Analysis of Improved Bids in the Scope of a Risk Arbitrage Strategy

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Analysis of improved bids in thescope of a Risk Arbitrage strategy

Stéphane Dieudonné, Fabienne Cretin, Slimane Bouacha

SEPTEMBER 2011


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Analysis of improved bids in the scope of a Risk Arbitrage strategy - OFI ASSET MANAGEMENT - 2

Analysis of improved bids in the scope

of a Risk Arbitrage strategy

Summary - conclusionThis document is a study of improved bids observed during announced mergers & acquisitions of

listed companies. The scope of the analysis is the North American market (US and Canada) over the

1998-2011 period. An improved bid is defined as an improvement on the terms of the initial bid for a

target either by the buyer or by a third party.

In the scope of a risk arbitrage strategy, improved bids are important events, since they offer

particularly interesting risk/return, similar to buying a call option. This document therefore aims to

analyse improved bids from the point of view of an investor setting up an arbitrage strategy.

The main conclusions are as follows:

Improved bids account for about 12% of finalised deals.

Prevailing market conditions on equity and bond markets have an impact on the volume of

improved bids as well as the observed yields. For example, towards the top of equity market

cycles, the number of improved bids is particularly high. Conversely, the 2008 liquidity crisis

led to a dramatic fall in yields on potential improved bid situations.

The market is efficient when it forecasts the outcome of certain improved bids. The higher

the target’s shares trade above the offer price in the days following the announcement, the

likelier it is that the deal will have a favourable outcome for the investor.

Even though improved bids are most commonly seen in hostile bid situations, it is hard to

establish the typical profile for an improved bid: neither the payment type nor the sector of

the target, nor the nationality of the buyer are deciding factors. Overall, the phenomenon is

therefore difficult to forecast.

IntroductionRisk Arbitrage is a strategy that consists of capturing the difference that may exist, after the

announcement of a merger & acquisition deal, between the target’s listed price and that

corresponding to the terms of the bid.

In setting up this strategy, the arbitrageur must anticipate four possible outcomes:

1. The deal is finalised according to the initial terms. The price of the target therefore converges

with the price offered by the buyer.

2. The deal fails, for example, following opposition from the target’s shareholders, a veto by the

competition authorities or adverse market conditions. The price of the target thereby returns

to a normal range of volatility for a share, generally returning to its pre-bid levels.

3. The terms of the bid are improved, either by the buyer itself, to obtain the agreement of all

the target’s shareholders, or by a third party in the context of a bidding war. The price of the

target adjusts towards the improved terms of the higher offer and sometimes above it.


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4. The buyer lowers the terms of the bid because it considers the target to have lost value

following an unexpected event such as a fire at a plant or the loss of an important patent.

The share price falls back to the downwardly corrected offer price.

These four potential outcomes have very different occurrence frequencies. Indeed, in most cases,

the deal is concluded on the terms initially decided. Conversely, the failure of a deal is rare (anaverage of 7% over 14 years) but the consequences for the arbitrageur can be penalising, as shown in

a previous study1. If we discard the downward revision of the offer, which is exceedingly rare, what

remains are the improved bid situations, which, in many cases, represent an additional source of

profit for the arbitrageur.

This note examines improved bid situations in the US and Canada from 1998 to 2011. In order to

do this we use a database that we have compiled and that features information on over 2000

mergers & acquisitions for an enterprise value of over USD500m. In particular, we analyse the

cyclical nature of improved bids, how the market can anticipate them and what returns may be

generated by the arbitrageur.

Why are improved bids important in Risk Arbitrage ?Improved bid situations are particularly important in the context of an arbitrage strategy for two

reasons.

Firstly, the returns to be made in an improved bid allow a classic argument of risk arbitrage’s

detractors to be tempered. As shown by Mitchell & Pulvino (2000), the yields of this strategy are

similar to those obtained when selling put options. In other words, this is a winning strategy when all

is going well, but becomes lossmaking when market conditions deteriorate significantly. Yielddistribution for this strategy should therefore be significantly asymmetric, with a cluster around

yields of between 0 and 10% flanked by a fat tail in yields more negative than -20%.

