Thread by @TaylorPearsonMe

1/ How to Size Your Investments (AKA A brief summary of what I have learned about the Kelly Criterion)

2/ I initially discovered the Kelly Criterion in @nntaleb's book, The Black Swan

3/ As Taleb pointed out, it is not enough to be correct as an investor, you must be correct in the right amounts, yet many investors don't think about it that way.

4/ If you make a little money on many trades but lose everything on one big trade, then your "win rate" may be 95%, but you are still broke because you were "picking up nickels in front of a bulldoze"

5/ On the flip side, if you are wrong 95% of the time, but your few wins more than make up for losses, you are profitable. (Successful options traders and angel/venture investors are prime examples)

6/ The Kelly Criterion was described initially by J. L. Kelly at Bell Labs in 1956. It is a formula for bet sizing (or investment sizing) that leads to more wealth than any other strategy in the long run. (LONG being the operative word - more on that in a bit)

7/ The Kelly Criterion optimizes for *typical wealth* not *expected wealth* (Said another way, it assumes markets are non-ergodic)

https://twitter.com/TaylorPearsonMe/status/1103029738438905858

8/ In effect, this means that the Kelly criterion makes it impossible to go bankrupt which is a pretty nice property.

9/ One of the challenging pieces of implementing the Kelly Criterion is that you have to be comfortable with lots of volatility and placing seemingly huge bets when you have lots of edge.

10/ This seems very reminiscent of Buffett's punch card strategy that @jamesclear has written about or Munger's line to "bet heavily when the odds are extremely favorable"

jamesclear.com/buffett-slots

11/ You can reduce the volatility by investing half the amount recommended by Kelly, but you also reduce the total expected return (and investing double the amount means you will go bankrupt eventually)

12/ Reducing the sizing may make the strategy easier to stick with in the long-term, which, in effect maximizes your own returns (compared to doing full Kelly but not sticking to it).

13/ A good rule of thumb is probably that a trade should be big enough that the profits are meaningful, but not so big the losses are catastrophic. If that size can't be found, there isn't enough edge to trade with anyway.

14/ One of the other challenges of sticking to the Kelly criterion is that the "long run" can be very, very long.

15/ To sum up, the benefits of Kelly include maximizing the long term potential with zero risk of ruin, but you have to be willing to bet big when the odds are in your favor and to be very patient

16/ Because of this (as well as principal/agent problems and lack of Skin in the Game), many investors and money managers don't seem to the Kelly Criterion

17/ So how does you actually use the Kelly Criterion to size bets/investments?

18/ @MonishPabrai has a chapter in his book where he describes a simplified version of the Kelly Criterion applied to the stock market:

19/ Edge/Odds = Fraction of Bankroll to Allocate

20/ The edge is the total expected value, obtained by adding up the multiplication of each scenario's possible outcomes by its corresponding probability

21/ To take a simple example, let's say you're offered a coin toss where heads you get $2 and tails you only lose $1.

Your odds are 2:1 (Bet $1 with the possibility of winning $2)

Your edge is .50
50%*$2 = $1.00
50%*-$1 = -$0.50
$1.00-$0.50 = .5

22/ Here's a real-world example: Let's say Apple stock (AAPL) was trading at $400 and you thought it was probably worth more than $600.

23/ According to the Kelly Criterion, you should bet 87% of your bankroll.

24/ That's a huge amount, hence why it might be more practical to use the half Kelly criterion which would be easier to stick to (and also build in some margin for error with your probability estimates).

25/ I built a super simple version of this calculator in Google Sheets if you want to make a copy and play around with it - docs.google.com/spreadsheets/d…

26/ Sources
The Dhando Investor - amzn.to/2Gk3ppR
The Black Swan - amazon.com/Black-Swan-Imp…
Volatility Trading - amazon.com/Volatility-Tra…

27/ As always, this is just me thinking out loud! Feedback, comments, and critiques are all welcome.

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