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) — geometric mean frontier and solve for peak
Optimal Kelly = maximum sharpe ratio portoflio (so have to leverage)
- 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?
|Name||Win %||Win Amount||Loss Amount||Bet Size||Gain Factor|
MU call Spreads
Use this one for gain factor