 1, . . ., N) are fixed unknown constants that are estimated along
with , and where is typically assumed to be i.i.d. over individuals and time.
To decide between fixed or random effect the Hausman test was run where null
hypothesis is that the preferred model is random vs. alternative the fixed effects.
The Hausman test statistic is computed as
= − !
,
"#$% & − #$% &'
()
− ! (3)
Where the #*+ denote estimates of the true covariance matrices. Under the null
hypothesis, which implicitly says that plim − !=0, the statistic has an
asymptotic Chi-squared distribution with K degrees of freedom, where K is the
number of elements in	 . Based on Hausman test result the fixed effect model
was chosen for further analysis. As a dependent variable in fixed effect model is
chosen short interest ratio and the explanatory variables are represented by a
market specific and fundamentals to price variables.
In the Table 5 are set correlation coefficients between variables. The correlation
coefficients are weak thus the effect of multicolinearity might be neglected.
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Table 5 Correlation matrix
SIR AB VOL BETA LOGKAP LOGVOL PBV PE PS PFCF YIELD
SIR 1 0.03 -0.12 -0.05 -0.27 -0.3 0 0.02 -0.01 0.01 0.02
AB 0.03 1 -0.06 0.04 0.01 -0.06 0.01 0.02 0.04 0 -0.04
VOL -0.12 -0.06 1 0.23 -0.24 0.25 0 0.04 0.06 0.01 0.15
BETA -0.05 0.04 0.23 1 -0.04 0.13 0 0.04 0.06 -0.01 -0.04
LOGKAP -0.27 0.01 -0.24 -0.04 1 0.48 0.02 -0.01 0.11 -0.01 -0.01
LOGVOLUME -0.3 -0.06 0.25 0.13 0.48 1 -0.01 0.03 0.08 0 -0.01
PBV 0 0.01 0 0 0.02 -0.01 1 0 0.02 0 0
PE 0.02 0.02 0.04 0.04 -0.01 0.03 0 1 0.2 0.02 -0.02
PS -0.01 0.04 0.06 0.06 0.11 0.08 0.02 0.2 1 0.02 -0.06
PFCF 0.01 0 0.01 -0.01 -0.01 0 0 0.02 0.02 1 0
YIELD 0.02 -0.04 0.15 -0.04 -0.01 -0.01 0 -0.02 -0.06 0 1
Source: Author in Eviews
3 Results
Table 6 and Table 7 provide the results of the fixed effect panel regression model
for the full period and for particular sub periods. The statistical significance
of determinants is stable long-term and also the impact of the determinants in
the level of short interest measures with short interest period is constant.
Table 6 Panel Regression Results – Full Sample
Variable Full Period
Constant 23.4620
Abnormal rate of return 0.3361***
Volatility -0.0181***
Beta coefficient 0.0834***
Market Capitalization (logarithm) -0.8108***
Volume of trade (logarithm) -0.6800***
Price-to-Book-Value 0.0000
Price-to-Earnings 0.0001**
Price-to-Sales 0.0301***
Price-to-Free-Cash-Flow 0.0000
Dividend yield 0.0015
R2
0.3617
Number of observations 73,752
*, ** and *** indicate significance at the 10%, 5% and 1% level, respectively
Source: Author in Eviews
Financial Assets and Investing
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For the full period the factor that positively affected the short interest ratio are
represented by an abnormal rate of return, beta coefficient, Price-to-Earnings
ratio and Price-to-Sales. A negative effect was recorded for volatility, market
capitalization and volume of trade. The strongest positive factor influencing short
interest level is an abnormal rate of return (0.336) and the strongest negative
factors are market capitalization (-0.811) and volume of trade (-0.680).
The power of other significant factors is considerably weaker. Statistical
significance of abnormal return, volume of trade and market capitalization
support the overpricing hypothesis. The negative impact of volatility on short sale
level indicates that investors do not open short position if they cannot anticipate
the future market movement and limited short sale activities with risky stocks.
A positive value of beta coefficient supports the idea about the arbitrage or
hedging. Only two fundamentals-to-price characteristics are statistically
significant but the effect of them on short sale level is against expectation.
The power of these variables to the total short interest ratio is weak.
The coefficient of determination is 36.2 percent.
