Using Option Prices to Infer
Overpayments and Synergies in
M&A Transactions
Kate Barraclough, Vanderbilt University
David Robertson, Duke University
Tom Smith, UQ Business School
Robert E. Whaley, Vanderbilt University
Overview
• Stock price reactions to M&A announcements
reflect market beliefs about:
– Stand alone values of the firms involved
– Potential synergies
– Bidder overpayment
• We show how call options written on the firms
involved can be used to augment stock prices
in uncovering market beliefs.
Event Study Approach
• Traditional method for determining takeover
value.
– Calculate abnormal returns to bidder
– Calculate abnormal returns to target
– Possibly use dollar values
– Add these together to get gains from takeover
• Bradley, Desai and Kim (1988).
Event Study Approach
Target Cumulative Abnormal Return
0
Bidder Cumulative Abnormal Return
0
Problems with Event Study Approach
• Market does not assess probability of takeover
at 1
• Gains from successful takeover computed
from stock price changes on announcement
will be understated.
Problems with Event Study Approach
• Takeover bid will result in new information
being released about the target and the
bidder
• News about the bidder and news about the
target needs to be treated separately to gains
to target and gains to bidder.
• Look at an example re the bidder
Bidder Example
Abnormal
Return
0
Bidder Example
Abnormal
Return
0
Bt  pB S  (1  p ) B F
Bidder Example
0
News
About
Bidder
Bt  pB S  (1  p ) B F
BF
Bidder Example
0
News
About
Bidder
BS
Bt
BF
Gain to
Bidder
Related Literature
• Problems widely recognised in M&A literature
but few attempts to circumvent.
• Closest papers are Hietala, Kaplan and
Robinson (2003) and Bhagat, Dong, Hirshleifer
and Noah (2005).
ZYbZXb1
110nX
– Hietala et al use a case study of Viacom and
Paramont merger.
– Bhagat et al use probability scaling and
intervention methods.
Related Literature
• Probability scaling method rescales
annoucement date returns by an ex post
measure of probability of success.
• Intervention method uses returns at dates of
intervening events eg a competing bid,
shareholder litigation or regulatory
opposition.
Related Literature
• Probability scaling method:
– Compute an estimate of market’s perception of
probability of success.
– Based on a logit of past outcomes and various expost explanatory variables.
– Condition on litigation, target management
opposition, competing bids, premium and
toehold.
– Probability not specific to a particular offer.
Related Literature
• Intervention method requires ex post data on:
– Probability of success of initial bidder
– Probability of success of initial bidder given the
arrival of a competing bid
– Expected price paid by initial bidder given a
successful bid
– Expected price paid by initial bidder if successful
given the arrival of a competing bid
Related Literature
• Ex post estimation based on actual outcomes
across all takeovers.
• Estimated probability of success is not specific
to each merger.
• Not possible to disentangle sources of
takeover value on announcement.
Contribution
• Our method provides ex ante estimation of
parameters of the takeover.
• We show that the ex ante parameters provide
a much better fit with actual outcomes than
the ex post parameters used in previous
literature.
• Can determine specific values for components
of takeover value.
Contribution
• We are able to estimate the ex ante
parameters right from the time of initial
announcement of takeover. Do not have to
wait for intervening event.
• We can update ex ante parameters daily or in
real time. Do not have to wait for intervening
events. Important as prices can change due to
informed trading and do not need public
announcements to update.
Model
• Bidder price is a probability weighted average
of price if successful and price if unsuccessful
Bt  pBtS k  (1  p ) BtFk
• Target price is a probability weighted average
of price if successful and price if unsuccessful
Tt  pOt k  (1  p )Tt Fk
Model
• Total value changes accruing to successful
bidder and target are
( BtSk  Bt 1 )  (Ot k  Tt 1 )
• The total value change can be written as the
sum of 4 components:
( BtSk  BtFk )  ( BtFk  Bt 1 )  (Ot k  Tt Fk )  (Tt Fk  Tt 1 )
Model
• The total value change can be written as the
sum of 4 components:
( BtSk  BtFk )  ( BtFk  Bt 1 )  (Ot k  Tt Fk )  (Tt Fk  Tt 1 )
Gains to bidding News
firm about bidding
Gains
firmto target firm
News about target firm
Model
• The total value change can be written as the
sum of 4 components:
( BtSk  BtFk )  ( BtFk  Bt 1 )  (Ot k  Tt Fk )  (Tt Fk  Tt 1 )
• Total synergy gains are
( BtSk  BtFk )  (Ot k  Tt Fk )
Model
• Using stock prices alone the problem is underidentified:
• 4 unknowns BtS k , BtF k , Tt Fk and p
• But only two stock prices Bt k and Tt  k
• Use call option prices to augment stock price
information.
