# Delta hedging - rebalancing

When using shares to delta hedge a long call option position, after a rise in the underlying share price, the hedger will need to rebalance the position by: A. increasing a short stock position. B. reducing a long stock position. C. reducing a short stock position.

The correct answer is A. Any idea why B wouldn’t work?

It’s Wiley’s free mock, so maybe there’s no explanation.

A delta hedge requires the opposite underlying position from the option position. You would not use a long stock position in the first place.

Mathematically,

Ns = -delta * Nc (Ns = Number of shares, Nc = Number of call options)

If the underlying share price increases in value, delta for call option will increase now. Number of call options (Nc) is fixed. This implies to maintain delta hedge, more number of stocks to short.

But if you had a long stock position in the first place – you later decided to delta hedge – this certainly would work.

It’s not a well-thought-out set of answer choices.

This math won’t work on AM 2012:

Delport needs to sell shares in the underlying equity.

“By selling put options to his client, Delport is net long the underlying equity. Therefore, the hedge needs to be a short position. He must sell shares to hedge his exposure.”

Therefore, Pintoj seems to be right. I used same math logic as you before.

Good find. I prefer the CFAI material over 3rd party mocks. This would likely solve the problem.