The curriculum for the first year of a Ph.D. program in economics is quite standard across universities (at least, within the US): two semesters of microeconomic theory, two semesters of macroeconomic theory, and two semesters of econometric theory. The level of mathematics you would need would vary depending upon the school, but it is safe to say that you would need some understanding of real analysis in order to get through the more theoretical parts of the program. The top programs would typically teach this to you in a "math camp" during the summer immediately before the program begins, or during the first semester alongside the above courses.
You might not even cover any finance at all in the first year of such a program. Economics is a very broad field, and finance / financial economics is but one specialization among many. Even if you are doing a Finance Ph.D. at a university which offers such a degree through their business school, for the first year of that program they would likely send you across the street (or wherever) to sit in the same first-year classes with the much larger group of Economics Ph.D. students in the Arts & Sciences division.
What you would learn in an MFE program is quite different: you would probably have two semesters of real analysis/probability/stochastic calculus and two semesters of numerical methods / partial differential equations, in addition to courses on financial instruments, etc. You would probably do a lot of programming in
C++ or similar languages which are applicable to creation of production-quality code at the firms which may eventually employ you. In an Economics Ph.D. program, what programming you do would more likely be using packages such as Stata, Matlab, Eviews, and perhaps R or S-Plus, depending on the preference of your instructors.
Another key difference between the programs is the following:
With an MFE, the program is expecting you to get a job, hopefully a good job at a prestigious firm, where you will (hopefully) earn a lot of money and, if you are feeling generous, you may donate a bit back to your alma mater. Also, you will hopefully rise up in the ranks at your firm to the level where you will eventually be able to hire some future MFE graduates from your school. The "placement statistics" of alumni from such programs into well-paying positions is a key metric of success for such programs.
For a Ph.D. program, especially a "top economics program" as you have indicated you seek to enter, the goals and metrics of success are quite different. People who are selected for such programs must demonstrate a commitment to a career in academic research.
First, they will want you to create a dissertation (which will be composed of three papers) where one or more of the individual papers can eventually get published in a prestigious journal (perhaps with your Ph.D. advisor's name as co-author.) The ultimate metric of success is your getting papers published in a handful of top journals (such as American Economic Review, Journal of Political Economy, or Econometrica). If finance is your specialization, then the top journals include Journal of Finance, Review of Financial Studies, and Journal of Financial Economics.
They will want you to get hired as an assistant professor at a prestigious university, which brings prestige back to them. Look at a listing of where the recent Ph.D. graduates have been placed from the programs you are considering. If you can't get hired into a top-tier academic position (perhaps because no one is recruiting the year you are completing your degree, or because there are simply other candidates who are better than you) then they would also tolerate your taking a research position at an organization such as the Federal Reserve (either the board of governors, or one of the various banks) or at the World Bank.
If those economics Ph.D. programs have any inkling that, after 5 years of training at their expense (because at the top schools you would not pay any tuition, and you would be paid a fellowship stipend) your real goal is to get hired by Goldman Sachs and make a fortune, they will not offer you a place on their program. Instead they will admit someone else. So, if working at a hedge fund or a bank is indeed your real goal, you have to completely hide such aspirations if you want to have any hope of getting admitted to such a program.
So, what you would learn on an MFE program is very different from what you would learn on an Economics Ph.D. program.
On the other hand, if you are seeking a Ph.D. program which would come much closer to covering what you would learn on an MFE program, I would suggest that you look at various programs in fields like Operations Research or Management Science, which do have a lot more in common with the content of the MFE program than you would find in an Economics Ph.D.
Good luck!
