I just use math, so I guess I just need one.
More seriously, for most fundamental analysis, you need these things:
- Arithmetic
- Algebra
- (A decent B.S. detector, but that’s not mathematical, necessarily)
That’s about it for fundamental analysis, although it also helps if you have an understanding of:
- Simple Statistics (mean, standard deviations, confidence intervals, basic linear regression)
- Basic Probability
- Simple Calculus
If you are doing portfolio construction, then it’s good to add
- Linear Algebra
- A deeper understanding of probability
- Optimization (minimum/maximum) processes
If you are doing macro analysis or attempting forecasting, you are going to want:
- Econometrics / time series analysis
If you are pricing derivatives you should add
- Monte Carlo Methods
- Advanced Probability
- Stochastic Calculus (though only the applied part is really necessary)
- Possibly some more advanced stuff like real analysis (behavior of real functions, etc)
The more exotic the derivatives are, the further the mathematics required. But at a certain point, the noise inherrent in human systems overwhelms the ability to use mathematics for rational analysis.
Fixed income tends to be more mathematical than equities, because in fixed income, the future cash flows are better defined, so you can treat them as numbers to do mathematics on. In equities, future cash flows are all estimates, which means they have a lot more noise, and therefore there are fewer calculations you can do with them before the noise just blows up and becomes unmanageable. You end up having a number, but the error bars are so wide as to be meaningless.
And yes, I do understand that “maths” is an abbreviation for “mathematics,” which is plural. ;-)