1 - Finance and Maths

Paul Volker, Ex chairman of US Fed in 2010, after financial crisis declared that the only useful financial innovation in 25 years was ATM that helped  people on the ground and others were of no use. He is the one who is credited for breaking the backbone of inflation in US as Fed Chairperson in early 80s.

Robert Shiller, Nobel Laureate, tends to disagree. He says financial innovation is evolving and there could be some loopholes. It will get plugged as it evolves. Sure, the instruments are getting complex but we have sophisticated system to handle the complexity. He bats for more innovative products to plug the current loopholes.

There are concerns expressed if top brains of a nation should be dedicated to finance industry in huge number rather than some other domain , say technology or healthcare.

Any major project you can think of, be it railways, hospitals etc, is financed through equity/debt or held by Government. Even many privately held firm will have their capital raised through venture capitals or through debt. Financial activities are enablers for economic activities.

Finance extensively uses Maths. If you want to calculate how many years it will take for your investments to double in value,
you need to solve compound interest formula P*(1+i)^n = 2P
to arrive at n = log 2/log (1+i) years where i would be your rate of return or interest on your investments.

(You might have heard  Rule 72. you need to have  approx  n=72/i years to double your money at i% of interest/rate of return. For example , at 10 percent annual interest rate, it takes 7.2 years to double your amount)

I don't think any other domain that common people face every day, that mathematics like logarithm comes into picture so naturally like it does in finance. (How logarithm evolved 400 years back and how calculators and computers compute log would be another interesting topic, for mathematically inclined.)

If your portfolio has grown 10% for the first year, on top of that 20% percent for the second year, 30% for the third year what would be the average rate of annualized return?
A one rupee investment would have made 1.1 at then end of first year, 1.1*1.2 at the second year end, 1.1*1.2*1.3 at the third year end.
We want to find what would be equal annual compounded return
       

P(1+i)^3 = P(1.1)(1.2)(1.3)
 i =cube root(1.1*1.2*1.3) -1

The first term is nothing but Geometric mean. Can we think of Geometric mean in real life in any other domain occurs so easily?

Finance is related to nation's economy(macro). You often need to deal with huge numbers. You need to deal with fractional numbers. Macro is related with public policies which is related to politics. Finance is also related to human behavior, psychology. In the Black Scholes model of option pricing , they deduce option pricing to heat transfer equation to solve the PDE. So, It is related to (makes use of) physics as well :)

Thanks for your interest.