The diversification you think you have
A book of strategies with a pairwise correlation of 0.2 on average feels diversified: when one line loses, the others shouldn't. The problem is that the average is dominated by the calm days — exactly the days when diversification is decorative. The only days diversification is paid to work are the bad ones, and on those days the correlation structure of most return series is not what its average advertises.
This is not a pessimist's intuition; it is one of the better-documented facts in empirical finance. Longin and Solnik, working with extreme value theory on decades of international equity data, showed that correlation of large negative returns is far higher than of large positive ones — dependence concentrates in the left tail (Longin & Solnik, 2001). Ang and Chen quantified the same asymmetry inside a single market: correlations conditional on downside moves systematically exceed those conditional on upside moves (Ang & Chen, 2002).
Why this happens to strategies too
Strategies inherit tail dependence from what they trade and how. Two systems on different symbols still share a volatility regime, common risk-off shocks, and often the same crowded exit. Signals that look unrelated in calm regimes synchronize when liquidity vanishes.
Diagnose your own book, not the literature
Three cheap diagnostics reveal what your average correlation hides:
- Rolling correlation. A pair whose ρ oscillates between −0.2 and +0.8 across windows does not "have a correlation of 0.3" — it has two regimes, and your sizing should assume the bad one shows up when it hurts.
- Drawdown-conditional correlation. Recompute pairwise correlations using only the days when the portfolio is in drawdown. This is the number your risk actually depends on. If it jumps from 0.3 to 0.7, your book concentrates exactly when it needs breadth.
- Pair drill-down. For the worst pair, look at the scatter of daily P&L: a cloud with a dense lower-left corner is tail dependence in person, whatever the headline ρ says.
In VEEMAN, the correlation matrix with pair drill-down does this on your own histories; the docs state the estimator exactly.
From diagnosis to sizing
Once you accept that co-movement is regime-dependent, the sizing consequences follow:
Simulate the portfolio, not the strategies. A per-strategy Monte Carlo, resampled independently, quietly destroys cross-strategy dependence — it simulates the diversified book you wish you had. A block bootstrap drawn on dates (all strategies move together within each block) preserves both each line's streaks and the joint bad days (Künsch, 1989; Politis & Romano, 1994). The tails of that simulation — the realistic maximum drawdown range, the probability of ruin — are the numbers to size against.
Cap risk per strategy, in contract space. Weights on an equity curve are abstractions; positions are integers. A per-strategy risk cap ("no line may risk more than x% of capital per contract") translated into contract counts keeps any single line — and any correlated cluster — from silently owning the book. This is what per-strategy sizing in the workspace computes.
Leave room for being wrong: fractional Kelly. The Kelly criterion gives the growth-optimal size if your edge and covariances are known. They are estimated — from the same sample you validated on. Half- or quarter-Kelly gives up a modest share of theoretical growth for dramatically flatter drawdowns and robustness to overestimated edges (MacLean, Thorp & Ziemba, 2011). Treat quarter-Kelly as a ceiling for scaling decisions built on backtests.
The checklist
- Rolling and drawdown-conditional correlations computed — not just the full-sample matrix.
- The worst pair inspected as a scatter, not summarized by one ρ.
- Monte Carlo run at the portfolio level with date-blocks, at intended size.
- Ruin probability and drawdown distribution read off the simulation, not the single history.
- Per-strategy risk caps enforced in contracts, not in weights.
- Total size at or below quarter-Kelly on the estimated edge.
References
- Longin, F., & Solnik, B. (2001). Extreme Correlation of International Equity Markets. Journal of Finance, 56(2).
- Ang, A., & Chen, J. (2002). Asymmetric Correlations of Equity Portfolios. Journal of Financial Economics, 63(3).
- Künsch, H. R. (1989). The Jackknife and the Bootstrap for General Stationary Observations. Annals of Statistics, 17(3).
- Politis, D. N., & Romano, J. P. (1994). The Stationary Bootstrap. Journal of the American Statistical Association, 89(428).
- MacLean, L. C., Thorp, E. O., & Ziemba, W. T. (eds.) (2011). The Kelly Capital Growth Investment Criterion: Theory and Practice. World Scientific.