the direction of trading for the two stocks, let us determine the specified
quantities. The quantity of the target stock (Compaq) to be bought is speci-
fied as 10,000. The bidder quantity, however, is not specified. We deduce the
bidder quantity from the target share quantity and the exchange ratio using
the formula given. In this case, it is 10,000 ×0.6325 = 6325 shares. There-
fore, this is an order to buy 10,000 shares of CPQ and sell short 6,325 shares
of HWP. Are there any additional constraints? The answer is yes, and it is
specified in terms of the spread value. The spread measured on the fill prices
of the two stocks must be greater than or equal to the specified spread value
of $2.30. This spread in this case may be measured using the formula
0.6325×price(HWP) + cash amount – price(CPQ) >= $2.30Thus, the order unambiguously specifies the tickers, the trade direction,
trade quantity, the spread constraint, and the ratio constraint that are to be
satisfied.
Verifying the Execution
The paired execution order as specified to the broker is usually for a con-
siderable size in terms of the number of shares involved. Given the large po-
sition sizes and the fact that this is a paired transaction, the order is worked
by the broker in a series of executions. This is done on a best-effort basis.
The broker then delivers to the arbitrageur a list of executions for both the
stocks. It is now up to the arbitrageur to evaluate the quality of execution.
The quality of executions may be measured two ways, speed and effi-
cacy. In situations when there is news in the market and quick action is re-
quired, execution speed is of utmost importance and may very well be the
criterion upon which the execution quality is measured. However, in most
other situations the arbitrageur is interested in capturing as high a spread as
possible when putting on the spread and unwinding at as low a spread as
possible. In such cases, the execution efficacy, characterized by how well the
executions measure up to the specified spread value, is more important.
While one would ideally want to be able to capture as high a spread as pos-
sible in the shortest possible time, it is conceivable that a quick execution
could mean that one gives up on efficacy, causing a trade-off between the
two criteria for measurement of execution quality.
We now look at issues related to measuring execution efficacy. Of
course, in the course of the discussion we will see how it affects execution
speed. To measure efficacy, one can attempt to pair up the executions and
check to see if each paired execution satisfies the spread constraint, how
many missed the specified spread value, and by how much. A ratio of the
dollar value of the hits versus the misses could very well be the measure of
execution efficacy. Another option is to compare the specified spread value
Trade Execution 155