Development of AI-based Optimal Position Sizing System
Position sizing determines how much capital to invest in each trade. No less important than signal quality: even good strategy collapses with too aggressive sizing, earns less potential with too conservative. AI-system adapts position size to current market conditions and signal confidence.
Classical Sizing Methods
Fixed Fractional:
Position_Size = Account_Size × f
Simplest approach. f = 1-2% risk per trade — standard for retail. Doesn't adapt to signal quality.
Kelly Criterion:
def kelly_fraction(win_rate, win_loss_ratio):
"""
f* = W - (1-W)/R
W: probability of win, R: average_win / average_loss
"""
return win_rate - (1 - win_rate) / win_loss_ratio
kelly_f = kelly_fraction(win_rate=0.55, win_loss_ratio=2.0)
# kelly_f = 0.55 - 0.45/2.0 = 0.325 (32.5% of capital!)
# This is full Kelly — too aggressive
half_kelly = kelly_f * 0.5 # Practice: 25-50% of Kelly
Kelly Problem: requires accurate estimates of win rate and R. Estimation error → overbet → accelerated ruin.
ML for Dynamic Position Sizing
Confidence-Adjusted Sizing: Position size proportional to ML-signal confidence:
def ml_position_size(model_proba, base_size, min_prob=0.55, max_prob=0.80):
"""
At probability 0.55 → base_size × 0.5 (minimum)
At probability 0.80 → base_size × 2.0 (maximum)
"""
if model_proba < min_prob:
return 0 # no trade
scale = (model_proba - min_prob) / (max_prob - min_prob)
return base_size * (0.5 + 1.5 * min(scale, 1.0))
Volatility-Adjusted Sizing: Normalize position size to instrument volatility:
def vol_normalized_size(target_risk_pct, price, volatility_daily, account_size):
"""
Position size: such that 1σ daily move = target_risk_pct of capital
"""
dollar_risk = account_size * target_risk_pct
position_value = dollar_risk / volatility_daily
n_shares = position_value / price
return n_shares
ATR (Average True Range) as volatility proxy: higher ATR, smaller lot.
RL for Adaptive Sizing
RL-agent learns optimal sizing depending on context:
Agent State:
- ML-signal confidence (probability score)
- Current volatility (ATR/10-day realized vol)
- Drawdown from peak (if already in drawdown — less risk)
- Macro regime (expansion vs. contraction)
- Portfolio correlation: if position highly correlated with open ones — reduce
Actions: discrete space [0%, 0.5%, 1%, 1.5%, 2%, 3%] risk per trade.
Reward:
Reward = PnL / max_drawdown_penalty
Agent learns not just maximize return, but limit drawdown.
Risk Parity Sizing for Portfolio
When managing multiple positions simultaneously:
def risk_parity_position_sizes(signals, volatilities, correlations, target_portfolio_vol):
"""
Position sizes such that each contributes equal amount to portfolio risk
"""
n = len(signals)
w = np.ones(n) / n # initial equal distribution
for _ in range(100): # iterative optimization
cov = np.diag(volatilities) @ correlations @ np.diag(volatilities)
portfolio_vol = np.sqrt(w @ cov @ w)
marginal_risk = cov @ w / portfolio_vol
risk_contributions = w * marginal_risk
# Adjust toward equal contribution
w = w * (1 / risk_contributions)
w = w / w.sum() # normalize
# Scale for target volatility
portfolio_vol = np.sqrt(w @ cov @ w) * np.sqrt(252)
w = w * (target_portfolio_vol / portfolio_vol)
return w
Drawdown-Adjusted Sizing (Anti-Martingale)
On portfolio growth — increase risk (compound growth). On drawdown — reduce:
def drawdown_adjusted_size(base_risk, current_equity, peak_equity, max_drawdown=0.20):
"""
At drawdown > max_drawdown: full stop trading
At drawdown 0-10%: linear risk reduction
"""
drawdown = (peak_equity - current_equity) / peak_equity
if drawdown > max_drawdown:
return 0 # circuit breaker
reduction_factor = 1 - (drawdown / max_drawdown)
return base_risk * reduction_factor
Simulation and Sizing Strategy Assessment
# Compare different approaches
strategies = {
'fixed_1pct': lambda signal, vol, eq: fixed_fractional(1.0),
'fixed_kelly': lambda signal, vol, eq: half_kelly_sizing(signal),
'vol_normalized': lambda signal, vol, eq: vol_normalized(vol, target_risk=1.0),
'ml_adaptive': lambda signal, vol, eq: ml_size(signal.probability, vol, eq.drawdown),
}
for name, size_fn in strategies.items():
equity_curve = simulate_strategy(trades, size_fn)
print(f"{name}: Sharpe={sharpe(equity_curve):.2f}, MaxDD={max_drawdown(equity_curve):.1%}")
Monte Carlo simulation of 10,000 paths for each sizing method — compare distribution of results.
Typical Result: ML adaptive sizing improves Sharpe by 15-30% and reduces max drawdown by 20-40% vs. fixed fractional with same entry signals.
Timeline: volatility-adjusted sizing + drawdown adjustment — 2-3 weeks. RL adaptive sizing with risk parity and full simulation — 6-8 weeks.