Career Acvice : non-native english speaker

Hey guys,

I just took level III exam and feel pretty confident about it this time. I have two years of investment research analyst experience and two years of emerging market equity fund manager at a boutique Korean hedge fund firm. I quit my job about four months ago and now I just started job searching. I want to use my bilingual Korean/English skills as well as my job experience to continue my career. The problem is… the company I used to work for was very small and a lot of work had to be done from scratch and on an Ad-hoc. Although I have a lot of experience here and there, it feels like I lack something that’s more common and widely acceptable in this field. I was wondering what’s the best way for me to approach to a bigger firm and which positions have more demand for bilingual CFA candidates. My English is proficient but my reading and writing is stronger than speaking. If any of you guys are working with many non-native English speakers, any tips from you will be gratly appreciated.