A company's stock trades at $47. An acquirer has announced a deal to purchase it at $50 per share. If the deal fails, the stock is expected to fall back to $32. An arbitrageur believes the true deal completion probability is 90%. What should she do?
AAvoid the trade — the spread is too small to justify the risk
BBuy the stock, because her estimated fair value ($48.20) exceeds the current price ($47)
CShort the stock, because the deal will probably close and the spread will collapse
DBuy the stock regardless of probability estimates, because announced deals always close
Fair value = p × deal price + (1-p) × break price = 0.90 × $50 + 0.10 × $32 = $45.00 + $3.20 = $48.20. Since $48.20 > $47, the arbitrageur believes the stock is undervalued relative to her probability estimate and should buy. If she believed the completion probability were only 75%, fair value = 0.75 × $50 + 0.25 × $32 = $37.50 + $8.00 = $45.50 < $47, and she should not buy. The formula makes explicit that the trade depends entirely on whether your probability estimate exceeds the market's implied probability.
Question 2 Multiple Choice
The payoff profile of a typical merger arbitrage position is best described as:
ASymmetric — similar-sized gains and losses with equal probability
BNegatively skewed — small frequent gains when deals close, large occasional losses when deals fail
CPositively skewed — small frequent losses while waiting, large gains when deals close
DRisk-free — the deal price is contractually guaranteed, so there is no downside
Merger arbitrage has a classically negatively skewed payoff: the gain (spread) is small — perhaps $3 on a $47 investment — while the loss (collapse back to pre-announcement price) is large — perhaps $15 on the same investment. When deals succeed (the common outcome), the arbitrageur earns the spread. When deals fail (rare but possible), the loss is 4-5× the potential gain. The strategy earns a positive expected return because it compensates investors for bearing this asymmetric, concentrated loss risk. It is decidedly not risk-free.
Question 3 True / False
The merger spread — the gap between the target's current stock price and the announced deal price — reflects the market's aggregate estimate of the probability that the deal will not close.
TTrue
FFalse
Answer: True
The spread is precisely this: V = p × deal_price + (1-p) × break_price. If you observe the current price and know the deal price and a reasonable break price, you can back out the implied completion probability p. A wider spread implies lower market confidence in deal completion; a narrow spread (stock near deal price) implies high confidence. Arbitrageurs compare their own probability estimate against the market's implied probability — if they believe the deal is more likely to close than the spread implies, there is an edge to exploit.
Question 4 True / False
Experienced merger arbitrageurs spend most of their time on fundamental equity valuation of the target company to assess whether the deal price is fair.
TTrue
FFalse
Answer: False
By the time a deal is announced, fundamental valuation is largely done — the acquirer and its bankers have determined what the target is worth and priced the offer accordingly. The arbitrageur's edge comes from accurately estimating deal *completion* risk: regulatory hurdles (antitrust precedent, sector-specific approvals), financing risk (credit market conditions, debt covenants), shareholder vote dynamics, and MAC clause interpretation. These require expertise in regulatory law, credit markets, and deal documentation — not primarily in forecasting the target's earnings or cash flows.
Question 5 Short Answer
Why does the merger spread not represent a 'free lunch' or risk-free arbitrage, even though the deal price is publicly known?
Think about your answer, then reveal below.
Model answer: Because the deal might not close. If the deal fails — due to regulatory rejection, financing collapse, shareholder opposition, or a MAC clause invocation — the target's stock collapses back toward its pre-announcement price, which is far below both the deal price and the arbitrageur's purchase price. The spread compensates for this deal failure risk: the expected loss on failures must be offset by the accumulated gains from successful deals. The strategy earns positive returns only when the arbitrageur's estimate of completion probability is more accurate than the market's implied probability. It is a risk premium, not an arbitrage.
Classic arbitrage means a riskless profit — buy low, sell high simultaneously with no possibility of loss. Merger arbitrage is misnamed by this standard: it bears real risk of large losses and requires skill to execute profitably. The persistence of the strategy's returns is evidence that it provides a genuine service — bearing concentrated deal-failure risk that diversified investors prefer to avoid — and is compensated accordingly.