Here we see how merger arbitrage works in practice and how investors calculate the potential returns in real deals.

Let's look at two common structures, a cash deal and a share for share deal.

Let's start with the simpler case, a cash takeover.

Suppose big US announces that it will acquire small US for $145 per share in cash at the time of the announcement.

Small US shares are trading at $140 and the deal is expected to close in 180 days.

That's a $5 difference known as the deal spread, and it represents the potential profit for an arbitrage who buys small US today expecting to receive $145 once the deal completes.

So the gross return is 145 minus 140, all divided by 140 equals 3.57%.

But because that return would be earned over roughly 180 days, we need to annualize it.

Since hedge funds and arbitrage desks compare returns on an annualized basis, just like bond yields or funding rates, converting 180 days to years, we take 180 divided by 3 6 5 equals 0.493 years.

Some desks prefer to use actual over 360 for short-term returns, which would make a little difference.

Then we divide the 3.57% spread by that duration.

So 3.57% divided by 0.493 equals 7.24%, so that's the annualized gross return, about 7.2%.

Of course, this assumes the deal goes through.

If the merger fails, perhaps because regulators block it or shareholders vote it down, small US shares could fall back towards their pre-announcement level of around $120, creating a significant loss.

That's why this strategy is called risk arbitrage.

The investor earns the spread as compensation for taking on deal completion risk.

Now let's look at a more complex structure, a share for share deal.

This time, big US has offered 0.453 of its own shares for each share of small us.

And again, the deal is expected to close in about 180 Days.

The current market price of big US is $320 and 9 cents.

So the value of the offer called the deal parity is 0.453 multiplied by 320.09 equals $145.

That means when the deal completes, each small US share will effectively be worth $145 in big US stock rights. Now, however, small US is trading US $140.

The deal spread is therefore the same $5 as before, and the gross return is the same as before.

Being five divided by 140 equals 3.57%.

Annualizing over 180 days, again gives 7.24%, but there's an important difference in a share deal.

The value of the offer changes every day because it depends on big US' share price.

If big US rises, the implied value of the offer rises too and vice versa.

To lock in that value and remove exposure to big us, the arbitrage needs to hedge.

For every 100,000 shares of small US bought, the trader would short sell 45,300 shares of big us.

That's 100,000 multiplied by the 0.453 exchange ratio.

This creates a market neutral position.

If big US rises, the short position loses value, but the implied value of small US rises equally.

If big US falls, the short position gains offsetting the loss on the long position.

That's how merger ARB traders lock in the spread, turning the trade into a relative value position.

That depends only on whether the deal completes When calculating expected returns, traders also adjust for dividends and transaction costs.

If small US is expected to pay a dividend before the deal closes and that dividend is not already included in the $145 offer, it must be added to the total expected value.

If it is already included in the offer terms, no adjustment is needed on the short side.

If big US pays a dividend while the position is open, the short seller must make a synthetic dividend payment to The lender of the borrowed shares.

This effectively reduces the trader's realized return.

So the true net return equals the gross spread minus all of these costs.

Trading commissions, financing costs, and stock borrow fees on the short leg after adjusting. For these, the net annualized return might fall from say, 7.24% to something closer to five or 6% depending on the complexity and duration of the deal in both cash and share deals.

The principle is the same arbitrages by the target company's shares and where needed hedge the exposure to the acquirer to lock in the deal spread.

The profit depends on the deal closing as planned.

If it does, they earn the spread.

If it doesn't, they face potential losses.

As the target's share, price falls back towards its standalone value.