Moment Js UTC to Local Time

I’m trying to convert UTC time to the local time. I’ve been following this example from this link: http://jsfiddle.net/FLhpq/4/light/. I can’t seem to get the right local output. For example, if its 10: 30 am in here, instead of getting 10:30 ill get 15: 30. Here is my code:

var date = moment.utc().format('YYYY-MM-DD HH:mm:ss');

var localTime  = moment.utc(date).toDate();

localTime = moment(localTime).format('YYYY-MM-DD HH:mm:ss');

console.log("moment: " + localTime);

No matter what I do the time always comes out at UTC time. I live in Houston so I know timezone is the issue. I’ve followed the code in the link but can seem to get the local time. What am I doing wrong?