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Risk Arbitrage in the Swedish Stock Market
1
Risk Arbitrage in the Swedish Stock Market
The remainder of the paper is organised as follows. In the next section we explain the theory
of risk arbitrage. Previous research is discussed in section III. In section IV we present the data
and method used in our study. Section V includes empirical results and section VI concludes
the results of our study.
II. Theory of Risk Arbitrage
Risk arbitrage should not be mistaken for the classical form of arbitrage, where advantage is
taken of price differences between equivalent securities in different markets. The arbitrageur
buys the equivalent security in one market and sells it simultaneously for a slightly higher
price in another market. This form of arbitrage involves no risk. However, this is not the case
of risk arbitrage, which will be discussed below.
When two companies announce a merger or one company announces a bid for another, a risk
arbitrage opportunity is created. In the case of an acquisition the share price of the target firm
will automatically rise sharply towards the offer price, but a discrepancy generally develops
between the price being offered and the market price. This discrepancy, normally called
”spread”, exists because there is a risk that the offer might be retracted. The spread increases
with the time prevailing until the settlement date1 and the probability of a failed takeover
[Boesky (1985)].
An arbitrageur seeks to take advantage of this situation by locking in the spread. This strategy
is known as risk arbitrage. Provided that the tender offer is successful, the arbitrageur can
secure a profit equal to the spread by using different types of transactions and securities. This
spread is earned no matter what happens to the subsequent share price of the two companies.
In this way the arbitrageur eliminates the market risk related to all securities. The strategy can
therefore be used to reduce the correlation between a portfolio and the market. The only risk
involved in risk arbitrage is that the merger or acquisition may fail. The arbitrageur is
therefore, by speculating on the outcome of the deal, providing liquidity to the market. The
arbitrageur is buying from those who do not want to bear the risk of waiting to see if the
tender offer will be successful. To estimate if the risks involved are worth the return earned
from the spread it is important for the arbitrageur to assess all the factors that will determine
the outcome of the offer. An important factor is the length of time until the settlement date. A
spread of for example 5% says nothing of how profitable the investment is, if there is no time
period to compare with.
A merger or acquisition may fail due to one of the following reasons:





1
The shareholders of the target firm do not accept the terms of the deal
Another company bids higher
The target firm has considerable takeover defences
Conflicts between company boards
Laws and regulations
The date when payment is made for the acquired shares.
2
Risk Arbitrage in the Swedish Stock Market
The positions that the arbitrageur will take depend on the terms of the deal. All positions
taken will be closed at the settlement date or, in the case of failure, at the date of termination.
The most basic form of payment for an acquisition is cash for the stock sought to be
purchased. To lock in the spread, the arbitrageur simply has to take a long position in the
target firm.
For example, in 1998 WM-Data made a cash offer, worth SEK 100 per share, for Caran. After
the announcement, the share price of Caran rose to SEK 97.50, which resulted in a spread of
SEK 2.50 (100-97.50). An arbitrageur could have locked in this spread by taking a long
position in Caran at the announcement date. At the date of settlement, the offer price of SEK
100 would have been received from the acquiring firm, WM-Data. This would have resulted
in a profit equal to the spread of SEK 2.50 or a return of 2.56% during the bidperiod2 of 49
days. The annual return on the investment would have been 18.8%.
If the offer had failed, the arbitrageur would have closed the position, at prevailing market
prices, at the date of termination. This would most likely have resulted in a loss, due to a
decline towards the pre announcement share price. Previous studies have shown that this is the
case provided that no competing bids are announced [Bradley, Desai, and Kim (1982)].
During times when the valuation of the stock market is high, common stock is frequently
issued to undertake an acquisition. Stock exchange offers (hereafter exchange offers)
introduce another element of risk; the risk of a decline in the share price of the acquiring firm.
In order to hedge against this risk and lock in the spread, the arbitrageur must in addition to
taking a long position in the target firm also take a short position in the acquiring firm. This is
illustrated with the following hypothetical example.
Company A with a share price of SEK 105 makes an exchange offer for company B. Suppose
one share of company A is offered for one share of company B and that the post
announcement share price of company B is SEK 100. To lock in the spread of SEK 5, the
arbitrageur takes a long position in company B and a short position in company A. By doing
this the arbitrageur earns the spread of SEK 5, regardless of the share price of company A
after the completion of the deal. This is illustrated in table I.
