Tim Olson
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description, tags
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| Institutional alpha combination: how to merge multiple weak signals into a single high-conviction output using the 11-step procedure and the Fundamental Law of Active Management. |
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Signal Combination — Alpha Stacking
Core Law
Do not search for one perfect signal. Combine many weak, independent signals.
Fundamental Law of Active Management:
IR = IC × √N
IR= Information Ratio of the combined system (risk-adjusted edge)IC= average Information Coefficient per signal (correlation of prediction to outcome)N= number of genuinely independent signals
Real institutional signals have IC = 0.05–0.15. A single signal at IC=0.10 is outperformed by 50 signals at IC=0.05 (IR = 0.05 × √50 = 0.354, over 3× better).
Critical: N counts effective independent signals, not raw signal count. Fifty correlated signals may yield only 10–15 effective ones. The 11-step procedure below forces honest accounting.
Five Signal Categories
| Category | What it measures | Why it persists |
|---|---|---|
| Momentum / Price | Direction/rate of price movement over lookback d |
Underreaction causes short-term trend persistence |
| Mean Reversion | Deviation from cross-sectional fair value | Related instruments maintain consistent relative pricing |
| Volatility | Implied vs. realized volatility gap | Vol risk premium: sellers demand compensation |
| Factor | Value, momentum, carry, quality, low-vol premiums | Persistent behavioral/structural inefficiencies |
| Microstructure | Order book imbalance, bid-ask spread, VPIN | Informed order flow leads price movement |
Dexorder scope: Only crypto OHLCV data is available. Factor signals (value, carry, quality) require TradFi data not available here. Momentum, mean reversion, volatility, and microstructure signals are all applicable.
11-Step Combination Engine
Given N signals with historical returns R(i,s) over M periods:
Step 1. Collect realized return series R(i,s) for each signal i, each period s.
Step 2. Remove drift — serially demean:
X(i,s) = R(i,s) − mean(R(i,·))
Step 3. Compute variance per signal:
σ(i)² = (1/M) × Σ X(i,s)²
Step 4. Normalize to common scale:
Y(i,s) = X(i,s) / σ(i)
Makes signals with different magnitudes directly comparable.
Step 5. Drop the most recent observation from Y — use only out-of-sample history.
Step 6. Cross-sectionally demean at each time period:
Λ(i,s) = Y(i,s) − avg_j(Y(j,s))
Removes any market-wide effect driving all signals simultaneously at that moment.
Step 7. Drop the final period from Λ to eliminate residual look-ahead.
Step 8. Estimate expected forward return per signal using d-day moving average, normalize:
E(i) = (1/d) × Σ R(i,s) over recent d periods
E_normalized(i) = E(i) / σ(i)
Step 9. (Critical) Regress E_normalized over Λ(i,s) without intercept, unit weights. Residuals ε(i) are each signal's independent forward-looking contribution — the component not explained by any other signal in the stack.
Step 10. Set weights:
w(i) = η × ε(i) / σ(i)
High independent edge + low noise → high weight. No subjective judgment.
Step 11. Normalize: scale η so Σ|w(i)| = 1. No unintended leverage.
Combined output = Σ w(i) × signal_i_current_value
Empirical Kelly Sizing
f_empirical = f_kelly × (1 − CV_edge)
f_kelly = (p × b − q) / b
CV_edge= coefficient of variation of edge estimates across 10,000 Monte Carlo path simulations of historical returns- Higher uncertainty → smaller fraction. The formula automatically scales confidence to what is warranted.
Key Failure Mode: Correlation Blindness
Believing you have 3 independent reasons for a trade when you have 1 reason expressed 3 times, sized as if for 3. This is the mechanism behind most systematic blowups where the trader was directionally correct but over-sized.
The cross-sectional demeaning (Step 6) and regression residualization (Step 9) structurally prevent this by exposing shared variance before weights are assigned.
Dexorder Application Note
When combining multiple indicators into a single entry/exit signal:
- Each indicator (momentum, RSI divergence, volume profile, spread, etc.) is a signal producing a score or directional estimate.
- Run the 11-step engine over backtested signal histories to derive weights.
- Combined score = weighted sum of current signal outputs.
- Size the resulting position using empirical Kelly with CV_edge from simulation.
If computing probability estimates (e.g. probability of upward breakout), substitute probability estimates for return estimates at each step — the math is identical.