Single Strategy vs Ensemble: The Diversification Math

"One Sharpe-2 strategy or four Sharpe-1 strategies?" The ensemble usually wins, but only if the diversification is real. Failure to verify the diversification is the most common reason ensemble portfolios underperform their headline math.

The basic math

For independent strategies with the same individual Sharpe:

Sharpe_portfolio ≈ Sharpe_individual × √N

Four independent Sharpe-1 strategies combine to a Sharpe-2 portfolio. This is the headline result that motivates ensembling.

Where the math breaks

The result depends on independence. Real strategies aren't independent; the operative formula uses correlation:

Sharpe_portfolio = (μ_portfolio) / σ_portfolio = ... → degrades with correlation

For correlation 0.5 between four Sharpe-1 strategies, the portfolio Sharpe is about 1.4 — substantially less than the independence-implied 2.0.

For correlation 0.8 (typical of stress-regime correlation decay), portfolio Sharpe is about 1.1 — barely better than the individual strategies.

The real comparison

Single Sharpe-2 strategy vs four Sharpe-1 strategies with stress-regime correlation 0.7:

Single: Sharpe 2.0; concentration risk in one strategy's regime sensitivity.
Ensemble: portfolio Sharpe ~1.2; less concentration but underwhelming aggregation.

The ensemble's diversification value is conditional: it's worth a lot in normal markets and almost nothing in stress, when correlation rises.

When ensembles win decisively

Strategies with genuinely different regime sensitivities. Trend-following (long convexity) + carry (short convexity) + stat-arb (microstructure). These have different stress sensitivities.
Strategies across asset classes. Equity strategies + rates strategies + commodities. Correlation in stress is meaningful but not catastrophic.
Strategies with capacity diversity. A small-cap stat-arb book is decoupled from a large-cap macro book in liquidity stress.

When single strategy is fine

Capacity-constrained strategies with Sharpe well above 2 and bounded regime sensitivity. The diversification benefit doesn't justify dilution.
Operational simplicity — one strategy is faster to run, easier to debug, cheaper to operate.
High-conviction edge with documented mechanism. If you really know it works, dilution is suboptimal.

The Sentivue approach

Ensemble — but with the diversification audited explicitly:

Strategy archetypes chosen for opposite-regime sensitivity. Not "different parameter values of the same archetype" — that's not diversification.
Stress-regime correlation matrix computed on worst-decile portfolio days. Used as the operative correlation matrix for risk parity allocation.
Capacity tier diversity. Small-cap, mid-cap, large-cap strategies all represented to buffer liquidity-stress correlation.

What "real diversification" requires

Different statistical signal generators. Not the same model with different parameters.
Different regime sensitivities. Pair short-vol with long-vol convexity; pair trend with reversion.
Different operational mechanics. Daily vs intraday strategies have different liquidity-stress correlation.
Different capacity profiles. Mixed-tier portfolios buffer the deleveraging-correlation risk.

Practical takeaways

Ensemble usually wins, but only if diversification is real.
Audit correlation under stress regimes, not just full-sample correlation.
Combine archetypes with opposite regime sensitivities, not parameter variations of one archetype.