Table I
Scenarios after the Acquisition
Scenarios after the
Acquisition
Gain/Loss on the
Long Position in B
of SEK 100
Gain/Loss on the
Short Position in
A of SEK 105
Total Gain/Loss
Rise in the share price of
company A to SEK 110
SEK 10
SEK –5
SEK 5
Fall in the share price of
company A to SEK 90
SEK –10
SEK 15
SEK 5
When the offer is a combination of cash and stock, the objective is to lock in the spread on the
part of the deal that may fluctuate. The cash will remain fixed so there is no need to lock in
2
The number of days between the announcement and settlement date.
3
Risk Arbitrage in the Swedish Stock Market
this amount. However, the value of the deal related to shares may change and therefore needs
to be hedged by selling shares short. The strategy used in exchange offers is therefore also
used when payment is a combination of cash and stock. This strategy also applies to mergers,
where the shareholders of both firms receive shares in the new firm according to the exchange
ratio3.
III. Previous Research
The amount of research concerning risk arbitrage is fairly limited. Most of the studies that
have been made are from the merger wave that occurred in the eighties.
Vinberg [1993] studies risk arbitrage in the Swedish stock market during 1987-1992. He
examines whether abnormal returns can be earned against the risk free interest rate and the
market index. Vinberg finds negative abnormal returns against the market index, and reports
insignificant positive abnormal returns against the risk free interest rate. The results further
indicate an average spread of 5% during the sample period. The results reported by Vinberg
are not consistent with empirical evidence from the American stock market. Dukes, Frohlich
and Ma [1992] show that between 1971 and 1985 mean daily returns of 0.47% could have
been earned from risk arbitrage. During the sample period, the mean daily market return was
0.002%. The results of Thosar and Trigeorgis [1994] also indicate that there are significant
post announcement risk adjusted returns on the target firms stock, but the returns are reduced
after controlling for transaction costs. They also examine an option-based strategy and find
that this strategy yields substantial returns even after transaction costs
Dukes et al also examine the possibility of reducing the risk and improving the return by using
a prediction model developed by Samuelson and Rosenthal [1986]. They find that the mean
daily return increases inversely with the level of probability for success. Thus, in order to
obtain higher returns, risk arbitrageurs need to take positions where the probability of a
successful tender offer is low. Samuelson and Rosenthal [1986] as well as Brown and
Raymond [1986] use price movements in the target firm as an indicator of the tender offer
success. The sample which Samuelson and Rosenthal use excludes exchange offers and all
competitive bids in the American stock market between 1976-1981. In contrast, Brown and
Raymond include exchange offers and competing bids and cover the period 1980-1984. The
results of both studies show that it is possible to use the post announcement share price of the
target firm to infer the probability of a successful tender offer. Thus, if the post announcement
share price of the target firm rises near the offer price, there is a high probability that the
takeover will be successful. Hoffmeister and Dyl [1981] use a different approach to determine
the outcomes of tender offers. They develop a discriminant analysis model with 17
independent variables (e.g. profit margin, payout ratio, and P/E) to determine if a firm is a
good takeover candidate. They examine the tender offers made during 1976-1977 and
conclude that management reaction to a takeover attempt is decisive in determining takeover
success. Firm size is the second most important factor in determining the success of a tender
offer.
3
The number of shares that have to be owned in the target firm in order to receive one share in the acquiring
firm.
4
Risk Arbitrage in the Swedish Stock Market
By observing price movements in the target share, investors can predict the market odds of
success. If the investors’ own odds of success are greater (less) than the market odds, they can
earn an excess return by purchasing (selling short) the target shares. In order to improve the
estimate of success, the investors need to engage in costly information acquisition. Larcker
and Lys [1987] investigate if risk arbitrageurs have incentives to engage in costly information
acquisition. The sample consists of all 13-D filings4 from December 1977 to December 1983.
The results indicate that arbitrageurs are able to acquire information that is superior to public
information about the outcomes of acquisition proposals. They also observe that arbitrageurs
earn substantial excess returns on the equity positions.
