Talk at the quantopian Boston meetup
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The document explores various financial fallacies, particularly focusing on the St. Petersburg game and the misinterpretation of logarithmic returns in finance. It critiques well-known financial strategies and concepts like the Sharpe ratio and highlights the importance of understanding the Kelly criterion for optimal betting strategies. Additionally, it discusses the Martingale strategy's pitfalls and the systemic issues in the finance industry related to risk management and investor behavior.
Talk at the quantopian Boston meetup
- 1. Financial Fallacies Igor Rivin (Temple U/Brown U/Meteque Holdings)
- 2. Fallacy I “A dollar is a dollar”
- 3. A dollar is a dollar?
- 4. A dollar is a dollar? Depends to whom. The question was first analyzed by Daniel Bernoulli back in 1735, prompted by his cousin Nicholas Bernoulli’s St Peterburg game paradox.
- 5. St Petersburg Game I offer you a game: I flip a fair coin. If it lands heads, I pay you $1. If it lands tails, we flip again, and if it lands heads, I pay you $2. If it lands tails, flip again, and if it lands heads, I pay you $4, and so on. Now, how big an entry fee will you pay to play this game?
- 6. St Petersburg game Easy to compute that the expectation is infinite! Will you give me all your money?
- 7. St Petersburg Game Empirically, the answer is a resounding NO! And it is unlikely that anyone will pay more than $10 or so to play. Why? Bernoulli’s thesis is that if Peter has $100000, and Paul has $1MM, then $10000 is worth about the same to Peter as $100000 is to Paul.
- 8. A dollar is a dollar? An example: a 10% per year return is viewed as a steady return. A $100000 per year return is strange. Bernoulli’s example: insurance. If you insure your house for a bit more than the expectation of loss, good for you and the insurance company.
- 9. A dollar is a dollar A bit of analysis leads to the conclusion that the UTILITY of N dollars is proportional to log N.
- 10. A dollar is a dollar So, giving the guy money is good for society (that way be socialism…)
- 11. St Petersburg game And of course, the logarithmic expectation of the St Petersburg game is finite.
- 12. Fallacy II log (1+x) = x prevalent in the finance community (because pension fund managers do not understand logs?)
- 13. log(1+x) = x leads to complete confusion, not the least manifestation of which is the Sharpe ratio. And its cousins, the CAPM and Markowitz portfolio optimization.
- 14. Sharpe Ratio Defined as the mean of portfolio excess returns divided by the standard deviation of excess return. Should be the mean of excess log returns divided by their variance. (call this the KT-ratio, for Kelly-Thorp, more on this below)
- 15. Harry Markowitz Paul Samuelson Three confused Nobelists Bill Sharpe
- 17. There are two methods to consider in a risky strategy: The first is to know all parameters about the future, and engage in optimized portfolio construction, a lunacy, unless one has a godlike knowledge of the future. Let’s call it Markowitz-style. Nassim Taleb
- 18. What if you do know about logs?
- 19. Optimal betting strategies Problem: you have an edge on the house (say, counting cards, or doing statistical analysis of stock returns). How much should you bet?
- 20. Optimal betting strategies ANSWER: depends on what you want. If you only have one shot, you should bet all of your money (if you are really, really sure you have an edge).
- 21. Optimal betting strategies But if you can play as long as you want, betting all your money every time is a terrible idea, since you will LOSE all your money quickly, even if you have an edge.
- 22. Optimal betting strategies But, the answer has been figured out (at Bell Labs! — not as surprising as it seems, since the phone company made a lot of money from bookies back in the day).
- 23. Optimal betting strategies The answer is “the Kelly Criterion”
- 25. The Kelly Criterion Interesting properties: betting LESS than the Kelly criterion reduces your returns, but also decreases the volatility Betting more ALSO decreases returns, while INCREASING the volatility
- 26. The Kelly Criterion ($1000 initial bankroll, p=0.51, 2000 bets) ($1000 initial bankroll, p=0.51, 2000 bets)
- 27. The half-Kelly ($1000 initial bankroll, p=0.51, 2000 bets)
- 28. The Kelly Criterion ($1000 initial bankroll, p=0.54, 2000 bets)
- 29. The half-Kelly ($1000 initial bankrol, p=0.54, 2000 bets)
- 30. Some Kellyists Jim Simons Ed Thorp Ray Dalio No Nobel prizes, and no regrets
- 32. Madoff Returns Impossible! Or is it?
- 33. Take a look: See any similarity?
- 34. The martingale strategy You go to the casino, and bet $1 on red. If you win, you walk away. If you lose, you bet $2 on red. If you win, you are up $1, and walk away. If you lose, you bet $4, and so on.
- 35. The martingale strategy It’s amazing! You win $1 with 100% probability. Well, except for running out of money (in a casino, there are table limits, but in the stock market, there aren’t…)
- 36. The martingale strategy So, we found a hedge fund — MG partners, which has $1000 under management to begin, and every day we run the martingale. What happens?
- 37. The martingale for fair coin toss (2000 bets, $1000 starting bankroll), betting $1 every time.
- 38. The martingale for fair coin toss, betting 0.05% every time ($1000 starting capital, 2000 bets)
- 39. The martingale with an edge ($1000 starting capital, p=0.54, $1 bet, 2000 bets)
- 40. Still looks a little variable… The “standard trick” (or so people tell me…) is to found a few funds, and only tell people about the good one(s), just to be on the safe side. As the amount of investment goes up, the risk of catastrophic failure goes down.
- 41. When things crash The investors are screwed, but the manager walks away with the 2/20. Of course, this is not nice to the investors, so…
- 42. We borrow money from the bank At the end, the manager has done well, the investors have done well, the bank, umm… Not so nice to the bank. But now there is a really simple solution.
- 43. Instead of $1000, use $10Bn Then, the manager does (very) well. The investors do quite well The bank earns nice interest income And when things blow up, the bank is too big to fail; the Fed bails it out with money it prints, so
- 44. Everybody wins!
- 46. How many “trading systems” are the martingale in disguise? People like winning every day…
- 47. Of course, once the fund gets big enough Hire enough physics PhDs to have SOME alpha. Then inertia is your friend.
- 53. (that was another fallacy): You need to have good performance to raise money.
- 54. Another fallacy (on a smaller scale): Ride your winners, dump your losers
- 55. Ride your winners, dump your losers Infinitely many backtests show that mean reversion is quite noticeable in the market. Which means that this is exactly the wrong thing to do.
- 56. Thank you for your attention!
- 57. Thanks to Quantopian for organizing!