Chart 1 shows the distribution of annualised yields observed for risk arbitrage operations in the US

and Canada over the 1998-2011 period. To highlight the residual distributions, we have combined

those deals showing respective yields of less than -20% and more than +20%. As expected, we find a

bell-shaped curve with its fat tail to the left. But there is also an even greater distribution residue to

the right, which is half due to improved bid situations (with the other half corresponding to the

finalisation of the deal as expected). Note that the left hand side of the bell (i.e. negative returns)

represents deals where the market expected an improved bid that did not ultimately materialise,which leads to a loss for the investor as we shall see later.

1Stéphane Dieudonné, Fabienne Cretin and Slimane Bouacha , Risk Arbitrage, A Probalistic Approach Over

1998-2010 in the US and Canada, SSRN, 2010

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1710194&download=yes#PaperDownload







Chart 1: distribution of annualised yields from risk arbitrage operations in the US and Canada over

the 1998-2011 period. Sources: OFI AM, Bloomberg

From a risk/return point of view, setting up an arbitrage strategy in the context of a deal that might

be subject to an improved bid may be compared to the purchasing of a call option:

If the improved bid fails to materialise, the share price of the target falls back to the buyer’s

bid price. The risk of a loss on the position should therefore be known and is generally

relatively low.

If there is an improved bid for the target, the potential gain from the position can be

significant.

Chart 2 shows that the risk arbitrage strategy may be analysed as a combination of:

The sale of a put option for the majority of deals, with the arbitrageur cashing in the option’spremium in the event of success and a loss in the event of a failure.

The purchase of a call option for potential improved bid situations with the arbitrageur

benefiting from the rise in the target’s share price in the event of an improved bid and losing

the premium invested if not.

0

50

100

150

200

250

300

350

N u m b e r o f b i d s

Range of annualised yields

Operations with improved bid

Operations without improved bid




Chart 2: analysis via risk arbitrage options with and without improved bid. Sources: OFI AM

The second reason behind the importance of improved bids for the investor is the frequency of this

event. Chart 3 shows the sliding 12-month average number of improved bids as a percentage of

finalised deals.

Chart 3: number of improved bids as a percentage of the number of deals finalised in the US and

Canada over 1998-2011 (sliding 12-month average). Sources: OFI AM and Bloomberg

P r o f i t &

l o s s o f t h e p o s i t i o n

Target price

Operation with improved bid

Operation without improved bid

Offer pricePremium invested to play

an improved bid

Premium cashed in to

play the operation

The operation is a failure:

loss on the position

The operation is a success:

the arbitrageur cashes in the

option's premium

Improved bid :

gain on the position

No improved bid :

the arbitrageur loses the

option's premium

0%

5%

10%

15%

20%

25%

30%

D e c - 9 8

N o v - 9 9

N o v - 0 0

N o v - 0 1

N o v - 0 2

N o v - 0 3

N o v - 0 4

N o v - 0 5

N o v - 0 6

N o v - 0 7

N o v - 0 8

N o v - 0 9

N o v - 1 0

N u m b e r o f i m

p r o v e d b i d s a s % o f t o t a l

Sliding 12-month average

Historic average




Although the frequency of improved bids is cyclical over time, they represent an average of 12% of

finalised deals. It is therefore a relatively frequent event that should be taken into account for

successful implementation of a risk arbitrage strategy.

There are two sorts of improved bids: expected and unexpectedDefinitions of the technical terms that we use in this next part of our analysis are given in the

appendices.

An arbitrageur may be faced with one of two cases when a new M&A deal is announced:

the initial annualised yield is positive. This is a classic case in which the investor setting up

the strategy expects a deal that should be finalised according to the terms and schedule

given. The yield is bigger or smaller depending on the markets perception of the failure risk

for the deal.

the initial annualised yield is negative. If the arbitrageur sets up the position when the yieldforecast is apparently negative, it means that he expects an event that could eventually

produce a positive annualised yield in line with his management objectives. In other words,

investors expect an improved bid.

