Kritzman and Li 2010

Mark Kritzman and Yuanzhen Li (both then at Windham Capital Management), “Skulls, Financial Turbulence, and Risk Management” (Financial Analysts Journal 66(5), 2010; CFA Institute). The paper defines the Financial Turbulence Index — a normalised, squared Mahalanobis distance of current asset returns from their historical mean and covariance — as a measure of statistical “unusualness” that captures both the magnitude of returns and how they interact. It builds directly on Chow, Jacquier, Kritzman & Lowry (1999) and reframes the centuries-old Mahalanobis distance (originally devised to classify human skulls, hence the title) as a portfolio-surveillance tool.

The paper’s empirical contribution is to show that turbulence is a real, persistent, identifiable property of markets: the index spikes during recognisable crises (1987 crash, Gulf War, Global Financial Crisis) and stays elevated for weeks after a spike. Its risk-management application scales market exposure inversely to the index — Kritzman & Li illustrate this on a G-10 currency carry strategy. Crucially, the turbulence index is an outlier / risk-scaling measure, not a directional alpha signal: it tells an investor when conditions are unusual, not which way prices will move. The benefit it delivers is volatility and drawdown reduction.

This is graded inconclusive for tradeable profitability — consistent with the vault’s Regime Classification verdict. The original paper estimates mean and covariance over the full 1980-2009 sample (a look-ahead concern), and reports no transaction costs or slippage. An independent look-ahead-free reproduction (rolling-window estimation, SPY/cash exposure scaling, 2009-2022) lifts the Sharpe from ~1 to ~2.2 and cuts maximum weekly drawdown from ~32% to ~6% at ~50% average exposure — but those figures are gross of costs, and the strategy structurally lags violent bull recoveries (e.g. post-COVID-2020). The honest reading: the turbulence index is a confirmed, replicable risk-management instrument and an inconclusive basis for standalone alpha.

Kritzman and Li 2010 [proposes_model] Financial Turbulence Index Financial Turbulence Index [supports] Regime Classification Kritzman and Li 2010 [part-of] Regime-Based Asset Allocation

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