The study by Bradley, Desai and Kim [1983] gives a fundamental understanding of how the
market reacts to tender offers. They examine the returns realised by the stockholders of firms
that were the targets of unsuccessful tender offers and firms that have made unsuccessful
offers. They find that the announcement of a tender offer causes an immediate increase in the
value of the target shares. If the tender offer is unsuccessful and another bid does not
materialise, the entire positive abnormal returns earned from the announcement of the initial
offer are dissipated over the following two years. They also find that the rejection of a tender
offer has differential effects on the share prices of the unsuccessful acquiring firms. If an
unsuccessful offer is the only offer the target receives, then there is no effect on the wealth for
the stockholders of the unsuccessful acquiring firm. However, if the offer is unsuccessful
because another firms makes a higher bid, then the value of the unsuccessful acquiring firm
falls significantly.
IV. Data and Method
Most previous studies of risk arbitrage are from the eighties and include only cash tender
offers. Our study differs from earlier studies in the aspect that we include exchange offers and
cover the time period 1990-1998. In order to obtain an independent sample distribution, raised
and competing bids will be excluded. Partial offers5 will also be excluded because the
arbitrageur is not guaranteed disposal of the entire position. The tender offers included in our
study must meet the following terms:





The target firm must be listed on the A-, O- or OTC list at the Stockholm Stock Exchange
at the time of the offer
The acquiring firm must be listed as above in the case of an exchange offer
In the case of several alternatives of payment, at least one must be in cash, an exchange of
stocks or a combination of both
The announcement and settlement or termination date of the deal, as well as the terms of
the offer, must be publicly available information
The offer price must exceed the post announcement share price
The database of this study, which is presented in table II, consists of 165 tender offers that
were made during the period 1990-1998.
4
A 13D-filing must be filed within 10 calendar days of any purchase of securities that causes an investor to
exceed an ownership limit of five percent of the outstanding shares.
5
A tender offer made for part of the target firm.
5
Risk Arbitrage in the Swedish Stock Market
6
Risk Arbitrage in the Swedish Stock Market
Table II
Sample before Screening Procedure
Cash
Exchange
All
1990
28
5
33
1991
17
5
22
1992
6
8
14
1993
2
5
7
1994
7
7
14
1995
11
6
17
1996
15
3
18
1997
11
14
25
1998
9
6
15
Total
106
59
165
As seen in table II, the database consists of 106 cash offers and 59 exchange offers. Worth
noting is that the percentage of cash offers has declined during the time period. The decline
may be explained by the fact that cash offers tend to decrease during time periods with a high
valuation of the stock market. The reason for this is that a high valued stock market makes it
more expensive to use cash as payment when acquiring firms.
The following data was acquired for each tender offer in order to carry out the study:






Announcement date
Expiration date (settlement or termination date)
Offer price
Post-announcement share price for the target firm and, in the case of a exchange offer, also
for the acquiring firm
If the tender offer fails, share price at the date of termination for the target firm and, in the
case of a exchange offer, also for the acquiring firm
Terms of payment (cash, stock for stock or a combination of both)
The terms for the tender offers that took place during 1990-1998 were obtained from quarterly
reports from the Stockholm Stock Exchange. The announcement dates were collected from
tender offer prospectus and the specific share prices were acquired from Findata, the
Stockholm Stock Exchange, and the Stockholm City Library. The settlement date in the
prospectus might be misleading, due to prolonged acceptance period or tender offer failure.
Therefore, the expiration dates were collected from the firms, banks or brokerage firms
involved in the tender offer. For the abnormal return calculations, data for the 360-day T-bills
as well as for AFGX was acquired from the Findata database. Information regarding the
margin requirement was obtained from the brokerage firm Hagströmer & Qviberg.
The screening procedure of our original population resulted in a reduction of 32 tender offers.
24 tender offers were additionally excluded due to lack of available information. A sample of
109 tender offers remained. The detailed breakdown of the sample is presented in table III.
Table III
Sample Remaining after Screening Procedures
Cash
Exchange
All
1990 1991
24
16
3
2
27
18
1992
5
2
7
1993
1
0
1
1994
5
1
6
1995
7
5
12
1996
14
2
16
1997
7
5
12
1998
7
3
10
Total
86
23
109
As mentioned earlier, the return from investing in risk arbitrage is strongly influenced by the
ability to predict whether the acquisition will be successful or not. It would therefore have
7
Risk Arbitrage in the Swedish Stock Market
been interesting to develop a prediction model to assess the probability for success. However,
because of the concentrated ownership structure in Sweden, the terms of the deal are normally
negotiated with the major stockholders of the target firm before the offer is announced. The
result of this is that most offers are accepted. In our sample a total of 9 offers failed, resulting
in a success ratio of 94,5%. Therefore we find no need for a prediction model, since this only
introduces another element of risk; the risk of making an inaccurate prediction. However, we
find it important to point out that arbitrageurs must estimate the likelihood of success for each
offer in order to reduce the risk.
