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On the White Board - May 2009
May 15, 2009
Merger Arbitrage Strategy
Merger arbitrage is an investment strategy that consists of betting on the success of announced, but not yet effective mergers or acquisitions. In its simplest form, a merger deal stipulates that each target stock will be exchanged against a fixed amount of cash, namely the bid price. Usually when a deal is announced the target's stock jumps to almost that level. A (merger) spread persists until the deal is effective. The arbitrageur's strategy consists of buying the stock of the target and cash in the spread as soon as the deal is completed.
The strategy bears at least two risks. The first risk is that the deal remains pending for a very long time before it is successful, thus lowering the return. The second risk - far more important - is that the deal fails. The acquiring company might withdraw its offer inducing the target's stock to plummet. To illustrate such case we show the behavior of the Yahoo stock following Microsoft's acquisition offer on Feb 2, 2008. The red arrow is at the announcement date and the dotted blue line is at the bid price. The offer was eventually withdrawn in Fall 2008.
Risk measurement
While merger arbitrage positions are equity positions and their risk measurement could be done using the traditional VaR methodology, this approach is not suitable as the target's stock typically undergoes an important regime shift after the deal is announced and further does not capture at all the deal failure risk. To correct this, we have built a risk model that captures these characteristics. In a nutshell we model the deal success with a binomial indicator, and describe the level of the stock price in case of deal failure with a simple jump-diffusion process.
One of the key ingredients to our risk model is the probability of deal success. We can infer this quantity based on fundamentals of the deal or back out the market implied probability. The market implied probability is a direct function of the observed spread, the larger the spread the lower the probability of success.
We have applied our risk model to the Yahoo/Microsoft deal. In the figure below we show the market implied probability of success as a function of time in the upper part. You clearly see the deal success deteriorating. In the second part of the figure we show the corresponding risk measure. We have chosen the expected shortfall on a horizon of 20 business days and a level of 95%. We clearly notice a shift from a low risk regime to a high risk regime.