Option Prices
• Call options on the bidding firm:
ct ( Bt ; X )  pcˆt ( BtSk , BS,t k ; X )  (1  p)cˆt ( BtFk , BF,t k ; X )
Observed call price Call price if successful
Call price if unsuccessful
Option Prices
• Call options on the target:
– Cash offers:
F
F
ˆ
ct (Tt ; X )  p max( Casht k  X ,0)  (1  p)ct (Tt k , T ,t k ; X )
– Stock offers:
Fixed cash offer price
S
F
F
ˆ
ˆ
ct (Tt ; X )  pct (Ot k ,  B ,t k ; X )  (1  p )ct (Tt k ,  T ,t k ; X )
 pcˆt (nBtSk ,  BS,t k ; X )  (1  p )cˆt (Tt Fk ,  TF,t k ; X )
Stock offer ratio
Parameters
•
•
•
•
•
•
•
Price of the bidder if it succeeds: BtSk
Price of the bidder if it fails: BtFk
Price of the target if unsuccessful: Tt Fk
Probability of success: p
Volatility of the bidder if successful: BS,t k
F

Volatility of the bidder if unsuccessful: B ,t k
Volatility of the target if unsuccessful:  TF,t k
Parameters
• Use stock prices and call option prices of
bidder and target to uncover parameter values
• Need at least three calls on bidding firm and two
calls on target firm.
• Ensure call prices contain information relevant to
the announcement.
• Exclude options expiring before effective/withdrawal
date.
• Exclude options with zero trading volume or zero bid
price.
Parameters
• To solve for parameter values we need an
option valuation model.
• Stock options traded in the U.S. are Americanstyle and firms may pay dividends.
• We use a dividend-adjusted binomial method and
Cox, Ross and Rubinstein (1979) parameters.
• Exclude day before ex-dividend to avoid problem
of early exercise.
Parameters
• Starting values are:
– Pre-bid average prices over (-T,-1) period.
– Pre-bid return volatility over (-T,-1) period.
– Pre-bid return correlation over (-T,-1) period
– Use T of 60, 30, 5 days
– Probability of success based on target stock price
Tt  k  Tt 1
response
p
Ot  k  Tt 1
Data
• US Domestic tender offers January 1996
through December 2008.
• SDC and Factiva for announcement details.
• CRSP for share price and dividend information.
• Datastream for Eurodollar spot rates.
• Compustat and Risk Metrics for firm
characteristics.
• Option Metrics for option data.
Results
A. Summary statistics of our analysis sample
Description
Number of offers
Number of successful offers
Number of offers in same industry
Number of hostile offers
Number of offers where bidder has toehold
Number of offers with termination fee
Average offer premium (t -60)
Average offer premium (t -30)
Average offer premium (t -5)
Average offer value in millions
Average number of days to completion/withdrawal
All offers
n
% of total
167
148
88.6%
104
62.3%
9
5.4%
5
3.0%
0
0.0%
34.4%
37.6%
34.7%
3,121.5
87.4
B. Comparison of our analysis sample to braoder M&A sample
In sample
Description
n
% of total
Number of offers
167
Number/percent cash offers
90
53.9%
Number/percent stock offers
77
46.1%
Number/percent successful offers
148
88.6%
Number/percent unsuccessful offers
19
11.4%
Market value of stock in millions
Bidder
Target