To test whether risk arbitrage leads to abnormal returns we will make the following
assumptions:




It is possible to take short positions in all listed firms
The liquidity of the shares for both the target and acquiring firm is adequate
The margin requirement is 130%6
The brokerage commission is 0.45% for 1990-1992, 0.35% for 1993-1995, and 0.25% for
1996-1998
The sample will be divided into two sub-samples; cash offers and exchange offers. Due to
similar calculations of the abnormal return for exchange offers as well as offers including a
combination of cash and stock, these two types of offers will be categorised into one group;
exchange offers. The time period 1990-1998 will be divided into three sub-periods, 19901992, 1993-1995 and 1996-1998. Depending upon the outcome and type of the tender offer,
the realised return for each observation in the sample will be computed using one of the
following approaches:
Cash Offer
If the cash tender offer is successful the return is computed as:
Ri 
( Poi  Pait )
Pait
[1]
where Poi = tender offer price
Pait = post announcement share price for the target firm
If the tender offer fails, the return is computed as:
Ri 
( Pti  Pait )
Pait
[2]
where Pti = share price on the termination date for the failed offer
Exchange Offer
6
The margin requirement varies between 110%-150%, depending upon the listing of the acquiring firm and the
credit rating of the investor (Hagströmer & Qviberg).
8
Risk Arbitrage in the Swedish Stock Market
If the tender offer is successful, the profit from the short and long position at the date of
settlement is computed as:
profit (short ) i  Paia  Psia
[3]
where Paia = post announcement share price for the acquiring firm
Psia = share price at the date of settlement for the acquiring firm
profit (long ) i  Psia  ER * Pait
[4]
where ER = exchange ratio
The rate of return for the period is computed as:
 profit ( short ) i  profit (long ) i  Paia * M
Ri  
Paia * M


  1

[5]
where M = the margin requirement for the short position
If we insert equations 3 and 4 into equation 5 we get the following:
 Pa  Psia  Psia  ER * Pait  Paia * M
Ri   ia
Paia * M


  1

[6]
Equation 6 can be simplified into the following expression:
Ri 
1 ER * Pait Paia
M
[7]
Psia is eliminated which means that the share price for the acquiring firm at the settlement date
has no effect on the return.
If the tender offer is unsuccessful equation 4 changes into the following:
profit (long ) i  ER( Ptit  Pait )
[8]
where Ptit = the share price of the target firm at the date of termination
If we insert equations 3 and 8 into equation 5 we obtain:
 Pa  Psia  ER( Ptit  Pait )  Paia * M
Ri   ia
Paia * M


  1

[9]
The returns will be computed from the announcement date to the settlement or the termination
date. Since this time period differs for the observations, the returns will be recalculated on an
annual basis as shown below:
9
Risk Arbitrage in the Swedish Stock Market
Ra i 
Ri * 360
d
[10]
where Rai = the annualised return
Abnormal Return
In order to calculate the abnormal return, we first need to choose a benchmark, which has a
level of risk equivalent to the risk of risk arbitrage. Since risk arbitrage is not risk free, we find
that the risk free interest rate does not reflect the risk involved in the strategy. Thosar and
Trigeorgis [1994] use the market model to risk adjust the realised returns. We find that it is
not appropriate to risk adjust the returns against the market since the market risk is eliminated
in risk arbitrage. Hence, AFGX is not an appropriate benchmark either. Since the risk level of
AFGX is too high, and the risk level of the risk free interest rate is too low, we find it more
suitable to use an index with a level of risk between the two. Since no such index exists we
will construct an ad hoc index including equal weights of the risk free interest rate and AFGX.
If abnormal returns can be earned against the weighted index, it would be interesting to study
if abnormal returns against AFGX also can be obtained. This in order to further assure our
results. If contrary results are obtained, it would be interesting to study if abnormal returns can
be earned against the risk free interest rate. Therefore, we will also calculate abnormal returns
against the risk free interest rate and AFGX.
