I'm a new comer to this bbs, but I'm not a beginer in finance. After viewing many posts in this bbs, i'm surprised to find people here attach so much importance to mathematics, and they always concern about what math i should learn to begin my study in finance. Is is a right way to learn finance? I think maybe I need to write a post to share some of my experience, and try to answer this question by my own way. Comments and suggestion are welcome
The basic principle in finance is NO ARBITRAGE. The weaker principles are optimality and equilibrium. Under these principles, we can devide finance roughly into three parts: asset pricing, corporate finance and derivatives.
Derivatives or so called financial engineering involves most mathematics, talking about option pricing etc. They are very popular in 1980's. But nowadays, it's very hard to publish these kind of papers in Journal of Finance. The reason is most basic theoretical problems in this area have already been solved, the remaining problems are mathematical or practical ones. Finance professors are not interested in these problems, they think this is the job of mathematicians or companies. Of course there are still a lot journals in this area such as Mathematical Finance, and many professor specialize in this area. But most professors are from math or physics. If you look at the composition of the faculty in U. of Chicago or NYU, most of them are not in this area.
Asset pricing is an area also requires a lot of maths. But the tools it requires are not very advanced. Most tools they use are still on the undergraduate level, except you need some special techniques in economics such as optimization. Some of the problems in asset pricing may need stochastic calculus, but they are theoretical. In fact 90% professors are working in empirical area. Only some professors in top US universities are working on theorectical problems. That is to say you do not need to learn a lot of maths, such as stochastic calculus, advance theory in probability or even real analysis. Even you encounter these math problem in your future research, the best way is to find a co-author, rather study by yourself. For reading most textbooks, undergraduate maths is enough. If you find a part you cannot understand because of math, just ask the math people or find related textbook. Do not try to learn all nessecary math before your reading of finance books, you can learn the math during your study of finance. Cochrane said in the preface on "Asset Pricing": The hurdles in asset pricing are really conceptual rather than mathematical.
Corporate finance is the part makes least use of maths. But since it borrows a lot theories in economics such as game theory, information economics, contract theory, you still should know some maths. This part becomes more and more hot recently, and personally i believe this part should be the most promising in China. The reason is there are still a lot of unsolved basic problems in this area. And for different countries, we can have different solutions. So researchers in China can have a lot publishing oppotunies in the international journals.
In all, what i'm argueing is that idea or intuition is always much more important than methods. Math or econometric method is useful, but they should serve for the your ideas or models. You should think more about why there is a financial market, why there is a firm, how the financial market works, how the firm makes financial or investment decisions. You can always borrow analytical tools from the econ or math people.
I recommend a book to you:
Financial Markets and Corporate Strategy written by Grinblatt and Titman, published by Tsinghua University 2002. This is a book full of intuition. Try to find your interests in finance first, then choose which topic you want to work, and then choose how much math you should know. The order should not be inversed.
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