I want to solve this problem and make a post out of it.
The puzzle:
A gambler has a 10% edge (60% win) and starts with $100 in a game of winning the amount risked or losing it. He uses the Kelly fraction to bet. What’s the probability (3% error) that in the course of playing 400 games the equity will drop to $10 (stopped out)?
BTW, for those who would like to simulate but are not familiar with the Kelly fraction, it is equal to K% = p-(1-p)/R, where p is the win probability and R is the payoff ratio. In this case, R =1, p = 0.6, and the Kelly fraction is 0.2, or 20% of equity risked at every step.
Michael Harris (Weekend puzzle)
This puzzle is inline with something I wanted to experiment. Which is about the advantage study on a similar problem. Like when people talk about Roger Federer 53% average point win made him the best.
I need to understand why it works. Someone on Reddit said to not use HMM, don’t know why.
DON’T use an HMM.
Start from hypothesis about why momentum might fundamentally drive some excess returns (ie attention, psychology) have an edge and what it is. Google frog-in-the-pan effect. Quants might use some sort of linear factor model return decomposition, removing the influence of sector, value, size factors from the returns. Then study the residual after that and see what went up the most over various lookback windows. You could also look at vol adjusted returns, outlier adjusted returns, seasonality adjusted, etc. You could look at things things like autocorrelation, moving average crossovers / differences.
This is my current book wishlist, I intend to update it regularly, maybe bring detailed comments on the books I read.
General
Topic
Title
Author
Luck
The Serendipity Mindset
Christian Busch
Entrepreneurship
A Busca
Jorge Gerdau
Finance
Topic
Title
Author
Factor Models
Portfolio Risk Analysis
Gregory Connor
Macro-level risk management
The Illusion of Control
Jón Daníelsson
Quantitative Finance
Quantitative Portfolio Management
Michael Isichenko
Mathematics
Topic
Title
Author
Comments
Probability
Probability, 5th edition
Rick Durrett
Probability
Probability with Martigales
David Williams
Must have, but I still don’t
Probability
The Fundamentals of Heavy Tails
Jayakrishnan Nair
Stochastics
Applied Probability Models
Sheldon Ross
Self Christmas gift
Functional Analysis
Optimization by Vector Space Methods
David G. Luenberger
Functional Analysis
Linear Analysis, 2nd edition
Béla Bollobás
Looks interesting but not enough
Machine Learning
Foundations of Machine Learning, 2nd edition
Mehryar Mohri
Amazing mathematical formality within this Buzzword topic. Covers a wide range of topics and it’s worth acquiring despite being too expensive. I am accepting as a gift.
Convex Optimization
Convex Optimization
Stephen Boyd
500 pages of bookshelf decoration, I prefer Mr. Boyd open lectures