Trading volume in millions
Bidder
Target
Stock return volatility
Bidder
Target
Cash offers
n
% of total
90
85
94.4%
51
56.7%
3
3.3%
5
5.6%
0
0.0%
45.3%
46.5%
36.6%
1,582.5
74.7
Not in sample
n
% of total
1,538
695
45.2%
843
54.8%
1,365
88.8%
173
11.2%
33,048.9
2,389.7
9,124.6
907.0
5,289.2
1,065.9
1,325.8
282.5
42.8%
55.5%
46.5%
65.4%
Stock offers
n
% of total
77
63
81.8%
53
68.8%
6
7.8%
0
0.0%
0
0.0%
21.7%
27.0%
32.6%
4,920.4
102.4
Market Activity of Options
Pre-announcement
period
Number of series
Bidder
Target
Open interest
Bidder
Target
Trading volume
Bidder
Target
Implied volatility
Bidder
Target
Announcement day
Mean
% change
Takeover period
Mean
% change
39.4
21.9
50.7
27.4
28.5%
25.0%
51.5
27.3
30.7%
24.5%
73,151.6
7,457.3
139,391.5
20,018.8
90.6%
168.4%
142,138.8
17,262.1
94.3%
131.5%
3,121.8
382.0
9,749.4
6,569.9
212.3%
1619.8%
5,536.4
683.8
77.3%
79.0%
30.8%
44.3%
31.6%
27.1%
2.6%
-38.8%
33.0%
22.2%
7.5%
-50.0%
Results Returns
All offers
All offers
Successful
Unsuccessful
All offers
Cash offers
Successful
Unsuccessful
All offers
Stock offers
Successful Unsuccessful
A. Base price: t-60
Abnormal returns
Bidder
Target
Gain to bidder
News about bidder
Gain to target
News about target
Gain from synergy
3.5%*
26.9%*
5.0%*
1.6%
31.9%*
6.9%*
36.9%*
3.2%*
28.1%*
4.4%*
1.5%
32.3%*
7.3%*
36.7%*
5.3%
17.8%*
9.7%
2.8%
28.8%*
4.3%
38.4%*
2.5%
35.4%*
6.0%*
-1.9%
40.4%*
5.0%*
46.4%*
1.4%
35.0%*
5.3%*
-1.9%
39.9%*
5.2%*
45.2%*
20.6%
41.4%
18.1%
-3.0%
48.2%
0.5%
66.3%
4.6%*
17.0%*
3.9%
5.8%*
21.9%*
9.3%*
25.8%*
5.7%*
18.7%*
3.3%
6.0%*
21.9%*
10.1%*
25.2%*
-0.2%
9.3%
6.7%*
4.9%
21.8%*
5.7%
28.5%*
B. Base price: t-30
Abnormal returns
Bidder
Target
Gain to bidder
News about bidder
Gain to target
News about target
Gain from synergy
0.3%
28.8%*
3.6%*
-1.3%
30.1%*
9.7%*
33.7%*
0.2%
29.7%*
3.1%
-1.3%
30.5%*
10.1%*
33.5%*
0.9%
21.3%*
7.3%
-1.7%
27.6%*
6.4%
34.9%*
-1.0%
38.0%*
4.1%
-4.5%*
39.0%*
7.5%*
43.1%*
-1.2%
37.6%*
3.7%
-4.4%*
38.7%*
7.2%*
42.4%*
2.8%
46.3%
10.4%
-5.7%
44.6%
13.7%
55.0%
1.8%
17.9%*
3.0%
2.4%
19.8%*
12.2%*
22.7%*
2.2%
19.1%*
2.2%
3.0%
19.4%*
14.1%*
21.6%*
0.2%
12.3%*
6.2%*
-0.3%
21.5%*
3.9%
27.8%*
C. Base price: t-5
Abnormal returns
Bidder
Target
Gain to bidder
News about bidder
Gain to target
News about target
Gain from synergy
-2.2%*
25.1%*
2.5%
-5.0%*
27.3%*
4.6%*
29.8%*
-2.2%*
25.5%*
2.0%
-4.8%*
27.6%*
4.6%*
29.6%*
-1.9%
22.1%*
6.8%
-6.9%*
24.8%*
4.9%
31.5%*
-0.2%
31.3%*
3.3%
-4.6%*
35.8%*
0.8%
39.1%*
-0.1%
31.1%*
2.9%
-4.2%*
35.8%*
0.7%
38.7%*
-0.6%
34.4%*
10.1%
-12.6%
35.5%
2.3%
45.5%
-4.5%*
18.0%*
1.6%
-5.5%*
17.4%*
9.1%*
19.0%*
-5.0%*
18.1%*
0.8%
-5.6%*
16.6%*
9.8%*
17.4%*
-2.4%
17.6%*
5.6%
-4.9%*
20.9%*
5.9%
26.5%*
Results Dollar Values
All offers
All offers
Successful
Unsuccessful
All offers
Cash offers
Successful
Unsuccessful
All offers
Stock offers
Successful Unsuccessful
A. Base price: t-60
Abnormal returns
Bidder
Target
Gain to bidder
News about bidder
Gain to target
News about target
Gain from synergy
