The initial deal break probability can be naively estimated using a num-
ber of robust statistical methods based on past data relating to deal an-
nouncements and successful completions. Alternately, an assessment of the
fundamentals of the two merging companies can be used to arrive at the deal
break probability. Yet another approach could be to base it simply on the in-
stantaneous reduction of the spread on deal announcement. The average of
the logarithm of the spread for the 10 days just prior to deal announcement
could be used as the logarithm of the spread corresponding to a failure prob-
ability of 1.
Reconciling Theory and Practice
To see how the theory bears out in practice, let us look at some implications
of the preceding model. According to the theory, the expectation is that the
spread will converge to zero in the case of successful completion of merger.
Alternately, we expect it blow up or widen in case the merger does not go
through. We present both examples and counterexamples. In cases where
the model might not hold, we also provide possible reasons as to why that
would be the case. All the examples presented are taken from the merger
boom period of the late 1990s.
Also, the key value in the theory relates to the logarithm of the spread.
If the logarithm of the spread goes down in a linear fashion, then the spread
goes down in an exponential fashion. As a matter of fact, in the case of
mergers with no glitches along the way, it is not unreasonable to expect the
logarithm of the spread to decrease in a linear fashion. We could therefore
expect the spread to exponentially approach zero as the merger date nears.
Now when the spread goes to zero, the logarithm of the spread goes to
negative infinity. In practice, we may assume a lower bound to the value of
the spread between the two stocks to be at least equal to or greater than the
bid-ask spread between them. At best, the spread could go to a penny. The
logarithm of the spread for a penny is –4.6. That would be about the lowest
value that we could expect for the logarithm of the spread.
With that said, let us look at some real-life deals. We start by looking at
some mergers where the spread behavior follows the model. Figure 11.3
shows examples where the theory holds. Figure 11.3a is a plot of the spread
for a successful merger. The bidder in this case was Newell Company, and
the target was Rubbermaid Corporation. The ratio for exchange was 0.7883.
The deal was announced on October 21, 1998, and completed March 24,
- Notice from the figure that it is conceivable that we could fit an ex-
ponential to the overall profile of the spread.
Figure 11.3b is a plot of the spread of an unsuccessful merger. The bid-
der was American Home Products (AHP), and the target was Monsanto
180 RISK ARBITRAGE PAIRS