Improved bids can materialise in each of the cases. In the first, they are unexpected insofar as the

market initially valued the risk of the deal’s failure but not the potential for the pleasant surprise

represented by the improved bid. In the second, they are partly forecast by the market as evidenced

by the negative initial annualised yield. Hereafter, we shall call:

expected improved bids are deals where the initial annualised yield is negative without pre-

empting the outcome of the deal (improved bid, finalisation or failure). Fulfilled improved

bids are those that actually end up with an improved bid.

unexpected improved bids are deals that end with an improvement of the terms and for

which the initial annualised yield was positive.

Chart 4 shows the breakdown between unexpected improved bids and fulfilled improved bids

recorded in the US and Canada over the period 1998-2011.




Chart 4: breakdown of improved bids recorded in the US and Canada over the period 1998-2011.

Sources: OFI AM et Bloomberg

As the nature of expected and unexpected bids is fundamentally different, we shall analyse them

separately.

Analysis of improved bids expected by the market In this section, we shall study the main characteristics of expected improved bids:

cyclicality

deciding factors

potential outcomes

yield for the arbitrageur

We shall look at the relevance of a statistical approach to the phenomenon of expected improved

bids.

Cyclicality of expected improved bids

Chart 5 shows the trend in the number of expected improved bids over the 1998-2011 period in the

US and Canada, i.e. the number of M&A deals for which the market expected a potential improved

bid. As M&A itself is very cyclical as we showed in a previous study2, we have also presented the

number of expected improved bids as a percentage of the total number of announced deals.

2Stéphane Dieudonné, Fabienne Cretin and Slimane Bouacha, Macroeconomics Drivers Behind Risk Arbitrage

Strategy , SSRN, 2010

Expected improved

bids

57%

Unexpected improved

bids

43%

http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1705548







Chart 5: trend in the number of expected improved bids in the US and Canada over the 1998-2011

period. Sources: OFI AM and Bloomberg

It emerges that the expectation by investors of potential improved bids is a very cyclical

phenomenon with very distinct high points and low points (respectively 45% and 15% expressed as

a percentage of the number of announced deals).

Chart 6 shows that these peaks and troughs coincide fairly neatly with those of the equity market.

0%

5%

10%

15%

20%

25%

30%

35%

40%

45%

50%

0

20

40

60

80

100

120

1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011

A s % o

f a n n o u n c e d d e a l s

N u m b e r o f e x p e c t e d i m p r o v e d b i d s

Expected improved bids

as % of announced deals




Chart 6: trend comparison for the S&P 500 and the number of expected improved bids in the US and

Canada over the 1998-2011 period (sliding 6-month average). Sources: OFI AM and Bloomberg

The market environment therefore has an impact on how investors perceive potential improved bids.

As such, by the time the cycle last peaked in 2007, investors expected bids to be improved in almost

half of deals!

The premium recorded over the first five days of listing is also subject to significant variation as

shown by chart 7.

Chart 7: change in the premium recorded for expected improved bids in the US and Canada over the

1998-2011 period. Sources: OFI AM and Bloomberg

700

800

900

1000

1100

1200

1300

1400

1500

1600

0%

10%

20%

30%

40%

50%

60%

J

- -

J

- -

J

- -

J

- -

J

- -

J

- -

J

- -

J

- -

J

- -

J

- -

J

- -

J

-

J

- -

J

-

S & P 5 0 0

E x p e c t e d i m p r o v e d b i d s a s %

o f a n n o u n c e d

d e a l s

Expected improved bids as %

announced deals

S&P 500

0%

1%

2%

3%

4%

5%

6%

1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011

P r e m i u m r

e c o r d e d f o r e x p e c t e d i m p r o v e d b i d s

Recorded premium

Historical average




Although investors tend to be very optimistic about the number of improved bids at the top of the

market, they are actually more reasonable about the price they are prepared to pay to take part in

the deal.