-17.5
462.7*
796.1
-894.6
402.2*
179.9*
1198.2
-22.8
391.5*
898.6
-982.8
382.8*
122.4*
1281.4
23.6
1017.5
-2.6
-207.6
553.1
628.3
550.5
737.6
344.2*
2029.0*
-1240.6*
353.0*
54.9*
2382.1*
772.0
352.1*
2206.1*
-1285.7*
359.0*
57.3*
2565.1*
152.3
208.6
-980.7
-474.6
251.6
14.3
-729.1
-900.1
601.2*
-645.0
-490.1
459.6
326.1*
-185.5
-1095.2
444.5*
-865.4
-574.1
414.9
210.2*
-450.6
-22.4
1306.4
346.7
-112.2
660.8
847.6
1007.6
B. Base price: t-30
Abnormal returns
Bidder
Target
Gain to bidder
News about bidder
Gain to target
News about target
Gain from synergy
-457.7
465.7*
796.1
-1319.2
402.2*
182.1*
1198.2
-487.7
394.0*
898.6
-1428.3
382.8*
126.9*
1281.4
-223.6
1023.5*
-2.6
-469.3
553.1
612.1
550.5
357.3
359.1*
2029.0*
-1785.7*
353.0*
69.9*
2382.1*
337.3
357.3*
2206.1*
-1894.3*
359.0*
62.6*
2565.1*
698.4*
389.2
-980.7
60.5
251.6
194.7
-729.1
-1410.3
590.2*
-645.0
-773.9
459.6
313.2*
-185.5
-1600.8
443.6*
-865.4
-799.5
414.9
213.6
-450.6
-552.9
1250.0
346.7
-658.6
660.8
761.2
1007.6
C. Base price: t-5
Abnormal returns
Bidder
Target
Gain to bidder
News about bidder
Gain to target
News about target
Gain from synergy
-662.6
388.9*
796.1
-1551.8*
402.2*
113.0
1198.2
-674.1
322.2*
898.6
-1645.1*
382.8*
61.1
1281.4
-572.9
908.5
-2.6
-825.2
553.1
517.1
550.5
-99.8
287.6*
2029.0*
-2280.5*
353.0*
-1.7
2382.1*
-66.4
285.3*
2206.1*
-2338.6*
359.0*
-9.3
2565.1*
-667.9
325.1
-980.7
-1292.9
251.6
127.1
-729.1
-1320.4
507.4*
-645.0
-700.0
459.6
247.0
-185.5
-1494.0
371.9*
-865.4
-709.3
414.9
156.1
-450.6
-539.0
1116.8
346.7
-658.2
660.8
656.3
1007.6
Sample Selection
• Focus on Takeovers where both Bidder and
Target have listed options
• Heckman Sample Selection Correction
• Shows that the Target Gain is understated
Overall Results
• Takeovers do add value – the Bidder gains and
the Target gains
• Split up of Gains using Returns:
– 90% to Target; 10% to Bidder
• Split up of Gains using Dollar Values:
– Closer to 50% Target; 50% Bidder
• Traditional Methods understate true synergy
gains of takeovers. Helps us to understand
why takeovers continue to be an everyday
business strategy.
Conclusions
• We show how call options written on the firms
involved in M&A activities can be used to augment
stock prices in uncovering market beliefs.
• Our method provides ex ante estimation of
parameters of the takeover.
• We show that the ex ante parameters provide a
much better fit with actual outcomes than the ex
post parameters used in previous literature.
Conclusions
• We are able to estimate the ex ante parameters right
from the time of initial announcement of takeover.
Do not have to wait for intervening event.
• We can update ex ante parameters daily or in real
time. Do not have to wait for intervening events.
Important as prices can change due to informed
trading and do not need public announcements to
update.
• Able to extend the model to multiple bidders
• Show that M&As are not value destroying as the
recent literature would have you believe.