Final_1.pdf

Interpreting Equation 10.4, the reciprocal of the exchange ratio is an av-
erage of the reciprocals of the realized exchange ratio in the pricing period.
We will exploit this idea in our approach to trade during the pricing
period. If we decide to put on a total spread position consisting of nB
shares of the acquirer, the number of shares of the target nTto be bought
is given as

(10.5)

(10.6)

We can write this as

(10.7)

where

(10.8)

In other words, the formula tells us the amount of target shares to buy
on a daily basis for a fixed number of bidder shares such that we would be
fully hedged at the end of the pricing period. We can mimic this equation

during execution by shorting shares of the acquirer and buying

shares of the target on the (i+ 1)th day. At the end of the pricing

period plus one more day, we will be perfectly hedged. Alternately, we could
start by holding a naked short position on the bidder stock and buy the cor-
responding number of target stock on each day in the pricing period. Of
course, the captured spread would vary depending on the timing of trades of
the bidder stock.
There is a small caveat in all of this, though. Recall from the introduc-
tory chapter that the dollar profit is calculated on a per-target-share basis.
However, the total number of target shares that we buy in this case is known
only at the end of the pricing period. Thus, it would be reasonable to say
that we would know our position size (in target share terms) and expected
profits only at the end of the pricing period. Hence, by trading in this fash-
ion we will have replaced our uncertainty on the ratio by the uncertainty on
the position size/profits.

n

n

p

p

Bi

× T

n

n

B

n

np

np

iT in

B

i

==...T ,,, 1

nnnTTT=++...+ 12 nnT

n

n

n

p

p

p

p

p

p

T

B

TT

n

=++...+T













12

n

n

r

T

B

=

162 RISK ARBITRAGE PAIRS