Chart 8: trend comparison between the S&P 500 and premium recorded on expected improved bids

in the US and Canada over the 1998-2011 period (sliding 12-month average). Sources: OFI AM and

Bloomberg

The premiums are actually at their lowest when equity markets are at their highest (2000-2001 and

2006-2007) as shown by chart 8. Conversely, when equity markets are at their lowest (2002-2003

and 2008-2009), investors are prepared to pay higher premiums.

Deciding factors in expected improved bids

When an M&A deal is announced, the arbitrageur analyses the situation by applying a (non

exhaustive) set of questions such as:

Is the buyer’s bid friendly or hostile?

Is the buyer an industrial player or an LBO fund?

Is the deal domestic or international?

Is it a cash or paper offer?

What premium is the buyer offering?

In which sector is the target?

We have endeavoured to identify the factors that prompt investors to expect an improved bid for an

announced M&A deal. We looked at all the expected improved bids in the light of these questions.

Note that in the scope of this study, we have deliberately left out the aspects of M&A deals that are

600

700

800

900

1000

1100

1200

1300

1400

1500

1600

-1%

0%

1%

2%

3%

4%

5%

6%

-

J

- -

J

- -

J

- -

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J

- -

J

- -

J

- -

J

-

J

- -

J

- -

J

- -

J

-

S & P 5 0 0

R e c

o r d e d p r e m i u m

Recorded premium

S&P 500




more difficult to quantify, such as the political implications or possible opposition of the competition

authorities.

To highlight the deciding factors, we compared the expected improved bids to all the deals in our

database that did not entail expected improved bids. Chart 9 records the results of this comparison.

Chart 9: possible improved bids behind expected improved bids in the US and Canada over 1998-

2011. Sources: OFI AM and Bloomberg

It is hard to identify a typical profile for improved bids. It nevertheless emerges that the market

tends to anticipate bids when the buyer is making a hostile cash bid paying less than historical

recorded average. Indeed, investors know that hostile bids can prompt company managers to seek a

white knight able to make a friendly and higher bid. This is especially the case when they deem the

price of the hostile bid to be unsatisfactory.

Conversely, it appears that the typology and nationality of the buyer have no particularly influence.

With regard to the sector of the target, analysis shows that relative to the scope of the data, there

are slightly more improved bids in the Basic Materials sector but less in Communications (chart 10).

13%19%

28%

65%

71%

5%

16%

23%

48%

53%

0%

10%

20%

30%

40%

50%

60%

70%

80%

% of hostile bids % of LBO bids % of cross border

bids

% of cash bids % of bids with

below the average

acquisition

premium

Expected improved bids

All operations excluding expected improved bids




Chart 10: sector approach to deciding factors behind improved bids in the US and Canada over 1998-

2011. Sources: OFI AM and Bloomberg

Potential outcomes to expected improved bidsWhen the market expects a bid to be improved, there are several possible occurences:

The buyer improves the terms of its bid under pressure from shareholders

The target is subject to a rival bid from a third party

The deal fails

The deal is finalised on the initial terms

We find that there are three possible outcomes for the investor that sets up the arbitrage strategy:

1. favourable (gross actual yield of over 2%) when the buyer improves its initial bid or a rival bid

appears

2. neutral (gross actual yield of between -2% and 2%) which corresponds to very tight deals

where the yield is low or those which trade slightly higher to begin with but then back

towards the initial terms

3. unfavourable (gross actual yield of less than -2%) when the deal fails or when the improved

bid is lower than that initially expected by the market.

Chart 11 shows the breakdown of expected improved bids according to the outcome for the

arbitrageur.