The abnormal return for each tender offer will be computed as follows:
ARi  Ra i  Rbi
where Rbi = the return of the benchmark
The abnormal return will be calculated before and after transaction costs7. To study whether
the abnormal return is significantly different from zero we have to choose an appropriate
parametric test. For those time periods and sub-samples where the central limit theorem can
be applied i.e. a normal distribution can be approximated, a z-test8 will be used. However,
when the central limit theorem cannot be applied, we will perform a t-test9. The hypotheses
for the tests are stated as below:
Ho:  = 0
7
8
Includes brokerage commissions and, for 1990-1991, tax on trading volume.
z
x

n
n
9
t
x
where s 
s n
 (x
i 1
i
 x) 2
n 1
10
Risk Arbitrage in the Swedish Stock Market
H1:   0
To find out if the abnormal returns from risk arbitrage have increased, decreased or remained
the same over the time period 1990-1998, we will use a two-sample t-test of means10. We will
test if the returns differ between the three sub-periods 1990-1992, 1993-1995, and 1996-1998.
The hypothesis for the test is expressed as:
Ho: 1 - 2 = 0
H1: 1 - 2  0
V. Empirical Results
The average spreads, at the announcement date, for risk arbitrage between 1990-1998 are
summarised in table IV. For the entire time period the average spread is 4.60%. This is
consistent with the findings of Vinberg [1993] who reports an average spread of 5%. Worth
noting is that the spread has declined over the time period.
Table IV
The Spread at the Announcement Date for Cash and Exchange Offers
The sample is divided into two sub-samples; cash offers and exchange offers. The spreads are given in percent for each year
and sub-sample during the time period 1990-1998. The spread for the exchange offers is the raw spread excluding the leverage
effect of the short position i.e. a margin of 200%.
1990
1991
1992
1993*
1994
1995
1996
1997
1998
Cash
Exchange
6,69
4,23
5,73
5,41
6,33
7,83
10
-
2,30
2,06
3,01
5,95
2,76
5,26
2,01
2,33
2,37
3,95
All
6,41
5,70
6,76
10,00
2,26
4,24
3,07
2,14
2,85
* Includes only one cash offer
The decline in the spreads over the time period implies that the potential return earned from
risk arbitrage has been reduced. This may be due to the decline of the risk free interest rate
and transaction costs. The low spreads confirm the low risk premium assigned by investors for
tender offers in the Swedish stock market. Since the duration11 of each offer varies, we
recalculated the returns on an annual basis. This makes the offers comparable. The results are
shown in table V.
Table V
Annualised Return for Cash and Exchange Offers between 1990-1998
The sample is divided into two sub-samples; cash offers and exchange offers. The annualised returns are given in percent for
each year and sub-sample during the time period 1990-1998.
10
t
( x1  x 2 )  D
sp
11
n1  n2
n1 n2
where s p 
(n1  1) s12  (n2  1) s 22
n1  n2  2
The bidperiod is on average 85 days.
11
Risk Arbitrage in the Swedish Stock Market
1990
1991
1992
1993*
1994
1995
1996
1997
1998
Cash
Exchange
23,64
44,12
28,82
59,82
19,02
95,92
69,23
-
13,33
66,87
22,89
68,32
14,66
74,21
14,13
104,41
8,86
57,11
All
25,92
32,09
40,99
69,23
22,26
41,82
22,10
52,83
23,33
* Includes only one cash offer
Table V shows that the returns earned from risk arbitrage are positive for all years. The
annualised returns for cash offers are much lower than the returns obtained by Dukes et al
[1992]. Worth noting is that the returns earned from exchange offers are much higher than for
cash offers. This is due to the leverage effect from the short position. We do not imply that an
investor could earn the returns shown above, as it would be unrealistic to assume that an
investor could repeat the process on a continuing basis.
However, the annualised return is not an appropriate measure of the profitability of risk
arbitrage. Abnormal return gives a better estimate since it adjusts the return for the risk
involved in the strategy. In table VI we present the abnormal returns, for the three sub-periods,
before controlling for transaction costs. The abnormal returns for the individual years are
presented in appendix I, table I.
Table VI
Abnormal Returns before Transaction Costs and Corresponding t-ratios
The sample is divided into two sub-samples; cash offers and exchange offers. The entire time period 1990-1998 is divided into
three sub-periods of equal length; 1990-1992, 1993-1995, 1996-1998. The abnormal returns are measured against the risk-free
interest rate (RF), an ad hoc equally weighted index of RF and AFGX, and AFGX.
