This return is usually compared with 2 ×90 day treasury bill rate as the
benchmark to determine if the trade is viable. Note that the return calcula-
tion here is slightly different from the return calculation used in the statisti-
cal arbitrage case. The return is calculated on the dollars invested in the long
position alone. This is more to adhere to conventions followed in practice.
Quantitative Aspects
In the following chapters, we focus on some quantitative aspects of risk arbi-
trage. The focus will be in the areas of trade execution and risk measurement.
When trading spreads in size, it is not possible to trade the entire quan-
tity in one go due to liquidity constraints. The position is therefore filled on
an incremental basis. Note, however, that the trades need to be executed in
what we shall call a paired transaction. We need to ensure that both legs of
the pair be filled in a manner so as to satisfy the ratio constraint and also in
the process manage to capture a spread that is greater than a specified value.
We shall discuss issues relating to the unambiguous specification and verifi-
cation of such trades.
We will then address executions in the fixed value exchange case. In the
fixed value exchange transaction, we noted earlier, the exchange ratio is re-
vealed gradually as the prices unfold during the pricing period. The exact ex-
change ratio is known only at the end of pricing period. However, it is
possible to trade during the pricing period and still manage to be perfectly
hedged. We will illustrate how trading may be done during the pricing pe-
riod when the exchange ratio is unclear.
Next, we demonstrate how market implied deal break probability can
be evaluated using the time series of the spread. This is followed by a dis-
cussion on how the measured probability may be applied to evaluate the
value at risk in risk arbitrage deals. It turns out that the evaluation of stable
estimates of the deal break probability requires us to work on a smoothed
version of the spread. We delineate an approach for smoothing. The
smoothing process leads us to a methodology that could be useful in timing
the unwinding of the spread position.
SUMMARY
Risk arbitrage relates to trading around corporate events, especially
mergers and acquisitions.
The practice of risk arbitrage has a long history and is a widely practiced
arbitrage technique.Risk Arbitrage Mechanics 149