11%5%

11%15%

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Expected improved bids All operations exc luding

expected improved bids

Utilities

Communications

Basic Materials

Technology

Industrial

Financial

Energy

Consumer, Cyclical

Consumer, Non-cyclical




Chart 11: breakdown according to the outcome of expected improved bids in the US and Canada

over 1998-2011. Sources: OFI AM and Bloomberg

Chart 12 shows the gross yields achieved by the arbitrageur according to each outcome.

Chart 12: gross yields achieved on expected improved bids in the US and Canada over 1998-2011.

Sources: OFI AM and Bloomberg

From the data featured in the two charts above, it is possible to calculate the weighted average yield

of expected improved bids. As such, an investor setting up an arbitrage strategy on all the improvedbid situations can expect a gross yield of 1.9% and an annualised yield of 6.5%.

23%

63%

14%

Favourable

Neutral

Unfavourable

15%

0%

-13%

-15%

-10%

-5%

0%

5%

10%

15%

20%

Favourable Neutral Unfavourable




This level of annualised yield prompts two observations. Firstly, the figure is an interesting one as it

may correspond to the portfolio management targets of a low-volatility, absolute performance fund,

hence the advantage of improved bid plays in the scope of a risk arbitrage strategy. However,

secondly it must be acknowledged that the calculation is rather theoretical. Indeed, given the

cyclical nature of the phenomenon, it would be hard to build a sufficiently invested and diversified

portfolio at the bottom of the cycle. Furthermore, the volatility of such a portfolio would probably be

too great in phases when many deals fail, as we shall see later in the study.

Influence of the initial premium on the outcome of expected improved bids

There is plenty to learn from analysing the influence of the initial yield, which measures the degree of

market anticipation around a potential improved bid.

We have segmented expected improved bids into five premium ranges: less than 0%, between 0 and

5%, between 5 and 10%, between 10 and 15% and over 15%.

The first category where the premium is negative warrants an explanation. A negative premiumsignifies that the price of the target is lower than the price of the bid. We should rather refer to it in

terms of a classic risk arbitrage discount. However, in certain cases such as in 2007, a very narrow

risk arbitrage discount diminished by a high interest rate can result in a negative initial gross yield.

This category corresponds to deals where the risk arbitrage discount is so tight that it is difficult to

say whether or not the market expects an improved bid or that the deal has virtually no risk.

Chart 13 shows the link between the outcome of the expected improved bid and the range of the

initial premium.

Chart 13: outcome of expected improved bids according to the initial premium range. Sources : OFIAM and Bloomberg

12%

25%

50% 50%

78%

84% 57%15%

3%

18%

35%

50%

22%

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

<0% 0%< <5% 5%< <10% 10%< <15% 15%<

N u m b e r o f i m p r o v e d b i d s b y o u t c o m e a s % o f t o t a l

Range of initial premium

Unfavourable

Neutral

Favourable




The market is ultimately fairly efficient when it expects an improved bid. A very narrow initial risk

arbitrage premium (< 0%) does not result in an improved bid in 84% of cases. Meanwhile, the

favourable outcome rate rises from 26% for the 0%< <5% range to 78% for the 15% < segment. In

other words, the higher the premium (i.e. the greater anticipation there is of an improved bid), the

greater the chance is of the improved bid materialising with a favourable outcome.

With regard to yields, the degree of anticipation by the markets is also a relevant indicator as shown

by chart 14. The more the market anticipates an improved bid, the higher the gross yield achieved.

Chart 14: distribution of gross yields achieved for expected improved bids according to the range of

the initial premium. Sources: OFI AM and Bloomberg

Trend over time of the yield from expected improved bids

The trend over the 1998-2011 period of the yield achieved on expected improved bids is also

interesting. Indeed, chart 15 shows that:

The yield made on expected improved bids was positive for 13 of the 14 years of the

observation period.

The 2001 bear market did not have the same impact on improved bids as that of 2008.