Cash
Period
1990-1992
1993-1995
1996-1998
1990-1998
RF
9,29
(4,81)**
13,71
(2,74)*
8,25
(1,70)
9,62
(4,80)**
Weighted
10,14
(2,05)*
5,61
(0,74)
0,76
(0,11)
6,40
(1,78)
Exchange
AFGX
11,00
(1,24)
-2,48
(-0,23)
-6,73
(-0,60)
3,19
(0,52)
RF
50,57
(4,93)**
61,24
(3,99)*
42,16
(5,23)**
49,70
(8,18)**
Weighted
57,37
(3,07)*
59,66
(3,77)*
29,08
(4,82)**
45,67
(5,90)**
All Offers
AFGX
64,18
(2,31)
58,08
(2,92)*
16,00
(2,72)*
41,64
(3,85)**
RF
14,84
(5,14)**
28,72
(3,73)**
17,17
(3,59)**
18,07
(7,06)**
Weighted
16,50
(3,07)**
22,68
(2,49)*
8,21
(1,45)
14,69
(4,07)**
AFGX
18,16
(2,06)*
16,64
(1,44)
-0,75
(-0,09)
11,30
(2,05)*
* Significant at the 5 percent level
** Significant at the 1 percent level
The abnormal returns are mainly positive for all sub-samples and time periods. The negative
abnormal returns are due to an extremely strong stock market. For the sample of all 109 tender
offers, during the entire time period 1990-1998, we obtained significant abnormal returns of
18.07% against the risk free interest rate, and 14.69% against the weighted index. Interestingly
enough, a significant abnormal return of 11.30% against AFGX was also obtained. The
abnormal returns, against the risk free interest rate, are significant for all three sub-periods.
With the exception of the sub-period 1996-1998, the same result applies to abnormal returns
against the weighted index. However, the abnormal return against AFGX is only significant
for the first sub-period. This can be explained by the deep recession in the Swedish economy
during 1990-1992.
For cash offers, we did not obtain significant abnormal returns against the weighted index or
12
Risk Arbitrage in the Swedish Stock Market
AFGX for the entire time period. However, a significant abnormal return against the risk free
interest rate of 9.62% was obtained. This result is not consistent with the evidence of Vinberg
[1993], who reports that abnormal returns against the risk free interest rate cannot be
obtained. The insignificant abnormal return of 8.25%, for the sub-period 1996-1998, is due to
a high standard deviation caused by a failed offer, which resulted in a negative return.
For exchange offers, we obtained a significant abnormal return of 45.67% against the
weighted index for the entire time period. Worth noting is that a significant abnormal return of
41.64% against AFGX was also obtained. With the exception of an insignificant abnormal
return against AFGX during 1990-1992, we obtained significant t-ratios for all calculations of
abnormal returns.
A comparison between the two types of offers implies that exchange offers are more
profitable than cash offers. However, the transaction costs for the positions taken in exchange
offers could significantly reduce the abnormal returns. Therefore we also calculated the
abnormal returns after transaction costs. The abnormal returns for the three sub-periods are
presented in table VII. The abnormal returns for the individual years are presented in appendix
I, table II.
Table VII
Abnormal Returns after Transaction Costs and Corresponding t-ratios
The sample is divided into two sub-samples; cash offers and exchange offers. The entire time period 1990-1998 is divided
into three sub-periods of equal length; 1990-1992, 1993-1995, 1996-1998. The abnormal returns are measured against the
risk-free interest rate (RF), an ad hoc equally weighted index of RF and AFGX, and AFGX. We have assumed the following
brokerage commission; 0.45% for 1990-1992, 0.35% for 1993-1995, and 0.25% for 1996-1998. The tax on trading volume
of 1% for 1990 and 0.5% for 1991 has also been taken into account.
