To construct our model, let us now go through the mechanics of a risk
arbitrage trade. Initially, a spread position is created. We do this by estab-
lishing a short position in the target and a long position in the bidder,
yielding a dollar value equal to the spread. The proceeds from the trades are
reinvested at the risk-free rate. Let us call this spread at time zero S 0. Upon
successful completion of the deal, the spread would converge to zero. The
position is reversed for no additional cost at time T, and the reward earned
by the investor will be erTS 0 , with rbeing the interest rate. In case there is
some cash paid out for the target shares, the payoff will be erTS 0 +cash.
However, if the deal ends in a failure, the spread will not converge to zero
as expected. Instead, it inflates to a value of, say, ST. The position will still
need to be reversed, and a cost equal to the spread at time T,ST, is incurred.
The net payoff in the event of deal failure is therefore erTS 0 – ST. The dis-
cussion of the scenarios here is illustrated in a state diagram as shown in
Figure 11.1.
176 RISK ARBITRAGE PAIRS
FIGURE 11.1 Single-Step Model.Current
Spread:S 0Payoff on
Success
ertS 0 +cashPayoff on
Deal Break
erTS 0 −STπsuccessπfailure