A very humble thought on math in trading. I say humble because I risk straw-manning quant (look, I have yet to meet an IYI type quant that Taleb would caricature. I've been blown away by the curiousity and brains of every quant I've worked with). So with that caveat...
I look at backtests. But their useful domain feels really narrow to me. I'm not a quant so maybe it's just fear of what's over my head. I'll give an example of the type of idea that diverts my eyes from backtesty work.
I'm more attracted to ideas that are upstream of past moves. Understanding flows is an example of that.
How does it interact with backtests?
At the meta level. When I see a backtest and long histories etc my first meta question is about is N really N?
If the same dynamic governs a long time period that dynamic is driving actions. Markets are theater. There's a meta game of beliefs and narrative that cause large accounts to hit buy and sell. If the narratives and players preside over a large period is N possibly much smaller?
I'd call it statistical regime shrinkage for lack of an educated term. Stickiness may be reinforcing N but what is reinforcing the stickiness? What mandates and rules are behind the money and what makes them change.
I like learning about portfolio construction math and I like playing with simple simulations. Simple simulations are limited bc they are generated by well-behaved distributions. But they are handy for intuition.
Backtests may offer more realistic distributions but they have their own baggage in the way they can limit your view. There's a siren song of understanding in them that is easily oversold if you open yourself to it.
If I'm making a type II error it's the error I prefer
So while I certainly like to indulge looking at backtests I'm almost never getting excited about them (at least any non-short term stuff).
I'm much more interested in what holds the theater together and activates flow or a new behavior. Something durable. With boundaries.
Things that you can see change, traceable back to humans giving a directive to convert money into risk or vice versa.
Compounded returns experience "variance drain". This will be true if your bet size or allocation is a fixed percent of your wealth, savings, bankroll etc
Was messing with some coin flip stuff and got diverted by an illustration of geometric returns I figured I'd post...
First some quick intuition.
If you bet 1% of your wealth on a coin flip and win then lose, you are net down money. This is symmetrical. If you lose, then win, still down money.
1.01 * .99 = .99 * 1.01
This is compounding land
In additive or non-compounding land we bet a fixed dollar amount regardless of wealth.
So if I start with $100 and win a flip, then bet $1 again and lose the flip I'm back to $100.
The $1 I bet when my bankroll was less than 1% of my bankroll.
In @Jesse_Livermore interview he mentions how exceedingly high valuations are increasingly dependent on liquidity or what he terms "networks of confidence".
He refers back to prior work that shows how you'd need a healthy discount to intrinsic to buy an asset you couldn't sell
The fact that you can sell your at an in line price lowers your risk threshold to buy expensive assets.
And we see assets with long durations now. I think of duration as how long it would take to recoup your initial investment. Stocks and bonds have long durations today.
If these long durations are acceptable because we trust liquidity, and the idea that the market will not wake up one day and just reset at much lower multiples, it feels like risk that should be priced in an implied distribution.
They say if you do not know the fish at the table it's you. It's a good way of saying calibration matters. You don't need to be the smartest player if you find the right games. Part of being aware is being able to evaluate where others and yourself sit in a pecking order.
This leads to an interesting opportunity. You may not be the smartest but if you are above average or put special effort into evaluating who is smart you can find ways to draft in their path. I think about this a lot.
Why?
I have been lucky in life in the sense that since college I have probably been in the lower half of the room in aptitude.
(It's not false modesty...in fact I'm super lucky to have that happen -- I got a chance to become smarter and have decent jobs).
This work-in-progress is an attempt to to connect the dots into a cohesive picture of how your financial picture over your life is connected to your daily decisions as well as what you actually do with your time.