The Costs and Risks of Arbitrage

Can't hold out until the day it converges

A convergence trade bets that a spread will eventually disappear, but before converging it may widen first. Arbitrageurs using high leverage get a margin call and are forced to close at the worst moment: risk-free in theory becomes a real loss.

The two legs can't fill at the same time

Arbitrage needs several trades to fill at the same time. If even one is slow, prices may move while you wait and someone else may grab the opportunity: that's leg risk. Add the no-arbitrage band set by trading costs and counterparty risk, and "risk-free" only ever exists on paper.

Everyone crowds the same exit

The same convergence trade is often run by many firms. When one is forced to close, the selling pressure widens the spread, and the others take paper losses, get margin calls and close in turn. This is a crowded trade. In 1998 LTCM collapsed before its spreads finally converged.

Key takeaways

• Trading costs and bid-ask spreads mark out a no-arbitrage band: mispricings inside it aren't worth trading.
• A spread can widen before it converges, and highly leveraged arbitrageurs can be forced to close at the worst moment for lack of margin.
• When the two legs can't fill at the same time (leg risk), prices may move during the few seconds you're waiting.
• The more people in the same trade (a crowded trade), the more they trample each other when forced to exit.

Try it yourself

You can do these exercises in this lesson's interactive simulation:

1. In "Funding stress," keep 8× leverage and press ▶: how much was left in the account at the hardest point? How much did you make in the end?
2. Set leverage to 15× and replay: on which day are you liquidated? How much did you lose? Did the spread converge afterwards?
3. Find out: what's the highest leverage that just barely survives the days when the spread is widest?
4. Switch to "Leg risk" and drag the delay from 0 to 300 ms: how much does the chance of loss rise? How much average profit is left?

Quiz and explanations

1. An arbitrage spread will eventually converge, but first it doubles. What might a highly leveraged arbitrageur do?

Answer: Get a margin call and be forced to close at a loss.If they can't hold on until convergence, the paper profit becomes a real loss.

2. Why does nobody bother arbitraging very small mispricings?

Answer: There's no profit left after trading costs.The mispricing sits inside the no-arbitrage band, so trading it would lose money.

3. Many funds hold the same convergence trade. One of them is forced to close after losses. What's most likely to happen?

Answer: The spread is pushed wider, and the other funds lose money too.That's a crowded trade: everyone squeezes toward the same exit, the closing itself widens the spread, and losses cascade (LTCM in 1998 is the classic example).

Terms in this lesson

• convergence trade (Convergence Trade): A bet that the gap between two prices will eventually narrow; before it does, the gap may widen first.
• counterparty risk (Counterparty Risk): The risk that the other side or the platform defaults or goes bust, so the deal can't be honored.
• crowded trade (Crowded Trade): Many institutions hold the same kind of position; once someone is forced out, everyone rushes for the exit at once, widening the spread further and causing a chain of losses.
• leg risk (Leg Risk): The legs of an arbitrage can't all fill at the same moment, and prices moving in the meantime can shrink the profit or turn it into a loss.
• leverage (Leverage): Controlling a large position with a small amount of margin; 1:100 means $1 controls a $100 position.
• margin call (Margin Call): When your account drops below maintenance margin, you must add funds or your positions will be closed.
• no-arbitrage band (No-Arbitrage Band): The price range set by trading costs: when a mispricing stays inside it, arbitrage isn't profitable after costs.