Table 7 Panel Regression Results – Sub Samples
Variable 2000–2006 2007–2009 2010–2014
Constant 24.8953 28.0434 44.3426
Abnormal rate of return -0.0134 0.7452*** 0.8643***
Volatility -0.0170*** -0.0132*** -0.0216***
Beta coefficient 0.1800*** 0.0767** 0.1440***
Market Capitalization (logarithm) -0.5071*** -0.3854*** -1.2985***
Volume of trade (logarithm) -0.9002*** -1.1901*** -1.6764***
Price-to-Book-Value -0.0003 0.0010* 0.0000
Price-to-Earnings 0.0004** 0.0000 0.0001
Price-to-Sales 0.0135** 0.0440** 0.0597***
Price-to-Free-Cash-Flow 0.0000 -0.0001* 0.0000
Dividend yield -0.1269*** 0.0019 0.0155***
R2
0.4527 0.5721 0.5879
Number of observations 29,987 15,557 28,209
*, ** and *** indicate significance at the 10%, 5% and 1% level, respectively
Source: Author in Eviews
In the pre-crisis period the abnormal rate of return misses statistical significance
and dividend yield becomes negative and significant. The other variables remain
unchanged. The strongest positive factor is a beta coefficient (0.180) and volume
of trade (-0.900) and market capitalization (-0.507) remain the strongest
negative factors. The coefficient of determination is 45.3 percent. In the crisis
No. 2/2015
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period the abnormal returns becomes again statistically significant and positive.
Compare with the previous period Price-to-Book-Value and Price-to-Free-CashFlow
are other fundaments that get statistical significance. On the other hand
only the variable Price-to-Sales has considerable interest. The beta coefficient
during this period falls notably, compared to the previous beta coefficient notably
indicating a decline in influence on the level of short sale. The abnormal rate of
return becomes the strongest positive factor, while the strongest negative factor
stays constant. The power of volume of trade increases and reaches the level of -
1.190. Also in this sub period, the motivation for short sale is confirmed,
summarized in the overpricing hypothesis and the arbitrage and hedging
hypotheses, with also the transactions costs being considered. The coefficient of
determination in this period is 57.2 percent. For the last period the R2
reaches the
maximum of 58.8 percent. The list of market specific variables is still same like in
all previous periods. The powerful positive factors are abnormal rate of return
(0.864) and beta coefficient (0.144). The power of market capitalization and
volume of trade increases and get new maximum of -1.299 and -1.676,
respectively. From the fundamentals variable, only Price-to-Sales is statistically
significant.
Summarized results indicate that variables affecting short sale level are a longterm
stable list of market specific variables. These variables are market specific
and correspond with the overpricing hypothesis, the arbitrage and hedging
hypothesis and support the influence of transactions costs on the level of short
sale. The results of fundamental-to-price variables are mixed. Generally, the
control of these variables to short sale level is weak.
Conclusion
The aim of the paper was to analyze short sale determinants in the period 2000–
2014 on NYSE and in a particular sub period. The short sale was defined as a
risky operation based on selling of borrowed security, aiming to gain from a
market decrease. Since the data structure the fixed effect panel regression model
was applied. The application of panel regression with fixed effect was also
confirmed by the results of the Hausman test. Based on a previous literature
review analyzed determinants were chosen with the respect to four hypotheses of
investor motivations to the short sale. The monitor variables were dividend in two
categories – company fundamentals-to-price ratios and market specific
characteristics.
The results for the full sample confirmed the overpricing hypothesis and arbitrage
and hedging hypothesis behind investors motivation for short sale. Based on
findings transactions costs must be also taken into account. The strongest
Financial Assets and Investing
34
significant positive variables are abnormal are of return and beta coefficient. The
strongest negative variables are represented by market capitalization and volume
of trade. Thus investors prefer stock of small cap companies with lower volume
of trade that noticed abnormal rate of return. More volatile securities are less
popular for the short sale. The correlation between security and market is also
important thus beta coefficient is positively related to the short sale level. These
variables (with exception of abnormal rate of return in pre-crisis period) were
confirmed as statistically significant during all analyzed sub periods. The results
for fundamental-to-price ratios are unambitious. Thus, there exists a group of
variables that is long term stable and has an effect on the level of short interest.
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