1,5% 1,6%

3,0%

4,8%

10,4%

0%

2%

4%

6%

8%

10%

12%

<0% 0%< <5% 5%< <10% 10%< <15% 15%<

A v e r a g e g r o s s y i e l d

Range of initial premium




Chart 16 helps us to understand why the yield of expected improved bids remained positive in 2001

whereas it collapsed in 2008. In both cases, the rate of favourable outcomes admittedly touched a

low point of 10%. But unlike 2001, in 2008 there was a sharp rise in unfavourable outcomes, which

rose from 13% to 50% in a year. We can see two possible explanations:

The equity market slump was more marked in 2008 (56% slide in the S&P 500 in 73 weeks)

than in 2001 (47% fall over 109 weeks). This dramatic trend took some potential buyers by

surprise, prompting them to withdraw their bids.

The two waves of M&A in 1998-2001 and 2003-2008 had different drivers, technological

innovation for the first and LBO type acquisitions for the second. As such, the shock in 2008

was accompanied by a major liquidity crisis after Lehman’s bankruptcy. As the credit market

became inaccessible, many LBOs had to be abandoned, hence the sharp rise in unfavourable

outcomes at the time.

Chart 16 also shows that favourable outcomes peak in times of market downturn as in 2002 and

2009. It therefore appears that potential buyers know how to take advantage of periods when the

equity market has appealing valuations and have no qualms about battling for their prey on the stock

market.

Modelling of expected improved bids

Using a statistical approach, we have tried to model the phenomenon of expected improved bids by

using the same exogenous and endogenous variables applied to the Risk Arbitrage strategy as those

implemented in our previous studies. In particular, we wanted to see whether:

The trend over time of the number of expected improved bids and the favourable outcome

rate could be explained by market variables (equity, credit, interest rates, volatility) and/ormacro-economic variables (confidence index, lead indicators, unemployment).

With the above mentioned deciding factors (hostile/friendly, strategic/financial, etc.) we

were able to build a solid predictive model of the outcome of expected improved bids.

The details of the multiple linear and logistical regressions supporting our modelling may be found in

the appendices. Overall, the results are actually fairly disappointing:

Although 71% of the variations in the number of improved bids may be explained, the

excessive number of variables in the model makes it difficult to use.

Only 53% of the variations in the rate of favourable outcomes may be explained with a modelfeaturing 9 variables.

The predictive model for the outcome of expected improved bids does highlight the

importance of the initial premium and the hostile nature of the bid. However, the R2-like

coefficients of the logistic regression show the very weak relevance of the model.

Analysis of unexpected improved bidsWe have seen that unexpected improved bids account for 42% of all improved bids recorded over

the 1998-2011 period. Chart 17 shows how they are spread over time. On average over a long

period, unexpected improved bids represent 5% of finalised deals.




Chart 17: change over time of unexpected improved bids over the 1998-2011 period in the US and

Canada. Sources: OFI AM and Bloomberg

We can see that there is a certain cyclicality with the peaks (expressed as a percentage of total

finalised deals) just ahead of high points in the markets (1999 and 2006) and the points at which

markets start to turn upward (2002 and 2009). It appears that the regained optimism of equity

investors in these market phases spreads to potential buyers, who are not afraid to be aggressive in

their M&A dealings.

As with the expected improved bids, there is not really a typical profile that emerges for unexpected

improved bids, as shown by chart 18.

0%

2%

4%

6%

8%

10%

12%

0

5

10

15

20

25

1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011

A s % o

f c o m p l e t e d e a l s

N u m b e r o f u n e x p e c t e d i m p r o v e d b i d s

Unexpected improved bids

as % of complete deals




Chart 18: Deciding factors for unexpected improved bids in the US and Canada over the 1998-2011

period. Sources: OFI AM and Bloomberg

As with expected improved bids, the hostile bids and, to a lesser extent, LBOs are more represented

in unexpected improved bids than in the rest of the deals. Yet unlike expected improved bids, the

price paid by the buyer is not a deciding factor: the acquisition premium recorded for expectedimproved bids is fairly similar to the average calculated over the rest of the sample. After all, with an

initial gross yield that differs little from classic deals, unexpected improved bids really are events that

are not anticipated by the market.

