Read MoreIPOs all wet as tidal wave of new offerings loom
Restaurant chains that have gone public in the past 12 months have had mixed fortunes on the stock market.
Shares of Zoe's Kitchen, a Mediterranean-style chain, have nearly doubled since their debut in April on the back of strong demand for healthier food, a trend that has also boosted Chipotle Mexican Grill's stock.
But pizza chain Papa Murphy's Holdings and sandwich maker Potbelly, which are striving to improve their market share in a highly competitive sandwich and pizza market, are both trading below their IPO price.
"We're not planning to be the next Chipotle. We will be a great El Pollo Loco,'' CEO Steve Sather told Reuters.
Read MoreCramer: Chipotle, McDonald's telegraph food trends
El Pollo Loco fire-grills its chicken in an open kitchen, allowing diners to see their meals being cooked. Since opening its first restaurant in Los Angeles in 1980, the chain has grown to more than 400 branches across the southwestern United States.
The Costa Mesa, California-based company says it combines the convenience of quick service with the quality of food expected of fast-casual chains.