Post-announcement merger arbitrage

Hey everyone,

So I have an example from an old colleague on a merger arbitrage idea which I thought was interesting. The stock traded at $7.80/share, the company had a takeover offer on the table for €8.00/share. Whether the deal was successful or not would be known in 6 weeks. The resulting gain of 2.6%, or rather a 25% annualised gain. Not too shabby.

But digging deeper shows some flaws. Prior to the announcement, the target company traded at €6/share. This means that at €7.80/share, the market prices in a 90% chance the deal gets approved by all stakeholders (regulators, shareholders, comp authorities etc).

For this to yield a positive expected outcome, you need to believe the probability of approval is greater than 90%.

Based on a probability-weighted basis, it doesn't look good!

Where it gets interesting is extrapolating this example to pre-covid. In early Feb 2020, my colleague's portfolio was up 5%. He didn't think covid was going to be a big deal in terms of the economic impact at the time. But he did believe that if it spiralled out of control, it would have some pretty hair-raising consequences.

He ran a scenario where the market continues to advance at its historic averages: somewhere between 5-7% p.a. The market was already up 1.4% at the time of the year, so by staying invested, he should expect further gains of roughly 1-2% over the next 3 months. What happens if covid does hit the market? Let's say it resulted in a bear market, something like a real bear drop of 20-25%. What probabilities do you need to believe in for this to be a 0 expected outcome event? 

My question may be elementary but how do you think he arrived at the probability numbers? especially the 90% chance the merger goes through?

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Comments (5)

Oct 6, 2021 - 6:30pm

Simple probability. 0.2p-1.8(1-p)=0 ($0.20 profit if merger happens, $1.80 loss if it doesn't happen). So 2p-1.8=0, so p=0.9. This assumes that this is a binary event (no chance of the deal price being changed and that the expected price if the deal fails is $6).

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Oct 6, 2021 - 6:40pm

If you are trading on it, you probably want to consider the risk that the price might be lowered as an alternative to the deal failing (due to bad market conditions) or raised if the deal isn't yet final. You also want to test your assumption that the expected value conditional on the deal failing is actually $6, it might be slightly lower (deal more likely to fail in bad market than good market, earlier price might have incorporated inside info of an upcoming deal, etc.), although given that its 2021 its also possible that the company is doing much better now than in 2020 and should have a higher price (hard to say how much). You also want to think about how the risk is correlated with your portfolio, since in many ways merger arb can behave like selling otm puts. Depending on the deal, 90% could actually be cheap and an attractive opportunity, unless the market knows something you dont. (if everything is final, the true odds of a deal failing can be much lower than 10%)

Oct 6, 2021 - 7:00pm

Some good points have already been made. I would also add that the "90% chance" is a little simple. The consideration value also needs to be discounted back to present value based on the expected timetable.

Normally it is also more complex than simply taking a long position in the target. You can short the acquirer, you can hedge with the industry sector, you can use options to shape your exposure.

BGH acquiring Village Roadshow is a good example of potential upside even after a deal has been made public. Also happened during covid. 

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Oct 6, 2021 - 8:29pm

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