Should i submit a stock analysis?

Should I submit a stock analysis, or something along the same lines, when applying for a job which runs concurrently with my studies (masters in finance)? I am from Denmark, so this might be different in the U.S., I don't know. I have an average GPA from my bachelor (I believe undergrad in the U.S), no financial experience, and I have completed the WSP self study course, which is why I wonder, if an stock analysis would help my case? - Also, is it best to mail my resume to the CEO, standard company mail, recruiters mail if available or a fourth option?

The firms I plan to apply is small investment firms (the majority of them are way smaller than "boutiques"), which mostly concentrate on equity. I am applying in Denmark, so keep in mind, that this is no where near as competitive as the U.S. --> I believe that I have a shot.