Gather your return history

Collect monthly (or weekly) return data for each asset in your portfolio. For Fig, this means your ETF and mutual fund proxies — DFSVX for Small Value, VIGRX for Large Growth, bond funds, international funds, etc. You need at least 3–5 years of history, ideally 10+.

Compute the Turbulence Index for each month

For every period, ask: "How statistically unusual was this month's combination of returns, given history?" This uses the Mahalanobis distance — a way to measure how far a data point is from the center of a cloud of points, accounting for how the assets normally move together.

Think of it like this: if stocks fell 5% in a month, that's unusual but not shocking. If stocks fell 5% AND bonds fell 3% AND gold fell 4% simultaneously, that's a very different kind of unusual — all your diversifiers failed at once. The Mahalanobis distance catches that.

Split history into "Quiet" and "Turbulent" regimes

Choose a threshold — say, the top 20% most turbulent months are labeled Turbulent and the remaining 80% are labeled Quiet. You now have two separate samples of return history. The turbulent sample typically contains the 2008 crisis, COVID crash, dot-com bust, etc.

The paper used 75% quiet / 25% turbulent as their baseline. In practice 80/20 is common. You choose based on how conservatively you want to stress-test.

Build two covariance matrices — one per regime

From your quiet-period returns, compute Σ_quiet. From your turbulent-period returns, compute Σ_turbulent. These will look very different. In turbulent periods, correlations between asset classes typically rise (everything falls together), and volatilities spike. This is the thing standard optimization ignores.

A key structural insight from the eigendecomposition: the turbulent covariance matrix is typically dominated by its first eigenvector — a single "everything falls together" factor — while the quiet matrix distributes variance more evenly across eigenvectors, reflecting genuine diversification. The Chow-Jacquier-Kritzman-Lowry framework exploits this structure to construct a more accurate and conservative picture of crisis-period risk.

Blend the two matrices using your beliefs and your risk aversion

Now the key innovation. Instead of using just one matrix, you blend them using two inputs: (a) your estimate of the probability that the next period is turbulent, and (b) your relative aversion to turbulent vs. quiet risk.

If you set λ_quiet = λ_turbulent and use historical frequencies for p, you recover standard Markowitz. The power is when you dial up λ_turbulent — you're saying "I'm more averse to losses in crashes than losses in normal times," which is true for almost every human investor.

Run mean-variance optimization on the blended matrix

Feed Σ* into standard Markowitz optimization with your expected returns. The resulting portfolio weights will be more conservative in assets that behave badly in turbulent periods (e.g. high-beta equities) and more generous to true crisis diversifiers (e.g. long-duration Treasuries, gold).

For Fig, you then map these optimal weights back to your ETF/fund proxies — each fund representing a cell in the factor surface (Large Growth → VIGRX, Small Value → DFSVX, etc.).