Each year, I receive a number of students that contact me by email to tell me about their interest in the Ph.D. program (a "personal admission request" kind of letter). I always have to return a note that says "All applications have to go through the formal process (the UCLA Graduate Division)." This is the brave new world we live in: everything has to go by the book. Otherwise, we would open UCLA up to law suits. It also has some rationale: We cannot treat some applicants differently from other applicants.
Admissions to the UCLA Finance PhD programs is very competitive. We usually accept only 10 out of 200 applicants. Unless a student had dramatic mitigating socio-economic disadvantages to overcome, students with quantitative test scores below the 90th quantile are better off saving their money by not applying. (We typically have 30-50 applicants with 95th quantile quantitative scores, and usually at most 1-2 of the admittees will not lie within the 95+ group.)
The next most important application aspect is relevant coursework GPA. We do not expect an A in Fine Arts and P.E., but we do expect A's in most math and economic courses. Roughly speaking, successful applicants typically rank top-5 out of 60 students in competitive prestige programs.
The next-most important application aspect are the reference letters from academic researchers whom we know and trust. Thus, having a top-school MFE degree often helps, as enrollment in such a program often helps facilitate such interactions, in addition to allowing the candidate to measure their performance against other good students. It is not too difficult to get accepted into an MFE program. Typically, 1 in 3 students gets accepted.
We do not expect an applicant to know exactly what they are planning to research, nor to write long essays about why they were longing for a finance phd since they were six years old. We are aware that most of this prose is nonsense.
(PS: Now that I have written and posted this, consider a 'personal admission request letter' to be a negative. It simply means that you did not bother reading my web pages before you wasted my time with a pro-forma email.)
Ranking of PhD Programs in Finance
The following is merely my personal opinion.
If I were trying to judge PhD programs, I would ask how many students they enroll, how many they graduate, and where they go to. Then I would reverse this by looking at various top universities to find out where their faculty graduated from. I would care only at graduates from the last 10 years.
If your interests are very technical (mathematical), then there is one standout school: Stanford. Otherwise, there are a cloud of schools that are all very good. In no particular order (west to east?): UCLA, UC Berkeley, Stanford, Chicago, Northwestern, NYU, Princeton, Yale, Harvard, MIT, NYU, Columbia, Duke. Another 10-20 schools produce PhD students that can end up at the top universities every so often: USC, UCSD, UIUC, Cornell, Rochester, LSE, LBS, Insead, Swiss Finance Institute, Carnegie, Washington, UBC, Toronto, Florida, Arizona, etc.
The PhD program does not have to be a finance program. Econ programs often produce students that become finance faculty, too.
Visiting Another PhD Program
It is an unusual but not a bad idea for an enrolled PhD student to visit another program for no more than one semester. This should be arranged via inquiry by the advisor of the student, not the student himself/herself.