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028

Case 028Event-driven and merger arbitrageCore

Stellan Pharma offers 0.5 of its shares for each Moravi Labs share. Stellan trades at Rs 800 and Moravi at Rs 370, and Moravi would fall to Rs 280 if the deal broke. What is the spread, how do you hedge it, and what completion chance is the market pricing?

ACAQR Capital ManagementGreenwich · 2021

1The situation

Stellan Pharma has agreed to buy Moravi Labs in an all-stock deal: each Moravi shareholder will receive 0.5 of a Stellan share for every Moravi share. Stellan trades at Rs 800 and Moravi at Rs 370. The deal needs competition approval and a shareholder vote, and both companies expect it to close in about six months.

Before the announcement Moravi traded at Rs 280, and your view is that it would return there if the deal broke. Stellan pays no dividend before the expected closing date, and its shares can be borrowed at a small cost.

2Your task

What is the spread, how do you set up the position so that Stellan's share price does not matter, what completion probability is the market implying, and how would you size the trade?

Quick check

What chance of completion is the market pricing?

Worked solution

Try it on paper, then open one step at a time.

30-second answerThe answer to give first

The spread is Rs 30 a share, 8.1% over about six months, against Rs 90 of downside if the deal breaks, which prices roughly a 75% chance of completion. Buy Moravi and short 0.5 Stellan for each Moravi share, so the Rs 30 is locked in whatever Stellan does. The trade makes sense only if you think completion is clearly more likely than 75%, and it is sized by the loss on a break, not by the spread.

Step 1What is the spread, and why is it not free money?

Moravi's shareholders will receive 0.5 Stellan shares, worth 0.5 x 800 = Rs 400 today, yet Moravi trades at Rs 370. The Rs 30 gap, 8.1% of the price, is what the market pays you to carry the risk that the deal breaks. Think of buying a concert ticket for Rs 370 that will be worth Rs 400 on the night, from someone worried the concert might be cancelled, in which case the ticket is worth Rs 280 as a souvenir. The seller is not being careless; the discount is the price of the cancellation risk. Compounded over two half-years, 8.1% is 16.9% a year, the number deal spreads are usually quoted in.

Step 2How do you remove Stellan's share price from the trade?

Buy one Moravi share and short 0.5 Stellan shares. If the deal closes, your Moravi share turns into 0.5 Stellan shares, which you deliver against the short. The hedge ratio equals the exchange ratio, so on completion the two legs cancel and you keep exactly the Rs 30 spread whatever Stellan's price does in between. If Stellan falls to Rs 700, Moravi converts into Rs 350 of stock, a Rs 20 loss on the long, but the short, sold for Rs 400, is bought back for Rs 350, a Rs 50 gain: net Rs 30 again. This is the merger arbitrageBuying the target of an announced deal and, in a stock deal, shorting the acquirer, to earn the gap between the market price and the deal value if the deal completes. position in its standard form.

Long Moravi, short 0.5 Stellan: plus 30 if it closes, minus 90 if it breaks280320360400Moravi, RsDeal value 0.5 x 800 = 400Today 370Break value 280+30-90Implied completion = 90 / (90 + 30) = 75%Deal closesLong Moravi turns into 0.5 StellanShort 0.5 Stellan: Rs 400 receivedStellan 800: legs +30 and 0+30Stellan 700: legs -20 and +50+30Deal breaksMoravi falls 370 to 280-90Stellan flat: short leg 00Stellan +5% to 840: short -20-20Net if it breaks: -90, or -110 if Stellan rallies
Moravi at Rs 370 sits Rs 30 below its Rs 400 deal value and Rs 90 above its Rs 280 break value, which prices a 75% chance of completion; hedged with 0.5 Stellan shares, the position earns Rs 30 on completion whatever Stellan does and loses Rs 90 or more on a break.
Step 3What completion probability is the market pricing?
The relationship
370=p×400+(1−p)×280  ⇒  p=370−280400−280=90120=75%370 = p \times 400 + (1-p) \times 280 \;\Rightarrow\; p = \frac{370-280}{400-280} = \frac{90}{120} = 75\%
400what Moravi is worth if the deal closes, 0.5 x Rs 800
280where Moravi falls if the deal breaks
pthe completion probability that makes today's Rs 370 a fair price
What it says in wordsToday's price is the probability-weighted average of the deal value and the break value; solve for the probability.

This ignores the time value of money and the cost of borrowing Stellan shares, both small over six months, so the true implied figure is a shade higher. The payoff is lopsided: you make Rs 30 three times in four and lose Rs 90 one time in four, so the trade behaves like selling insurance. That shape is why merger arbitrage returns look steady for long stretches and then fall sharply when several deals break together in a market sell-off.

OutcomeLong 1 MoraviShort 0.5 StellanNet per Moravi share
Closes, Stellan still Rs 800+300+30
Closes, Stellan falls to Rs 700-20+50+30
Breaks, Stellan flat at Rs 800-900-90
Breaks, Stellan rallies 5% to Rs 840-90-20-110
On completion the hedged position earns Rs 30 whatever Stellan's price, but on a break it loses Rs 90 with Stellan flat and Rs 110 if Stellan's shares rise 5% on the news.
Step 4How would you size it?

Start from your own probability, not the market's. If your work on the competition review says completion is 90% likely, the expected gain is 0.9 x 30 minus 0.1 x 90, which is Rs 18 a share, 4.9% over six months. Size by what a break would cost, because that is the number that hurts: a break costs 90 / 370 = 24.3% of the Moravi position. If the fund allows a single deal to lose at most 1% of NAV, the position can be about 4.1% of NAV. The table shows why to keep a margin below that: acquirers often rally when a deal dies, and the short leg then adds to the loss.

Where candidates lose it

The common miss is quoting the 8.1% spread, or its annualised 16.9%, as the return. That is the return only if the deal closes. A trade that makes 8% three times in four and loses 24% once in four is not a 17% a year trade; at the market's own odds its expected gain is roughly zero.

The second is hedging with the wrong ratio. Shorting one Stellan share per Moravi share, instead of 0.5, leaves you short an extra Rs 400 of Stellan, a directional bet on the acquirer that nobody asked you to take.

What the interviewer asks next

  • If the deal were all cash at Rs 400, how would the hedge change?
  • Stellan's shares rally 10% on news that competition approval looks harder. What happens to your position?
  • Why do merger arbitrage funds tend to lose money at the same time?
  • What does a collar on the exchange ratio change for the arbitrageur?

Asked at AQR Capital Management, Quantitative Research, Greenwich, 2021 (Wall Street Oasis): Questions about merger arbitrage strategies. Hedging. Python programming. Data analysis and regression.

← Case 027Castrelle Fashion reports revenue growth of 18%. New stores add 12 points, same-store footfall is down 2% and the average bill is up 8%. Break the growth down and say what it tells you about demand.Case 029 →Build the month-end NAV for Ovelle Partners from gross assets of Rs 1,050 crore, a prime broker loan, accrued fees and redemptions payable, with 9.9 crore units in issue. What is the NAV per unit?

Company names and figures are illustrative.

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