By Craig Bewick
MAY 24 2021

In Thursday’s Question of the Day, we asked how many Micro WTI Crude Oil futures contacts would one have to buy or sell to achieve a near delta-neutral position if they had sold two 40 Delta Calls.  As we know, Delta represents the amount that the value of the option would be expected to move given a one point move in the futures.  As such, Delta represents the “futures equivalent” exposure of the options position (Delta is also used as the probability that an option will end up in the money at expiration but we will use Delta in the context of “futures equivalent” for this question).

Therefore, a 40 Delta Call would be expected to move .4 points for every one point move in the futures market.  A futures position is said to have a delta value of 100 (when deltas are represented as a decimal, the future would be represented with a delta value of 1; when deltas are represented as a whole number, the future would be represented with a value of 100).  The other element of this question is whether the position is long or short.  Many traders think of long futures positions with a positive sign, short futures positions with a negative sign, Calls as positive and Puts as negative.  In this context, the following is true (using your old Algebra skills):

• Long futures position is positive
• Short futures position is negative
• Long Call is Positive  (+ * + = +)
• Short Call is Negative (- * + = -)
• Long Put is Negative (+ * - = -)
• Short Put is Positive  (- * - = +)

So, if a trader sold two 40 Delta Calls, they would assume an overall Delta position of -80 (remember, a short Call is negative as we just went over and because the position has 2 Calls, you’d simply multiply -40 Delta position by two to get -80).  In order to delta hedge this position then (and achieve a delta neutral position) a trader would need to offset the -80 delta.  In the absence of the upcoming Micro WTI Crude Oil futures product, the trader would not be able to precisely delta hedge this position using futures because buying 1 standard size WTI Crude Oil futures (CL) product would result in a Delta position of +20 (futures position has a Delta value of +100 plus the -80 Delta in the options position equals +20).  However, since the new Micro WTI Crude Oil futures product effectively has a Delta value of 10 relative to the standard size product (again, ignoring any differences that might result from the one day difference in expiration date), the trader could effectively hedge their position by buying 8 (+8*10 = 80) Micro WTI Crude Oil futures.  Therefore, the answer is D.