Furthermore, given that the unexpected improved bids only account for 5% of finalised deals, a

statistical approach, such as that applied to expected improved bids, will clearly be of no use in

establishing a valid predictive model.

Although they are difficult to forecast, unexpected improved bids give investors very appealing yields

averaging about 15% as shown by chart 19.

19%

25%

30%

54%

62%

6%4%

15%

23%

48%

52%

5%

0%

10%

20%

30%

40%

50%

60%

70%

% of hostile bids % of LBO bids % of cross borderbids

% of cash bids % of bids withbelow the

average

acquisition

premium

Initial gross yield

Unexpected improved bids

All operations excluding unexpected improved bids




Chart 19: trend in the gross yield achieved on unexpected improved bids in the US and Canada over

the 1998-2011 period. Sources: OFI AM and Bloomberg

Conclusion

Risk arbitrage is often seen as a strategy with an asymmetric risk/return profile. That said, thisschematic approach fails to take into account important events that nevertheless count for 12% of

finalised deals, i.e. improved bids.

We consider there to be two sorts of improved bid: those that are expected by the market and those

that are not.

Investors forecast an improved bid when, in the days following the announcement of the deal, the

target’s shares trade at a premium, i.e. above the offer price. The level of this premium is the

measure of the market’s conviction about a favourable outcome for the potential improved bid. We

have shown that the market is efficient in its approach to improved bids: the higher the premium,

the higher the chance of a favourable outcome with an attractive yield for the arbitrageur.

Conversely, unexpected improved bids are deals where there is no premium in the first trading days,

but rather a classic risk arbitrage discount.

As with M&A activity in general, improved bids are subject to significant cycles. As such, expected

improved bids may account for up to 50% of deals announced (vs. 15% at the lowest) when the

equity market nears its peak.

There are rather more expected improved bids than unexpected ones, respectively 58% and 42% of

total improved bids made. Conversely, unexpected improved bids naturally offer higher yields for thearbitrageur than expected improved bids (15% vs 2%).

0%

5%

10%

15%

20%

25%

30%

1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011

G r o s s y i e l d

Achieved gross yield

Historical average




All told, it is hard to establish a typical profile for an improved bid even though, as expected, there

are often improved bids in instances of hostile offers. Indeed, in this case, the managers of the target

are more inclined to seek a “white knight” able to offer a friendly and higher bid. Conversely, it

appears that the typology of the buyer (strategic or financial), its nationality, payment type and

sector of the target are not deciding factors in an improved bid. For these reasons, the explicative

and predictive models that we can build with a statistical approach are unusable.




Modelling the number of expected improved bids

We have applied a multiple linear regression to the number of improved bids expected as a

percentage of the number of deals announced. We have tested the same variables as those used in

our study on macroeconomic drivers behind risk arbitrage strategy3. We used the datamining

software Tanagra.

The results of the regression are recorded below:

Chart 20 shows the number of expected bids and its estimate according to the explicative model.

3Stéphane Dieudonné, Fabienne Cretin and Slimane Bouacha, Macroeconomics Drivers Behind Risk Arbitrage

Strategy , SSRN, 2010

Global results

Endogenous attribute Nb de surenchères

anticipées

Examples 156

R² 0,725945

Adjusted-R² 0,71103

Sigma error 0,059084F-Test (8,147) 48,6735 (0,000000)

Analysis of variance

Source xSS d.f. xMS F p-value

Regression 1,3593 8 0,1699 48,6735 0

Residual 0,5132 147 0,0035

Total 1,8725 155

Coefficients

Attribute Coef. std t(147) p-value

Intercept -0,526141 0,11294 -4,658576 0,000007

HY 3m -0,597217 0,11233 -5,31663 0

S&P 500 0,000428 0,000045 9,438594 0

S&P 500 6m change -0,463328 0,059406 -7,799322 0

PE -0,014958 0,002757 -5,424676 0

Pente 3m-10y -3,545724 0,675809 -5,246641 0,000001

IG spread -0,001993 0,000252 -7,906766 0

Conference Board Consumer Conf 0,002111 0,000622 3,393162 0,000888

US Initial Jobless Claims SA 0,001541 0,000171 8,994971 0




Chart 20: trend comparison of the number of expected improved bids in the US and Canada over

