Portfolio construction
Fractional Kelly
A fixed share of the Kelly portfolio, half by default: most of the growth with much smaller swings.
L’idée en termes simples
The growth curve is flat near its top: betting half of Kelly still earns three quarters of the maximum growth, with half the volatility and far shallower drawdowns. And because Kelly overbets when the estimates are too rosy, a fraction is also insurance against your own errors.
Mode de calcul
Compute the Kelly weights, multiply by the fraction (Settings › Kelly fraction, 0.5 by default), then apply the maximum-leverage cap.
w = c × w_Kelly, 0 < c ≤ 1
g(c) = c(2 − c) × g_max (½ Kelly → 75% of the growth, 50% of the volatility)Comment l’utiliser
- The practical way to use Kelly: start at 0.25–0.5.
- Lower the fraction when you trust the estimates less (short history, few tickers).
Tirer des conclusions
- If Fractional and full Kelly give the same weights, both hit the leverage cap.
- The growth column in the study shows what the fraction gives up.
Exemple
Running example (used in every portfolio guide): US500, GER40, gold (XAUUSD) and EURUSD, two years of daily data. Expected returns 8%, 7%, 7% and 1% a year; volatilities 18%, 20%, 15% and 7%. US500 and GER40 move together (correlation about 0.7); gold hardly moves with the indices (about 0.04). Half of the full Kelly portfolio would still be 2.7× leverage, so here it also hits the 2× cap and comes out the same as full Kelly (80% US500, 10% GER40, 111% gold). Lower the maximum leverage or the fraction (0.25 gives 1.35×) to see it differ.
Les données d’entrée de l’exemple sont illustratives ; les pondérations et les chiffres sont ceux que renvoie notre optimiseur.
Points de vigilance
- Still leveraged in many cases; check the gross exposure.
- The fraction does not fix wrong estimates; it only limits the damage.
Un peu d’histoire
Fractional Kelly was studied by MacLean, Thorp and Ziemba among others; Thorp and many professional gamblers and investors have long recommended half Kelly or less.
Contenu éducatif uniquement. Aucun modèle de portefeuille ne connaît l’avenir : chacun repose sur des estimations tirées du passé, et rien ici ne constitue un conseil en investissement.