Case 090Event-driven and merger arbitrageCore

Tolvan Cement bids for Ondari Cement at a fixed ratio of 0.8 Tolvan shares while Tolvan trades between Rs 450 and Rs 550, with the value fixed at Rs 360 or Rs 440 outside that range. Map Ondari's deal value against Tolvan's price and say how the hedge changes across the range.

The situation

Tolvan Cement agrees to buy Ondari Cement in an all-share deal. Each Ondari share receives 0.8 Tolvan shares if Tolvan's average price before closing is between Rs 450 and Rs 550. Below Rs 450, the ratio rises so that Ondari holders receive Rs 360 of Tolvan shares; above Rs 550, it falls so that they receive Rs 440. This is a collarA clause in a share-for-share deal that fixes the ratio inside a price band and fixes the value outside it, protecting one or both sides from big moves in the share price of the acquirer..

Tolvan trades at Rs 500 and Ondari at Rs 385. Your fund wants to capture the spread without taking a view on cement prices.

Your task

Map Ondari's deal value against Tolvan's price, work out the spread, and say how the hedge must change across the range.

Quick check

Tolvan is at Rs 420, below the collar. How many Tolvan shares should you be short per Ondari share?

Worked solution

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

30-second answerThe answer to give first

Inside the collar Ondari is worth 0.8 Tolvan shares, so you hedge by shorting 0.8 shares; outside it the value is fixed at Rs 360 or Rs 440, so you hold no Tolvan hedge. At Tolvan Rs 500 the deal is worth Rs 400 against Ondari at Rs 385, a Rs 15 spread, 3.9%. The hedge must be cut as Tolvan crosses the edges, and near them it behaves like options.

Step 1What does the collar do to Ondari's deal value?

Think of a salary paid partly in company shares, with a promise: if the shares fall below a floor, the company tops you up; if they rise above a ceiling, you get no more. Inside Rs 450 to Rs 550 Ondari's value moves 0.8 rupees for every rupee Tolvan moves; outside that band it does not move at all. The value line is flat at Rs 360, climbs to Rs 440 across the band, then goes flat again.

Ondari's deal value is fixed at Rs 360 below a Tolvan price of Rs 450, rises 0.8 rupees per rupee of Tolvan between Rs 450 and Rs 550, and is fixed at Rs 440 above, so the hedge is short 0.8 Tolvan shares in the middle band and zero outside it.

Step 2What is the spread, and how do you capture it?

At Tolvan Rs 500 the deal pays 0.8 x 500, Rs 400, and Ondari trades at Rs 385. Buy one Ondari and short 0.8 Tolvan, and if the deal closes you collect the Rs 15 gap, 3.9%, whatever cement prices do, as long as Tolvan stays inside the band. The spread pays you for the risk that the deal fails, which a collar does nothing to remove.

Step 3What goes wrong if you keep the 0.8 hedge below Rs 450?

Run it. Tolvan falls from Rs 500 to Rs 420. The short of 0.8 shares gains 0.8 x 80, Rs 64. The deal value falls only from Rs 400 to Rs 360, Rs 40, because the floor kicked in at Rs 450. You are up Rs 24 a share, not flat, which sounds pleasant until you see it means you now hold a naked short in Tolvan. If Tolvan bounces back to Rs 500, that Rs 24 disappears. The hedge should have been cut to zero as Tolvan crossed Rs 450.

The relationship

V(P) = 0.8P + 0.8\max(450 - P, 0) - 0.8\max(P - 550, 0)

V(P)	Ondari's deal value per share at Tolvan price P
0.8P	the fixed-ratio part: 0.8 Tolvan shares
0.8 max(450 - P, 0)	0.8 puts struck at Rs 450: the floor
0.8 max(P - 550, 0)	0.8 calls struck at Rs 550, sold: the cap

What it says in wordsA collared deal is 0.8 Tolvan shares plus 0.8 puts at Rs 450, less 0.8 calls at Rs 550, which is why its hedge ratio changes like an option's.

Step 4Why does the hedge get awkward near the edges?

Because the value is shares plus options, and options change their hedge ratio as the price moves. Far inside the band the hedge is 0.8; near Rs 450 or Rs 550 it swings between 0.8 and zero with every move, so you rebalance often and pay for it. Collars are also set on an average price over a window before closing, which smooths the edge but means the final ratio is only known late. Many arbitrage desks hedge the edges with listed options on Tolvan, buying back the puts and calls embedded in the deal, rather than trading the stock back and forth.

Where candidates lose it

The common miss is hedging with the headline 0.8 ratio across the whole range. Outside the collar the deal value stops moving with Tolvan, and a short that is still on is a directional bet, not a hedge.

The second is forgetting that the collar protects against Tolvan's price, not against the deal failing. If the deal breaks, Ondari falls back to its own value whatever the collar says.

What the interviewer asks next

Tolvan is at Rs 548 with two weeks to the pricing window. How would you hedge?
Why would a target's board ask for a collar, and why would an acquirer accept one?
How does the spread change if the market doubts the deal will close?

Company names and figures are illustrative.