1998-2011 and its estimate according to our multiple linear regression model. Sources: OFI AM and

Bloomberg

Modelling the percentage of favourable outcomes among expected bids

There regression results are recorded below:

0%

10%

20%

30%

40%

50%

60%

Number of expected improved bids as % of announced deals

Estimate




Modelling of expected improved bids with favourable outcome

We have applied a logistical regression to build a model capable of predicting favourable outcomes

among expected improved bids. The variables of the modem are endogenous to risk arbitrage:

hostile/friendly offer, strategic/LBO offer, level of the initial premium, sector of the target,

nationality of the buyer, size of the target, acquisition premium.

The results of the regression are recorded below:

Global results

Endogenous attribute % d'issue favorable

Examples 150

R² 0,563075

Adjusted-R² 0,538285

Sigma error 0,067151

F-Test (8,141) 22,7137 (0,000000)

Analysis of variance

Source xSS d.f. xMS F

Regression 0,8194 8 0,1024 22,7137

Residual 0,6358 141 0,0045

Total 1,4552 149

Coefficients

Attribute Coef. std t(141) p-value

Intercept 0,306833 0,130672 2,348113 0,020259

ECRI 0,006652 0,001046 6,358652 0

E/P / 10y yield 0,04761 0,024687 1,928536 0,055798

University of M ichigan Survey 0,003568 0,001525 2,3401 0,020681

Pente 3m-10y -4,723298 0,784532 -6,020527 0

S&P 500 -0,000157 0,000052 -3,045393 0,002774

SSLO 0,004631 0,001215 3,812071 0,000205

VIX 0,002981 0,00108 2,759703 0,006554

Conferenc e Board Consumer Conf -0,002354 0,00105 -2,242808 0,026469




Results

Classifier performances

Value Recall 1-Precision NON OUI Sum

NON 0,9499 0,204 NON 398 21 419

OUI 0,2031 0,4468 OUI 102 26 128

Sum 500 47 547

Classifier characteristics

Data description

Target attribute

# descriptors

Adjustement quality

Predicted attribute

Positive value

Number of examples

Criterion Intercept Model

AIC 597,211 533,168

SC 601,516 546,081

-2LL 595,211 527,168

Chi-2

d.f.

P(>Chi-2)

McFadden's R²

Cox and Snell's R²

Nagelkerke's R²

Attributes in the equation

Attribute Coef. Std-dev Wald Signif

constant 2,663267 0,2512 112,4313 0

Intent of Offer -0,990892 0,294 11,356 0,0008

Prime -0,709602 0,1195 35,236 0

Odds ratios and 95% confidence intervals

Attribute Coef. Low High

Intent of Offer 0,3712 0,2086 0,6606

Prime 0,4918 0,3891 0,6217

2

R²-like

0,117

0,1764

Surenchère avec issue favorable (2 values)

2

68,0434

0

0,1143

Error rate

Values prediction

NON

547

Surenc hère avec issue favorable

Model Fit Statistics

Model Chi² test (LR)

0,2249

Confusion matrix



Bibliography

Mark Mitchell and Todd Pulvino, Characteristics of Risk and Return in Risk Arbitrage, Journal of

Finance, 2000

Stéphane Dieudonné, Fabienne Cretin and Slimane Bouacha, Risk Arbitrage, A Probalistic

Approach Over 1998-2010 in the US and Canada, SSRN, 2010

Stéphane Dieudonné, Fabienne Cretin and Slimane Bouacha, Macroeconomics Drivers Behind

Risk Arbitrage Strategy , SSRN, 2010

Analysis of Improved Bids in the Scope of a Risk Arbitrage Strategy

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