Cash
Period
1990-1992
1993-1995
1996-1998
1990-1998
RF
4.70
(2.41)*
11.30
(2.33)*
6.26
(1.22)
6.20
(2.99)**
Weighted
5.55
(1.13)
3.21
(0.43)
-1.23
(-0.17)
2.99
(0.83)
Exchange
AFGX
6.41
(0.73)
-4.89
(-0.45)
-8.71
(-0.78)
-0.22
(-0.04)
RF
13.82
(0.82)
44.47
(2.98)*
32.17
(4.12)**
29.79
(4.06)**
Weighted
20.63
(0.80)
42.89
(2.99)*
19.09
(3.23)*
25.76
(2.92)**
All Offers
AFGX
27.43
(0.79)
41.31
(2.32)
6.00
(1.00)
21.73
(1.86)
RF
5.92
(2.15)*
21.78
(3.30)**
13.08
(2.82)**
11.18
(4.62)**
Weighted
7.58
(1.41)
15.74
(2.00)
4.12
(0.74)
7.80
(2.24)*
AFGX
9.24
(1.05)
9.70
(0.94)
-4.84
(-0.58)
4.41
(0.81)
* Significant at the 5 percent level
** Significant at the 1 percent level
After the introduction of transaction costs a great decline in the abnormal returns and t-ratios
can be observed for all sub-samples and time periods. For all offers, significant abnormal
returns against AFGX can no longer be observed for the entire time period 1990-1998.
However, it is interesting to note that a significant abnormal return of 7.80% against the
weighted index was obtained.
For exchange offers, similar results were obtained for the entire time period. A significant
abnormal return against the weighted index can be observed, but not against AFGX. A further
examination of the data reveals that the abnormal return against AFGX is not significant any
sub-period and that the abnormal returns against the risk free interest rate and the weighted
index are significant both the second and third sub-period.
13
Risk Arbitrage in the Swedish Stock Market
For cash offers, a significant abnormal return against the risk free interest rate can still be
obtained for the entire period. However, the abnormal return has now been reduced from
9.62% to 6.20%. Insignificant abnormal returns of 2.99% and –0.22% were obtained against
the weighted index and AFGX for the entire time period. The insignificant abnormal return
against the market index is not consistent with the findings of Thosar and Trigeorgis [1994].
This inconsistency exists because their abnormal returns are risk adjusted. Their findings
further support that the risk level of risk arbitrage is lower than the market risk.
After the introduction of transaction costs, the great difference in abnormal returns between
cash and exchange offers remains. The difference is statistically confirmed at the 0.01 level.
This is explained by the leverage effect of the short position taken in exchange offers.
We have shown that the spread has declined during 1990-1998 (see table IV). To study if this
also implies a reduced abnormal return, a two-sample t-test was performed. The results are
shown in table VIII.
Table VIII
T-ratios for Two-sample Test of Means of Abnormal Returns
The sample is divided into two sub-samples; cash offers and exchange offers. The time period 1990-1998 is divided into
the sub-periods 1990-1992 (1), 1993-1995 (2), and 1996-1998 (3). The tx,y-ratio applies for the difference in the mean
abnormal return, against the ad hoc weighted index, after transaction costs between sub-period x and y. We have assumed
the following brokerage commission; 0.45% for 1990-1992, 0.35% for 1993-1995, and 0.25% for 1996-1998. The tax on
trading volume of 1% for 1990 and 0.5% for 1991 has also been taken into account.
t1,2
t1,3
t2,3
Cash
0.28
0.80
0.37
Exchange
-0.66
0.06
1.66
All
-0.80
0.44
1.22
* Significant at the 5 percent level
** Significant at the 1 percent level
The results above show that the abnormal returns do not differ significantly between the three
sub-periods. Despite the decline in the spreads, the abnormal returns from risk arbitrage have
not been reduced. This is due to the decline in the risk free interest rate and transaction costs.
Reliability and Validity
14
Risk Arbitrage in the Swedish Stock Market
Regarding the reliability and validity of our study, the following points need to be taken into
consideration. First, several of the settlement dates were approximated with the date stated in
the prospectus. Since these might be misleading, due to prolonged or shortened acceptance
period, the actual abnormal returns may differ from the abnormal returns obtained in our
study. Second, the lack of failed offers in our sample may have overstated the obtained
abnormal returns. Third, it can be questioned if the ad hoc weighted index includes the correct
level of risk involved in risk arbitrage. The actual risk level is very difficult to estimate, but is
with certainty higher than the risk level of the risk free interest rate and lower than the risk
level of AFGX.
