Taylor Expansion

Think fast
Trading is fast. In trading interviews (with the exception of Citadel and Optiver), studying 'higher' mathematics is considered nearly useless. After all, what does a deep thinker have in common with a successful trader? Working on discipline or training your nerves is much more likely to lead to profits than developing a new strategy. What a mathematician may understand with a lot of work, the trader will feel.

The privilege of having a blog is the ability to say whatever I like. Math is incredibly helpful to gain intuition. Math may be more precise than feeling, but it's not the precision that I am emphasizing.

Estimating your wealth
Let's assume the adage that money makes money. In fact, a universal power has decided that your wealth will be given by f(x) = x*x or x squared, where x is your age in years and f(x) is your wealth in euros or dollars. You at 21 years old right now and you are making 42,000 a year. How rich will you be by the time that you are thirty? (please refer to the top picture)

In words
You could assume of course that you will be making 42,000 for the next couple of years. You would be saying, let's discard the higher order effects, like acceleration of salary. Your wealth is where your salary is coming from, where it derives from. Your salary is the first derivative of wealth because it is the first order effect that directly affects your wealth. With this approximation in mind, you can make the first calculation (see second picture). I will make forty two thousand every year for the next nine years so I will make 378,000. That means if I starting with 441,000, my wealth will be 819,000 by the time I am thirty.


In Math
f ' (x) = 42,000 every year (every 1 x that goes by)
f '' (x) = assumed to be 0
f (21) = 441,000
f(30) = f(21) + 9* f ' (21) = 819,000

Damn it
I know what many of you are thinking: 'igor, I want you to make more money since you have such a nice blog. After all, you don't even have any advertising on your site.' I have to go to work to make our next assumptions more probable.

In the next post, I will finish the example and introduce taylor's theorem to help us do the math in a second instead of belaboring the point.