Limited Arbitrage in Equity Markets
In this paper, the authors, Mark Mitchell, Todd Pulvino and Erik Stafford, illustrate the limits of arbitrage in equity markets using discrepancies between the market values of a parent company and its subsidiary. If the value of the parent company is smaller that its stake in a traded subsidiary (a negative stub value), there should be an arbitrage opportunity by going long the parent company and short the subsidiary.
They show that these opportunities are however not riskless because of:
- Uncertainty of the nature of the mispricing and of the expected payoff can restrict arbitrage activities
- Undiversified arbitrageurs who need to specialize to gain expertise are exposed to idiosyncratic trading risk and might not be fully invested.
- The timing of trade convergence is often uncertain
- Some trades do not converge before a breakout of the link between a parent company and its subsidiary
- Financing risk: because of the volatility of returns, the amount of required collateral (margins) to insure against large losses can undermine the profitability of these trades.
They use pairs of companies with negative stub value between 1985 and 2000. Data come from CRSP, Datastream and SDC.
The negative stub value is defined by either:
- Rule 1: The market value of the company stake in its subsidiary is larger than the market value of the company itself (70 pairs)
- Rule 2: The sum of the market value of the company stake in its subsidiary and the book value of non-subsidiary assets is larger than the market value of the company itself (82 pairs)
The trades are implemented using entry and exit rules, some financial leverage and margin requirements.
They explore three different types of leverage:
- A textbook leverage based on a percentage of initial investment (Regulation T initial margin, 50% of the long investment and 50% of the short position) and not maintenance margin calls
- A textbook leverage based on a percentage of initial investment (Regulation T initial margin, 50% of the long investment and 50% of the short position) with maintenance margin calls (25% of long positions and 30% of short positions, mark-to-market, margins met by liquidating assets).
- A perfect foresight leverage, with a amount sufficient to avoid margin calls
The authors discuss in detail the different risks of the trades:
- Fundamental risk (risk of no convergence)
- Financing risk:
o Uncertainty of the timing of the convergence or horizon risk,
o Margin risk
o Inability to maintain a short position or buy-in risk (lenders of shares ask the shares to be returned)
o Specialization of the arbitrageur
They argue convincingly that such strategies are rarely implemented on their own but are combined in special situation funds so that the financing risk is reduced. Why do these negative stub values seem to persist? It is most likely because of the imperfect information on the distribution of returns of these arbitrage trades combined with the previously mentioned risks.
Mark Mitchell, Todd Pulvino, Erik Stafford , “Limited Arbitrage in Equity Markets”, The Journal of Finance, Vol. 57, No. 2 (Apr., 2002), pp. 551-584