Delta neutral position

An option position on its own moves with the underlying, just not one-for-one — that ratio is its delta. A delta neutral position takes that same option position and adds an offsetting position, sized precisely by delta, so the combined position stops moving with the underlying at all, at least for small price changes.

The workbook's own words, describing exactly this construction: "the delta of the combined position (short call and long futures) is equal to zero. This position is called a 'delta-neutral' position."

The workbook builds delta neutrality from a short option position hedged with futures:

1. Start with the option position's delta. If a trader is short 10 lots of at-the-money call options, lot size 50, and the call's delta is 0.50, the position delta is −0.50 × 50 × 10 = −250. A one-rupee rise in the underlying would cost the trader Rs 250 on this short call position.
2. Offset it with futures, whose delta is roughly 1. Since a stock futures contract has a delta of about one (the futures price moves hand in hand with the spot price), going long 5 futures lots of 50 each gives a futures position delta of +1 × 50 × 5 = +250.
3. Net the two together. −250 (short calls) + 250 (long futures) = 0. The combined position is delta neutral: a small rise in the underlying causes a loss on the short calls that is exactly offset by a gain on the long futures, and vice versa for a small fall.

Why "small" matters. Delta itself changes as the underlying moves — a call's delta might rise from 0.50 to 0.60 as the stock rallies. When that happens, the combined position is no longer delta neutral (the short calls' delta grows to −0.60 × 50 × 10 = −300 against a still-fixed +250 of futures), and the trader must add another futures lot (taking the futures position to 6 lots, delta +300) to restore neutrality. This continuous process of rebalancing to keep the combined delta near zero is called delta hedging, and it is the mechanism by which a delta neutral position is maintained, not just built once.

A trader is short 10 lots of ATM call options on a stock trading at Rs 100, lot size 50, with the call's delta at 0.50.

Short call position delta = -0.50 x 50 x 10 = -250

To neutralise: long futures delta needed = +250
Futures delta per lot (lot size 50)       = 1 x 50 = 50 per lot
Futures lots required                     = 250 / 50 = 5 lots

The trader goes long 5 futures lots. Combined position delta = −250 + 250 = 0 — delta neutral.

The stock rises to Rs 110. The call's delta increases (as calls do when the underlying rises towards or past the strike) from 0.50 to 0.60.

New short call position delta = -0.60 x 50 x 10 = -300
Existing long futures delta   = +250
Net delta                     = -300 + 250 = -50   <- no longer neutral

The position is no longer delta neutral — it now behaves like a small net short position. To restore neutrality, the trader adds one more futures lot, taking the long futures position to 6 lots:

New futures delta = +1 x 50 x 6 = +300
Net delta          = -300 + 300 = 0   <- delta neutral again

This buying and selling of futures to keep the combined delta near zero, repeated every time the underlying moves enough to shift the option's delta, is delta hedging — a delta neutral position is a snapshot that constant hedging keeps re-establishing, not a static state.

Chapter 5 (Strategies using Equity Futures and Equity Options), section 5.4 (Delta-hedging), builds the delta neutral position step by step with the short-call, long-futures example above, drawing on the delta concept introduced in Chapter 4's treatment of Option Greeks. Expect a computation question — given an option delta, lot size and number of lots, calculate the number of futures lots needed for delta neutrality — and a follow-up question on why the neutrality does not persist as the underlying moves.

• Delta neutral means the combined position's net delta is zero — it does not mean risk free. The position remains exposed to gamma (delta itself changing), theta (time decay) and vega (volatility changes); only the small-move, first-order price risk is offset.
• "Small" changes only. The workbook is explicit that a delta neutral position is unaffected by small changes in the underlying — a large move changes the option's delta enough that the hedge is no longer accurate, which is exactly why delta hedging is a continuous process.
• A futures contract's delta is roughly 1, sized in lots — the number of futures lots needed is the option position's delta magnitude divided by the futures delta per lot, not simply equal to the number of option lots.
• When the underlying moves, the option's delta itself changes, which then requires more or fewer futures lots to stay neutral — this is the rebalancing that delta hedging describes, and it is what separates a delta neutral position (a snapshot) from delta hedging (the ongoing process).
• Do not confuse this with a directional hedge, such as simply buying futures against a cash holding — a delta neutral position specifically zeroes out the combined delta of an options-plus-underlying (or options-plus-futures) book, calculated position by position.