Effective Strategies (N-eff)

Effective number of independent strategies in a collection, from the eigenvalues of the correlation matrix: (Σλ)² / Σλ². Near the report count = well diversified; near 1 = everything moves as one bet.

Computed from: Equity curve
Scope: Across reports
Range: ≥ 0
Direction: Higher is better

Effective Strategies (N-eff) answers the one question that the count of reports in your collection cannot: how many genuinely independent strategies do you actually have? You might hold ten reports — but if they all move together, N-eff might be 3. You don't have ten bets; you have three real ones wearing ten tickets. N-eff is the honest diversification headcount, and it's almost always smaller than the number of reports you think you're diversified across. It's a portfolio (cross-report) metric, computed over the reports in a collection.

Key takeaways

What it is — the effective number of independent strategies in a collection: the eigenvalue participation ratio of the reports' return-correlation matrix, (Σλ)²/Σλ². It collapses a whole correlation matrix into one number.
Range 1 to N (N = number of reports). N-eff = N when every strategy is uncorrelated (genuine diversification — you really have N independent bets); N-eff = 1 when they're perfectly correlated (one bet wearing many tickets). Real portfolios land in between.
Higher is better — more effective strategies means more real diversification. The gap between N and N-eff is your diversification illusion gauge: N=10 / N-eff=2 means eight of your strategies are redundant.
CRITICAL — it's a CALM-MARKET count. N-eff is built on ordinary Pearson correlation, so it measures diversification in quiet markets only. In a crash the true effective count collapses toward 1, and N-eff does not show it. Always pair it with downside correlation.
In EquityTruth — computed on the Pearson matrix only (not Spearman or downside), and only when every pair of reports mutually overlaps with enough shared history; otherwise it shows "—". Needs at least 2 reports.

How it's calculated

The usable version is the 1-to-N rule: N-eff = N means fully diversified, N-eff = 1 means a single bet. The box below is the exact math for the curious — skip it if eigenvalues aren't your thing.

N-eff = (Σλ)² / Σλ²

λ: the eigenvalues of the Pearson (standard) return-correlation matrix — a math operation that finds how many genuinely separate "directions" your strategies move in; you don’t need to follow it to use the metric
Σλ: sum of eigenvalues (= N for a correlation matrix with unit diagonal)
Σλ²: sum of squared eigenvalues — large when the variance concentrates in a few directions

In this product: The ratio runs from 1 to N. With zero correlation the matrix is the identity, every λ = 1, and (Σλ)²/Σλ² = N²/N = N (full diversification). With perfect correlation one λ = N and the rest are 0, giving N²/N² = 1 (a single bet). It is computed on the Pearson matrix only — Spearman and downside matrices are assembled pairwise and aren't guaranteed positive-semidefinite, so the participation ratio would be undefined on them. It also needs the full matrix valid: if any pair lacks enough shared history, the cell is empty, the matrix is partial (pairwise deletion breaks the PSD guarantee), and N-eff returns "—". Needs ≥ 2 reports.

What it tells you

N-eff is read against your report count N — the raw number means little until you compare it to how many reports you hold. The gap N − N-eff is the signal: it's how many of your strategies are redundant.

Value	Reading	Notes
N-eff ≈ N	Genuine diversification	Your strategies are largely independent — you really do hold N distinct bets, and the portfolio’s risk reduction is close to the full √N benefit.
N-eff ≈ N/2	Half redundant	Roughly half your strategies are duplicating each other — you have the diversification of N/2 independent bets, not N.
N-eff ≈ 1–2 (any N)	One bet, many tickets	Whatever N you hold, you effectively have one or two bets. Adding more of the same does nothing; this is a concentrated portfolio masquerading as a diversified one.

You think you hold 10 strategies; you actually have 3 independent bets. The other 7 are redundant — they move with the strategies you already own and add risk without adding diversification.

Worked example

Take a collection of 6 reports. If they were genuinely uncorrelated, the correlation matrix would be near-identity and N-eff ≈ 5–6 — six real bets. Now suppose those six are all variations of the same trend-following idea, with an average pairwise correlation around 0.7. The eigenvalues concentrate: one large eigenvalue soaks up most of the variance, the rest shrink, and N-eff drops to roughly 2. Same six reports, but you hold only two effective strategies.

The count is the lie; N-eff is the truth. And it matters because the diversification benefit scales with the effective number of bets, not the nominal one. Two effective strategies cut your risk only to about 71% of a single strategy's (1/√2); six truly independent ones would cut it to 41% (1/√6) — and lower is better, so the gap is real money. You paid for six and you're getting two.

Calm-market headcount vs crisis

This is the caveat that matters most. N-eff is computed on ordinary Pearson correlation, which averages across every period — and most periods are calm. So N-eff is your calm-market diversification headcount. It tells you how independent your strategies look on a normal day.

In a crash, correlations spike toward +1 ("all correlations go to 1"), the eigenvalues collapse into one dominant direction, and the true effective count falls toward 1 — exactly when you need diversification to hold. N-eff, built on the calm-dominated Pearson matrix, does not see this. A portfolio with a comfortable N-eff = 5 in quiet markets can behave like N-eff = 1 in a crisis.

So never read N-eff alone. Pair it with downside correlation, which measures co-movement only over losing periods — the crash regime N-eff is blind to. N-eff is the calm headcount; downside correlation is the crisis stress test. You want both numbers, and you want the second one to confirm the first.

Pitfalls

Pitfalls & caveats

Calm-market / Pearson only — the headline caveat. N-eff measures quiet-market diversification and collapses in a crash without telling you. Always pair it with downside correlation.
Needs the full matrix valid. Every pair must mutually overlap with enough shared history. If even one pair is too short, the matrix is partial and N-eff shows "—". Add a young report to a mature collection and the whole number can disappear.
It's a noisy estimate, and biased low in short samples. N-eff is built from a correlation matrix estimated off limited history (cells clear at ~30 daily observations). Small-sample correlation matrices have their largest eigenvalue overstated, which pushes N-eff downward — so on short histories it tends to under-report your true diversification. Read it as a directional gauge with a margin of error, not a precise headcount; the fewer the overlapping observations, the softer the number.
It's an average-structure measure. N-eff tells you how many effective bets you hold, not which strategies are the redundant ones. To find the duplicates, read the correlation matrix itself — its simple companion KPI, average pairwise correlation, moves the opposite way (high average correlation → low N-eff).
Equal-weight, equal-vol assumption. The participation ratio treats all reports symmetrically — same size, same volatility. If you actually size them very unequally, or they have very different volatilities, the effective diversification of your real capital differs from this report-symmetric number.
More reports isn't automatically more N-eff. Adding a correlated clone barely moves the number — that's the whole point. N-eff rewards independence, not count. Use it actively: when screening a new strategy, ask "does it raise N-eff?" (does it add a genuinely different return driver), and budget risk by N-eff, not by the raw report count.

Return Correlation — the pairwise version; N-eff is the whole-matrix summary of it · Downside Correlation — the crisis companion, since N-eff is calm-market only · Max Drawdown — the severity that real diversification is meant to tame.

Related metrics

Built fromReturn Correlation