Slides from a finance talk I gave in Boston; the original is keynote: https://www.dropbox.com/sh/6j1swb2w6v490mw/Vlie9SCQ0a

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

16. And their intellectual
offspring

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”

24. 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

31. Back to fallacies

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!

45. Quantopian exchange

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!