KellyBoost: Growth-Optimal Portfolio Construction with Gradient-Boosted Trees

Jiayu Li

q-fin.PMAug 24, 2026

KellyBoost: Growth-Optimal Portfolio Construction with Gradient-Boosted Trees

Authors: Jiayu Li

Abstract

KellyBoost is a single multi-output XGBoost model whose softmax output is the portfolio: with y the vector of per-asset holding-period returns, the training loss is - log(1 + w y), the negative log growth rate, so the fitted model is the growth-optimal (Kelly) allocation conditioned on the features. The objective is exact rather than a surrogate: we derive the gradient, the analytic diagonal Hessian and the full Hessian in closed form, verify them by finite differences, and ship a dependency-free reference engine.

Figures & tables

Method	( $\times 100$ , 20d)	return	vol.	Sharpe	DD	vs. KellyBoost (%)
	$\overline{\log G}$	Ann.	Ann.		Max	$\Delta$ ann. log growth
KellyBoost (ours)	0.47	6.2%	23.9%	0.30	-46.2%	—
MLP, same loss	0.56	7.1%	20.5%	0.35	-55.5%	-0.9 [-9.2, +8.9]
Two-stage LGBM + optimizer	0.82	8.2%	20.9%	0.40	-40.4%	-1.9 [-12.3, +10.0]
Multiclass surrogate	0.35	4.0%	19.2%	0.21	-42.7%	+2.0 [-5.6, +9.4]
MLP, surrogate loss	0.20	2.0%	21.8%	0.12	-47.4%	+4.0 [-5.1, +14.2]

Table 1: Out-of-sample results on the evaluation segment (2013-01 to 2026-07, 163 monthly decisions, gross of costs).

\overline{\log G}

is the mean realized log growth per 20-day decision (

\times 100

). Sharpe is daily returns in excess of T-bills, annualized. The last column is the moving-block-bootstrap 95% interval for the difference in annualized daily log growth versus KellyBoost (negative = worse than KellyBoost).

Figure 1: Out-of-sample equity curves (log scale), all methods, evaluation segment. Every learned method is deployed identically: frozen development-tuned parameters, expanding-window refits every 21 trading days,

K_{\mathrm{ens}}=4

leave-one-out ensemble.

Figure 2: KellyBoost’s deployed allocation over the evaluation segment (committee average). The model was never told what an asset class is — the rotation structure is learned from the features alone.

Cell (growth $-$ surrogate)	( $\times 100$ , 20d)	95% CI	$\Pr(\Delta>0)$
	$\Delta\overline{\log G}$
Boosted tree, searched	+0.12	[-0.52, +0.75]	0.65
Boosted tree, hand-built	+0.07	[-0.34, +0.45]	0.63
MLP, searched	+0.37	[-0.26, +0.99]	0.87
MLP, hand-built	+0.18	[-0.32, +0.75]	0.77
Pooled (four cells)	+0.18	[-0.11, +0.50]	0.89

Table 2: The loss effect, cell by cell: paired per-decision differences in realized log growth, growth objective minus argmax surrogate, holding the learner class and feature pipeline fixed within each cell (

K_{\mathrm{ens}}=4

, 163 decisions). Intervals: circular moving-block bootstrap, block 6 decisions, 10,000 draws. The pooled row averages the four aligned difference series at each decision date, preserving cross-cell correlation.

			$\overline{\log G}$	Ann.	Ann.		Max
Method	Features	$\|F\|$	( $\times 100$ )	return	vol.	Sharpe	DD
KellyBoost	hand-built	174	0.39	5.7%	22.9%	0.28	-48.3%
KellyBoost	searched	5	0.47	6.2%	23.9%	0.30	-46.2%
MLP, same loss	hand-built	174	0.67	8.5%	19.4%	0.43	-40.4%
MLP, same loss	searched	19	0.56	7.1%	20.5%	0.35	-55.5%
Two-stage LGBM + optimizer	hand-built	174	0.38	5.2%	23.8%	0.26	-36.2%

Table 3: What the feature search bought. Hand-built: the 174-column set with random-search hyperparameters (the pipeline as first designed); searched: Section 3.5 . Deployment metrics,

K_{\mathrm{ens}}=4

Feature	Gain share
INTL_Q2Y_SH2P90	35.9%
WHEAT_Q2Y_RH2P25	27.7%
COPPER_Q2Y_SWP10	22.0%
SOYBEAN_Q2Y_RH2P50	7.7%
XLF_SKEW1Y	6.7%

Table 4: KellyBoost’s searched feature list, with each column’s share of the committed fit’s total split gain.

	Dev. score	$\overline{\log G}$	Ann.		Max
Variant	( $\times 100$ )	( $\times 100$ )	return	Sharpe	DD
analytic Hessian (model)	4.19	0.47	6.2%	0.30	-46.2%
constant Hessian	1.43	0.67	8.3%	0.63	-23.6%
$g^{2}$ Hessian	0.54	0.45	5.0%	0.26	-51.7%
one output per tree	3.50	0.65	8.8%	0.40	-45.7%

Table 5: Ablations. Dev. score: mean log growth (

\times 100

) under the development tuning protocol at the frozen KellyBoost parameters. Deployment columns as in Table 1 , all with

K_{\mathrm{ens}}=4

Method	Turnover	0 bps	5 bps	10 bps	20 bps
KellyBoost (ours)	7.9x	6.2% / 0.30	5.8% / 0.28	5.3% / 0.27	4.5% / 0.23
MLP, same loss	11.8x	7.1% / 0.35	6.5% / 0.32	5.9% / 0.30	4.6% / 0.24
Two-stage LGBM + optimizer	16.5x	8.2% / 0.40	7.3% / 0.36	6.4% / 0.32	4.7% / 0.24
Multiclass surrogate	13.1x	4.0% / 0.21	3.3% / 0.18	2.7% / 0.14	1.3% / 0.07
MLP, surrogate loss	16.8x	2.0% / 0.12	1.2% / 0.09	0.3% / 0.05	-1.4% / -0.03
Unconditional Kelly	1.8x	4.1% / 0.22	4.0% / 0.21	3.9% / 0.21	3.7% / 0.20

Table 6: Transaction-cost sensitivity: annualized return / excess Sharpe under one-way proportional costs applied to each method’s measured turnover.

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Aug 4, 2021J/K move · Enter open · S save

Machine Learning Classification and Portfolio Construction: Does the Loss Function Matter?

Yang Bai, Kuntara Pukthuanthong

College of Business and Economics, California State University, Fullerton · Trulaske Sr. College of Business, University of Missouri

Quantitative Finance Classification Portfolio Optimization Finance Financial Decision-Making

Open paper AskPDF arXiv

Classification outperforms regression across matched machine learning models in portfolio construction. A stacking ensemble of gradient boosted tree, random forest, and neural network yields a value-weighted annualized Sharpe ratio of 1.83 for classification and 1.11 for regression. This outperformance persists in multiclass settings, across subsamples, and after transaction costs. Spanning tests show that classification retains economically large alphas after we control for regression, whereas regression alphas shrink substantially once we control for classification. These results indicate that classification extracts more return information than matched regression. Our diagnostics trace classification's advantage to sharper and more precise separation of return deciles.

Abstract

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