## The Portfolio Risk Is Not the Sum of Individual Risks
A portfolio's total risk (variance) depends on the correlation between strategies. Independent strategies partially offset each other's variance; correlated strategies amplify each other.
## Measuring Cross-Strategy Correlation
For two strategies A and B, track weekly P&L for 52 weeks. Calculate the Pearson correlation coefficient between the two weekly P&L series.
ρ = Σ(A_i - Ā)(B_i - B̄) / √(Σ(A_i-Ā)² × Σ(B_i-B̄)²)
If ρ > 0.7: strategies are highly correlated (consider reducing combined allocation).
If ρ < 0.3: strategies are largely independent (diversification benefit confirmed).
If ρ < 0: strategies are negatively correlated (very valuable diversification).
## Common Correlation Sources
**High positive correlation:**
- Football 1X2 and Football AH (same matches, similar model inputs)
- NBA props and NBA totals (both driven by game pace/scoring environment)
- Multiple strategies using the same base model
**Low/negative correlation:**
- Football and horse racing (different sports, different models)
- Pre-game and in-play (different information states, different timing)
- Match winner and goalscorer props (partially different driver)
## Portfolio Variance Calculation
Total portfolio variance = Σᵢ wᵢ² σᵢ² + 2 Σᵢ Σⱼ wᵢwⱼ σᵢσⱼρᵢⱼ
Where w = allocation weight, σ = strategy standard deviation, ρ = pairwise correlation.
Run this calculation quarterly. If total portfolio variance is higher than the variance of your best single strategy (which would indicate negative diversification due to positive correlations), reallocate toward less correlated strategies.
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