Ponyboy is able to see that the sunset is the same on both sides of town. As has been mentioned, I think it is Ponyboy's ability to empathise and walk in another's shoes that will help him move beyond the gang culture.
I also think that by writing the events for his English composition, Ponyboy is able to share his experience of being a Greaser and is opening up the intricacies of gang life to widen the understanding of how these young people live, think and get by. By sharing the story of the Soc's and the Greasers, Ponyboy promotes discussion and exploration of such groups, and may encourage support and understanding.
Ponyboy represents intelligence and sensitivity. Both are what seem to be lacking in the group. They need to reach beyond the social roles they have made for themselves. Ponyboy demonstrates this hope by leaving and trying to get away from the crime, which is actually a journey of self-discovery.
I think Ponyboy comprises the hope in this story because of his ability to transcend gang titles. Look at his relationship with Cherry Valance! It takes a deep thinker and a true philosopher to look past the surface of the names "Soc" and "Greaser." Only Ponyboy can do it. Not only does he look under the surface to discover the people on the other side, but he looks under the surface to discover the meaning of life apart from his gang. It's found in Frost's poem:
Nature's first green is gold,
Her hardest hue to hold.
Her early leaf's a flower;
But only so an hour.
Then leaf subsides to leaf.
So Eden sank to grief,
So dawn goes down to day.
Nothing gold can stay.
One more thing must be mentioned about the reason why Ponyboy can be even a symbol of hope: He is able to look beyond his own problems in order to achieve empathy for the enemy. This is an epiphany that comes to him in his conversations with Cherry, but should not be minimized. (Heck, even people NOT involved in gangs aren't usually "big" enough to be able to do this!)
Stop and smell the flowers, Greasers. Kiss a Cherry Valance or two. Why? Because nothing gold can stay.
Are you wondering why Ponyboy is like this? I agree with Post #2 as to what makes him the "hope." But what is it about Ponyboy that makes him be less likely to be like Dallas? I think you can point to the fact that he's the only one of the greasers that has (so far as we know) any sort of a loving family. I think that the support he gets from Soda and Darry is a major part of what allows him to have a good chance of success.
Ponyboy Curtis is "the hope" of the group because he is the representation of successful habits that will allow a "Greaser" to "make it" in a "Soc" world. He is the hope of the group because he is a success. He is the singular representation that a "Greaser" does not have to sacrifice his values and his beliefs in order to make it. Through him, there is hope that the Greasers can have one of their own in the position of redemptive success. Another reason why he is the hope of the group is because he does not emulate the self- destructive habits of other Greasers. Ponyboy is not going to be a Dallas, taking excessive risks and dying in a hail of bullets in front of his friends. Rather, Ponyboy understands what reality is and grasps how he is to navigate through it. Within this, he represents hope and redemption, a chance to be successful and to live a life worth living. It is here where Ponyboy resides and where his hope for the Greasers resides with him.