How Can a Synthetic Future Be “Delta-Neutral” at the Money?

A synthetic future is created by combining a long call and a short put with the same strike price. At the money, a European call option has a delta of approximately +0.5, and a European put option has a delta of approximately -0.5.

When you buy the call (+0.5) and sell the put (-(-0.5) = +0.5), the total delta of the long synthetic future is approximately +1.0, not delta-neutral. A delta-neutral position would require a different combination, such as a long put and a short call (short synthetic future) combined with a long position in the underlying.