# How to tell if gamma on specific option in delta hedge portfolio is positive or negative

I know that the gamma for a long non derivative asset is going to be 0, since delta does not change with price of this item.

However, I am wondering how you could tell if the Gamma on the option of the stock is going to be positive or negative? How can we tell this information?

Gamma is positive.

(OK: technically, it’s positive for a long position in an option, negative for a short position. Whatever.)

The short answer: Gamma is the change in the delta as the underlying changes. For long calls/puts gamma is > 0 and short calls/puts gamma is < 0.

If you are delta hedge with a short call, then given that a stock’s delta is always 1, its gamma is 0. A delta-hedged portfolio with a long position in stocks and a short position in calls will have negative gamma exposure.

If you’re delta hedge with a long put, then you guess!

How would a short call position always have a negative gamma (even if used as delta hedge)?

If the underlying stock price fell, wouldn’t that reduce a negative delta on the stock and thus make gamma positive?

A negative change in price, a positive change in delta: positive divided by negative is negative.

How is there a positive change in delta when the price is going down? Even though this is a short position, this is still a call option, thus the delta would increase as the option becomes more in the money (as the stock price rises), and this would create a positive gamma, even on the short position

Draw a picture of a short call with a strike of, say, 50.

What’s the delta at a price of 80? You can approximate.

What’s the delta at a price of 20? You can approximate.

How much has delta changed when the price drops from 80 to 50?

Delta is higher at 80 vs. 20 @ 50 strike price.

That would imply that the delta s higher than a higher underlying price and thus make the relationship between delta and the underlying price positive.

No, it isn’t.

Did you draw a picture? Do you see the slopes (deltas)? Please post your estimates of the deltas for each price.

I drew a picture, it is essentially the opposite of the long call position. What I am confused on is in a long call position, the 80 would have a higher delta than the price at 20.

I know a short call position is different than the long call position, but the stock price at 80 would still be in the money for the counter party in the option contract. So even though we may be short the call, the overall delta on the option would still be higher at 80 than at 20 (if that makes sense).

Thanks for the help

Absolutely correct.

Looking at it from whose perspective?

You’re welcome, but note that we’re not done here yet.

How would you calculate the delta in this situation? I am not sure how you calculated the delta

I’m not asking you to calculate delta, just estimate it. Does it look like a slope of 0.1, or 0.9, or −0.2 or whatever. Just get close.

So the delta for the option at 80 would be around 0.8 and the delta of the option at 20 would be around 0.2.

Which implies that the option moves in the same direction as the underlying price (thus the delta would still be positive for a short call position).

Did you really draw a picture of a short call?

Are the slopes really positive?

ahhhh. ok I know what you mean.

Basically, from the short call position (since the payoff will be the opposite of the long call position) the delta will decrease as the option becomes more in the money.

As such, the delta in a short call would decrease as the underlying price increases, which means the GAMMA on this position would be negative.

So essentially, the gamma on a short position is going to be the exact opposite of the long position, since we are “betting” on the opposite side of the long position on a option contract.

Does this same philosophy follow for put options as well?

Bingo!