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Ergodicity & Kelly Betting

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Books

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RatingTitleAuthorArenaCoverDojo TopicMy Notes & Ideas (Files)TypePagesRecommendDateStatusSubtitleTaglineTakeawayURL
4 ⭐⭐⭐⭐
Positional Option Trading
Euan Sinclair
Textbook
198
September 20, 2020
Read
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Future ValueNameFull TitleCategoryAuthorArenaP.A.R.A.ThemeTagsDojoURLProjectsGoal OutcomesLast HighlightedLast SyncedNotesNotes & IdeasPDFSatusCreatedUpdatedValue Goals
4 ⭐⭐⭐⭐
11 Texas Holdem Odds
Article
Source
Dec 29, 2019 3:12 AM
Dec 30, 2020 6:32 PM
4 ⭐⭐⭐⭐
Odds Conversion To Percentage
Source
Active
Dec 27, 2019 11:56 AM
Jun 24, 2022 12:35 PM
4 ⭐⭐⭐⭐
Breaking the Market
Bookmark
NP
Investing
Active
Sep 28, 2020 1:18 PM
Sep 28, 2020 1:20 PM
5 ⭐⭐⭐⭐⭐
Kelly Investing is About Slope -
Article
breakingthemarket
Source
Investing
portfolio
Read
Oct 12, 2020 11:42 PM
Dec 30, 2020 6:32 PM
4 ⭐⭐⭐⭐
How to Know if I have an Edge
Tweets
Robot James
Source
InvestingTrading
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Apr 15, 2021 11:39 PM
May 30, 2021 12:17 PM
5 ⭐⭐⭐⭐⭐
Retail Trading Edge
Article
dpg ref from Squeeze
Source
Trading
Read
Apr 7, 2021 12:50 AM
May 30, 2021 12:17 PM
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Links

Arithmetic return is over 1 period. Over long run, geometric return is what matters. Higher vol drags down geometric return. Ex: Heads win 50%, tails lose 40%. You would obviously play this one time (actually more) but if you have to play forever you will mathematically go broke.

He is maximizing the geometric return (not leveraged) β€” geometric mean frontier and solve for peak

Optimal Kelly = maximum sharpe ratio portoflio (so have to leverage)

Key Takewaways:

  • Geometric return is all that matters in long run
  • If two assets have same geo return, mix them 50/50, correlations and variance do not matter
  • Negative correlation helps, positive hurts. Can include -ve return assets if they hvae -ve correlation.
  • Variance is additive, standard deviations are not (for calcing SD of a portfolio)

Geometric Return Formulas:

GR = Geometric Return, AR = Arithmetic Return

Kelly Criterion, Generalized

W = win probability

B = loss %

A = gain %

Kelly Growth Factor Formula:

Flip a coin. Heads you win 50%, tails you lose 40%. How much do you bet?

Kelly Calculator

NameWin %Win AmountLoss AmountBet SizeGain Factor
Game 1
10%
2,000%
100%
0
1
Tail Puts
70%
50%
100%
NaN
NaN
MU call Spreads
90%
100%
100%
0
1
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Simple Examples

Coin has 60% chance of heads, 40% tails. You win 1 when heads, lose 1 when tails. In this case, bet 60-40 or 20% of bankroll each time.

If you got 2:1 odds (make $2 when heads, lose $1 when tails) then bet 40%. You take 40% and divide it by 2 (20%). Subtract 60% cahnce of winning from 20% chance of losing (with odds) and bet 40%.

If odds were reversed (lose 2 tails, make 1 heads). Take the 40% chance of losing, divide by .5 (80%). 60-80 = NEGATIVE 20 so you dont bet

Use this one for gain factor

Everything We’ve Learned About Modern Economic Theory Is Wrong - Bloomberg
The Kelly Criterion - Quantitative Trading
Wall Street University: BettingΒ Markets
10K Kelly Criterion
The Kelly criterion: How to size bets