VI. Conclusions and Further Research
The findings of this study indicate that stock exchange tender offers yield substantial
abnormal returns, both before and after transaction costs. The abnormal return is calculated
against an ad hoc equally weighted index of the risk free interest rate and the major index of
the Stockholm Stock Exchange, AFGX. Cash offers, on the other hand, do not yield
significant abnormal returns against this index. A comparison between the two types of offers
reveals that exchange offers, due to the leverage effect of the short position, are more
profitable than cash offers. The evidence of the whole sample suggests that risk arbitrage
yields a significant abnormal return of 7.80%, against the weighted index, after transaction
costs. The results indicate further that significant abnormal returns against AFGX can be
earned before transaction costs, but the conclusion does not hold after controlling for
transaction costs.
On the basis of these findings we conclude that abnormal returns can be earned from risk
arbitrage in the Swedish stock market. In addition, a comparison between the three subperiods reveals that the abnormal returns from risk arbitrage have not changed over the time
period 1990-1998.
Overall, because of the non-existent market risk in risk arbitrage and due to the leverage effect
of exchange offers, we find this strategy useful to reduce the risk and increase the returns in a
portfolio. Thus, risk arbitrage is a useful strategy for hedge funds.
It would be worth while for future research to examine the actual risk level of risk arbitrage. It
would also be interesting to examine how an increased number of failed offers affect the
realised return from risk arbitrage. An additional suggestion for further research is to perform
the study in an international perspective, including mergers.
15
Risk Arbitrage in the Swedish Stock Market
Appendix I
Table I
Abnormal Returns before Transaction Costs
The sample is divided into two sub-samples; cash offers and exchange offers. The entire time period 1990-1998 is divided into
three sub-periods of equal length; 1990-1992, 1993-1995, 1996-1998. The abnormal returns are measured against the risk-free
interest rate (RF), an ad hoc equally weighted index of RF and AFGX, and AFGX.
Cash
Year
1990
1991
1992
1993
1994
1995
1996
1997
1998
RF
9,27
9,73
7,93
60,70
4,81
13,35
8,85
10,43
4,84
Exchange
Weighted
11,00
10,44
5,07
68,83
2,28
-1,03
-8,18
10,66
8,75
AFGX
12,74
11,14
2,21
76,95
-0,26
-15,41
-25,22
10,88
12,66
RF
29,33
48,75
84,23
60,07
61,48
69,06
25,20
52,51
Weighted
18,40
50,99
122,22
90,60
53,47
44,70
18,05
37,05
Total
AFGX
7,46
53,23
160,20
121,13
45,47
20,35
10,90
21,59
RF
11,50
14,07
29,73
60,70
14,02
33,40
16,38
16,59
19,14
Weighted
11,83
14,94
38,54
68,83
17,00
21,68
-1,57
13,74
17,24
AFGX
12,15
15,82
47,35
76,95
19,97
9,95
-19,53
10,89
15,34
Table II
Abnormal Returns after Transaction Costs
The sample is divided into two sub-samples; cash offers and exchange offers. The entire time period 1990-1998 is divided
into three sub-periods of equal length; 1990-1992, 1993-1995, 1996-1998. The abnormal returns are measured against the
risk-free interest rate (RF), an ad hoc equally weighted index of RF and AFGX, and AFGX. We have assumed the following
brokerage commission; 0.45% for 1990-1992, 0.35% for 1993-1995, and 0.25% for 1996-1998. The tax on trading volume
of 1% for 1990 and 0.5% for 1991 has also been taken into account.
Cash
Year
1990
1991
1992
1993
1994
1995
1996
1997
1998
RF
3.54
5.90
6.41
58.28
2.75
10.70
7.36
8.55
1.76
Weighted
5.28
6.60
3.55
66.40
0.21
-3.69
-9.68
8.78
5.67
Exchange
AFGX
7.01
7.30
0.69
74.53
-2.32
-18.07
-26.72
9.00
9.58
RF
-22.23
14.05
67.66
26.02
48.16
58.33
16.14
41.45
Weighted
-33.17
16.29
105.65
56.55
40.16
33.98
8.99
25.99
Total
AFGX
-44.10
18.53
143.63
87.08
32.15
9.62
18.36
10.53
RF
0.68
6.80
23.91
58.28
6.63
26.31
13.73
11.71
13.67
Weighted
1.00
7.67
32.72
66.40
9.60
14.58
-4.22
8.86
11.77
AFGX
1.33
8.55
41.53
74.53
12.58
2.86
-22.18
6.02
9.87
16
Risk Arbitrage in the Swedish Stock Market
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17