How to solve Orderbooks questions

Each board shows bids and asks for A, B and the bundle A+B. Find the trade that locks in a risk-free profit, or say there is none. Press 1 to 6.

How to solve them

1. Cue: three prices that should be linked: A, B and the bundle A+B. A bundle should cost about the sum of its parts.
2. You sell at the bid and buy at the ask. Never mix them up.
3. Check 1: A bid + B bid compared with A+B ask. If you can sell the parts for more than you pay for the bundle, buy the bundle and sell the parts.
4. Check 2: A+B bid compared with A ask + B ask. If you can sell the bundle for more than the parts cost, sell the bundle and buy the parts.
5. Check 3: any single book where the bid is above the ask is crossed. Buy at the ask and sell at the bid.
6. Speed: only add small numbers. 20 boards in 8 minutes is about 24 seconds each. If no check shows a gap, answer "No arbitrage".

Worked examples

• Which trade locks in a risk-free profit?

  	Bid	Ask
  A	41	45
  B	12	15
  A+B	49	50

  1. No arbitrage
  2. Buy A+B, sell A and sell B
  3. Sell A+B, buy A and buy B
  4. Buy A at the ask, sell A at the bid
  5. Buy B at the ask, sell B at the bid
  6. Buy A+B at the ask, sell A+B at the bid
  Answer: Buy A+B, sell A and sell B

  1. Check 1: A bid + B bid = 41 + 12 = 53. A+B ask = 50. Gap = 3.
  2. Check 2: A ask + B ask = 45 + 15 = 60. A+B bid = 49. Gap = -11.
  3. Check 3: bid minus ask for A, B and A+B = -4, -3, -1.
  4. A positive gap is a profit: Buy A+B, sell A and sell B locks in 3 per unit.

• Which trade locks in a risk-free profit?

  	Bid	Ask
  A	21	26
  B	8	11
  A+B	30	36

  1. No arbitrage
  2. Buy A+B, sell A and sell B
  3. Sell A+B, buy A and buy B
  4. Buy A at the ask, sell A at the bid
  5. Buy B at the ask, sell B at the bid
  6. Buy A+B at the ask, sell A+B at the bid
  Answer: No arbitrage

  1. Check 1: A bid + B bid = 21 + 8 = 29. A+B ask = 36. Gap = -7.
  2. Check 2: A ask + B ask = 26 + 11 = 37. A+B bid = 30. Gap = -7.
  3. Check 3: bid minus ask for A, B and A+B = -5, -3, -6.
  4. No gap is positive, so there is no risk-free trade.

• Which trade locks in a risk-free profit?

  	Bid	Ask
  A	18	23
  B	59	63
  A+B	80	82

  1. No arbitrage
  2. Buy A+B, sell A and sell B
  3. Sell A+B, buy A and buy B
  4. Buy A at the ask, sell A at the bid
  5. Buy B at the ask, sell B at the bid
  6. Buy A+B at the ask, sell A+B at the bid
  Answer: No arbitrage

  1. Check 1: A bid + B bid = 18 + 59 = 77. A+B ask = 82. Gap = -5.
  2. Check 2: A ask + B ask = 23 + 63 = 86. A+B bid = 80. Gap = -6.
  3. Check 3: bid minus ask for A, B and A+B = -5, -4, -2.
  4. No gap is positive, so there is no risk-free trade.

Firms that test this

Optiver

All guides