IMC Trading Market Making Practice Test

Example

HOW IT SCORES
One of the 13 rows is drawn at random as the winning row. Every
row is equally likely. A letter scores its own row number minus
the winning row number, and a wager pays that score in dollars
per unit.

ROW      LEFT   RIGHT
---------------------
  1      K      P
  2      F      S
  3      M      T
  4      Q      L
  5      Z      W
  6      A      R
  7      Y      U
  8      G      E
  9      O      B
 10      D      X
 11      I      J
 12      C      N
 13      H      V

What is the probability a wager on W scores at least 1? Answer as a percentage.

Answer 30.8

W scores 5 - W, so it reaches 1 when W is 4 or lower. That is 4 of 13 rows: 30.8%.

Example

HOW IT SCORES
One of the 13 rows is drawn at random as the winning row. Every
row is equally likely. A letter scores its own row number minus
the winning row number, and a wager pays that score in dollars
per unit.

ROW      LEFT   RIGHT
---------------------
  1      G      A
  2      V      O
  3      E      R
  4      I      Q
  5      K      L
  6      Y      X
  7      N      S
  8      H      W
  9      T      U
 10      Z      B
 11      M      P
 12      J      D
 13      F      C

You cannot lose more than $60 on this position under any outcome. What is the largest whole number of units of A you can hold?

Answer 5

The worst case is row 13 winning, which costs 12 a unit. 60 ÷ 12 = 5, so 5 units. Sizing on the worst case is a different number from sizing on the average.

Example

You are short 100 of the $40 calls and the stock closes at exactly $40 on expiry day. What is the problem?

• Gamma is infinite there, so the position cannot be hedged at any price.
• Nothing - at the strike they are worth zero, so they simply expire.
• You do not know how many will be exercised, so you do not know what stock position you are left with.
• The options settle in cash at the strike, so the level is irrelevant.

Answer You do not know how many will be exercised, so you do not know what stock position you are left with.

Right at the strike the options are worth nothing but the assignment is a coin flip taken by 100 different holders after the close. Short 100 contracts means anywhere from 0 to 10000 shares delivered, and the news arrives when the market is shut. Hedging to the expected assignment leaves a position either way. The real answer is to be flat well before the bell - pin risk is managed by not having it.

Example

HOW IT SCORES
One of the 13 rows is drawn at random as the winning row. Every
row is equally likely. A letter scores its own row number minus
the winning row number, and a wager pays that score in dollars
per unit.

ROW      LEFT   RIGHT
---------------------
  1      G      J
  2      X      K
  3      I      C
  4      W      L
  5      T      O
  6      V      F
  7      Y      E
  8      H      S
  9      N      Q
 10      U      P
 11      B      D
 12      A      Z
 13      M      R

A single-letter wager carries 3.74 dollars of standard deviation
per unit, because the winning row is uniform on 1 to 13.

A counterparty offers you V at minus 1, with no fee either way. What do you do?

• Sell as much as the limit allows, because minus 1 is the fair price
• Buy as much as the limit allows, because minus 1 is the fair price
• Pass. The edge is zero and each unit still carries 3.74 of risk
• Buy a small amount, because a fair price is worth 1.87 a unit in option value

Answer Pass. The edge is zero and each unit still carries 3.74 of risk

V is worth 6 - 7 = -1, which is exactly what is being quoted. Trading at fair value pays nothing and still takes 3.74 of standard deviation a unit. Variance with no edge attached is a cost.

Example

You roll a fair die 3 times. Probability of at least one six?

• 50%
• 32.1%
• 42.1%
• 0.5%

Answer 42.1%

Complement: 1 − (5/6)^3 = 42.1%. Adding 1/6 each time double-counts.