Outline how event-driven strategies such as merger arbitrage work and what risks they carry.

FRM® Part II · Risk Management and Investment Management · Hedge Fund Investment Strategies · FRM2.IM.8.c

The idea

Event-driven funds earn returns from corporate events, such as mergers, spin-offs and restructurings, rather than from market direction. In merger arbitrage the fund buys the target after the announcement because it trades below the offer. In a cash deal it simply holds the target. In a stock deal it also shorts the acquirer at the exchange ratio, so it is long the target and short acquirer shares, equal to the exchange ratio for each target share. The spread is the reward for bearing completion risk, and a wider spread signals more perceived risk or a longer wait. Payoffs are asymmetric: a small gain if the deal closes and a large loss if it breaks, like selling an out-of-the-money put. Breaks cluster in market stress, so correlation with equities rises just when it hurts. Exam point: let P be the target price, B the break price and O the offer. The implied completion probability is then found as follows. Prob = (P − B) ÷ (O − B).

Formulas

Completion probability implied by a target's price

p = (P − B) ÷ (O − B)

P: the target's current price
B: the expected price if the deal breaks
O: the offer value

Ignores time value. 1 − p is the implied break probability; dividing price by offer ignores the break price.

Acquirer shares to short in a stock-for-stock merger arbitrage

shares short = exchange ratio × target shares

exchange ratio: acquirer shares offered per target share
target shares: the number of target shares bought

Use the contractual exchange ratio, not the ratio of share prices, and multiply rather than divide.

A practice question

From the question bank, with the reason each wrong option is wrong.

A hedge fund buys the shares of a target company trading at USD 50 after an all-cash takeover offer of USD 53 per share is announced. What is the fund's basic merger arbitrage position and its main risk?

It is long the target and earns the spread if the deal closes; the main risk is a failed deal. - correct
It is short the target and long the acquirer; the main risk is that the deal completes on time.Why not: Reverses the positions; in a cash deal the fund simply holds the target.
It is long the target and short the acquirer's shares; the main risk is a rise in the acquirer's price.Why not: Applies the stock-deal hedge to a cash offer, where the acquirer's price does not affect the payout.
It is long the target and long put options on the market index; the main risk is rising interest rates.Why not: Invents a market hedge; the central risk is deal completion, not interest rates.

In a cash deal the target converges to the offer if the deal closes, so the fund holds the target and earns the spread. If the deal breaks the price falls back toward its undisturbed level, and that loss is much larger than the gain.

A harder one

A target trades at USD 50. A cash offer of USD 56 has been announced; if the deal breaks, the target is expected to fall to USD 40. Ignoring time value, what completion probability is implied by the market price?

37.5%Why not: This is the implied probability of the deal breaking, not completing.
89.3%Why not: Divides price by offer (50 / 56) and ignores the break price.
62.5% - correct
80.0%Why not: Divides the break price by the current price (40 / 50), which is not a probability measure.

Price = p x offer + (1 - p) x break price gives 50 = 56p + 40(1 - p), so p = (50 - 40) / (56 - 40) = 10 / 16 = 62.5%.

The hardest tier

A target trades at USD 50. A cash offer of USD 53 is outstanding and the fallback price if the deal breaks is USD 38. A fund believes the true completion probability is 90%. Ignoring time value and costs, closest to what expected return does the fund anticipate?

6.0%Why not: Counts only the return if the deal completes (3 / 50) and ignores break risk.
3.0% - correct
5.4%Why not: Scales the 6% completion return by 90% but never deducts the break loss.
-18.6%Why not: Deducts the full 12 loss from the probability-weighted gain, ignoring that the loss occurs only 10% of the time.

Expected value = 0.9 x 53 + 0.1 x 38 = 51.5. Expected return = 51.5 / 50 - 1 = 3.0%, half the 6.0% available if the deal were certain.

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