Execution During the Pricing Period
In this section, we focus on trading in the context of fixed value exchange
transactions. In such transactions, the exchange ratio is determined based on
the stock price of the acquiring firm during the pricing period and is gradu-
ally revealed as the pricing period unfolds. Since knowledge of the exchange
ratio is important to executing a paired transaction, this would imply that
we can trade only at the end of the pricing period.
However, in some cases, this strict constraint may not be ideal for trad-
ing. To appreciate the fact, let us consider the situation wherein the end of
the pricing period is very close to the shareholders’ vote, or even worse, the
end of the period is well past the shareholders’ vote (these situations are not
uncommon in real life). In such situations, the time interval between the end
of the pricing period and the date of deal completion is rather short, leav-
ing very little time to put on a position of substantial size. To further com-
pound the situation, one has to deal with the prospect of rapidly narrowing
spreads.
Given this, the arbitrageur would prefer to not have to wait until the end
of the pricing period to put on a spread position. Therefore, even though the
exchange ratio is not known exactly, the arbitrageur would want to begin
trading before the end of the pricing period but trade in a way that leaves
him or her perfectly hedged (meet the ratio constraints on the pair) eventu-
ally. In this section, we will discuss an approach where we trade during the
pricing period and still manage to satisfy the ratio constraint at the end of
the period.
Consider the case where the exchange ratio is computed on a fixed
value of the target stock pTand the average closing price of the bidder
stock in the pricing period. Let the closing prices of the bidder stock be
p 1 ,p 2 ,...,pn. starting from day 1 to day n, the last day in the pricing pe-
riod. Now, according to the terms of the fixed value exchange transac-
tions, the ratio (number of bidder stock exchanged for one target stock) is
given as
(10.3)
This is the fixed value of target stock divided by the average of the closing
prices of the bidder stock in the pricing period. The reciprocal of the ex-
change ratio ris therefore
(10.4)
(^1112)
rn
p
p
p
p
p
TT p
n
=++...+T
r
np
pp pTn=
12 +++...
Trade Execution 161