KellyOptimizer

KellyOptimizer is Horizon’s default sizer. It implements the classical Kelly formula with realistic extensions: transaction cost drag, gross leverage cap, per-market and per-signal notional caps, per-venue budget routing.

When the existing v1 horizon.fund._portfolio_optimizer.PortfolioOptimizer is importable (i.e., when running alongside the v1 codebase), KellyOptimizer delegates to it. using Ledoit-Wolf shrinkage covariance and projected gradient descent. Otherwise the standalone fallback runs.

Import

from horizon.portfolio import KellyOptimizer

Signature

KellyOptimizer(
    kelly_fraction: float = 0.25,
    max_gross_leverage: float = 2.0,
    transaction_cost_bps: float = 5.0,
    covariance_model: str = "ledoit_wolf",
)

Validation

The constructor raises ValueError on invalid arguments:

KellyOptimizer(kelly_fraction=0)         # ValueError
KellyOptimizer(kelly_fraction=1.5)       # ValueError
KellyOptimizer(max_gross_leverage=0)     # ValueError

The math

For each signal:

edge_net   = (expected_edge_bps - transaction_cost_bps) / 10000
vol        = max(expected_vol_bps, 10) / 10000
kelly_full = edge_net / vol²
kelly_cap  = min(kelly_full, 1.0)        (hard-capped at 100% of equity)
weight     = kelly_cap × kelly_fraction × confidence × direction.sign

Then across all signals:

1. Gross cap: if Σ |weights| > max_gross_leverage, scale all weights proportionally
2. Convert to USD: notional_usd = weight × total_equity
3. Per-market cap: apply constraints.max_notional_per_market_usd
4. Per-signal cap: apply signal.max_notional_usd if set
5. Venue routing: apply per-venue budgets for signals prefixed by a venue key (e.g., polymarket:...)

Use it

import horizon as hz
from horizon.portfolio import KellyOptimizer

result = hz.run(
    portfolio=KellyOptimizer(
        kelly_fraction=0.25,
        max_gross_leverage=1.5,
        transaction_cost_bps=5,
    ),
    ...
)

Delegation to fund module

try:
    from horizon.fund._portfolio_optimizer import PortfolioOptimizer
    self._fund_optimizer = PortfolioOptimizer(
        kelly_fraction=kelly_fraction,
        max_gross_leverage=max_gross_leverage,
        covariance_model=covariance_model,
    )
except Exception:
    self._fund_optimizer = None

When self._fund_optimizer is not None, the v1 math runs with:

• Ledoit-Wolf covariance shrinkage for robust correlation estimation
• Projected gradient descent for constraint-aware optimization
• Rebalance trigger tracking (drift, VaR, correlation change)

When unavailable, the standalone fallback runs the simpler formula above.

See v1 PortfolioOptimizer for the full math of the fund module.

Verified behavior

Hand-calculated cases in tests/test_portfolio.py::TestKellyMath:

8 tests, all passing.

Pitfalls

Fractional Kelly selection

Full Kelly is theoretically optimal but practically too aggressive:

• Full Kelly (1.0): maximizes expected log wealth but has ~40% probability of 50% drawdown
• Half Kelly (0.5). 75% of expected growth, much lower drawdown probability
• Quarter Kelly (0.25). 44% of expected growth, very conservative
• Eighth Kelly (0.125): very low risk, but growth is only 22% of full

Most practitioners use 0.25 to 0.5. The default is 0.25.

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