Multi-Period Momentum Composites: 13612U and 13612W Explained

Multi-period momentum composites combine trailing returns across several timeframes into a single score that captures momentum information more comprehensively than any individual lookback period. The two most widely used composites in tactical allocation are the 13612U (unweighted) and 13612W (weighted), both developed by Wouter Keller and used across numerous strategies in his influential research on breadth momentum, canary universes, and asset selection.

The 13612U Formula (Unweighted)

The 13612U composite calculates the simple average of four trailing return periods: one-month, three-month, six-month, and twelve-month total returns. Each period receives equal weight in the average. If an asset returned 2% over the last month, 5% over three months, 8% over six months, and 12% over twelve months, its 13612U score would be (2 + 5 + 8 + 12) / 4 = 6.75.

By averaging across four horizons, the composite captures momentum information at different frequencies simultaneously. The one-month component detects very recent shifts in direction. The three-month component identifies emerging trends. The six-month component confirms intermediate-term persistence. The twelve-month component validates long-term trend health. An asset must show consistent strength across all four windows to score well — a sharp one-month spike embedded in otherwise weak performance produces only a modest composite improvement.

The 13612W Formula (Weighted)

The 13612W composite applies declining weights that heavily emphasize recent returns: 12 times the one-month return, plus 4 times the three-month return, plus 2 times the six-month return, plus 1 times the twelve-month return. Using the same example returns: (12 × 2) + (4 × 5) + (2 × 8) + (1 × 12) = 24 + 20 + 16 + 12 = 72.

This weighting structure makes the signal highly responsive to recent price action. A sharp one-month decline weighs heavily because the monthly return is multiplied by twelve, potentially turning the entire composite negative even if longer-term returns remain positive. Keller designed this sensitivity deliberately for use in crash detection — the 13612W was intended to identify momentum deterioration at the earliest possible stage, accepting higher false alarm rates as the price of faster protection.

Why Multi-Period Beats Single-Period

The research motivation for multi-period composites comes from a fundamental limitation of single-period signals. A twelve-month return can be heavily influenced by a single extreme observation — the return from exactly twelve months ago. When that observation drops out of the trailing window, the signal can jump discontinuously. By blending four different windows, the composite smooths this "drop-off" effect because no single historical observation dominates the calculation.

Multi-period composites also capture the full spectrum of the momentum effect, which academic research shows operates across multiple horizons simultaneously. Short-term momentum (one to three months) captures different behavioral and structural dynamics than intermediate-term momentum (six to twelve months). Blending both into a single score produces a more comprehensive reading of an asset's trend health than any individual horizon can provide.

Strategies That Use Multi-Period Composites

13612U (unweighted) is used for asset ranking and selection:

• GTAA13, GTAA-AGG3, GTAA-AGG6 — rank 12-13 assets by composite score
• HAA-B and HAA-S — per-asset momentum filter
• CAA-OFF and CAA-DEF — expected return input for optimization

13612W (weighted) is used primarily for crash detection and canary signals:

• VAA-G4 and VAA-G12 — breadth-based crash detection
• DAA — canary scoring for VWO and BND
• BAA-B and BAA-A — fast canary gate
• KDA — canary universe scoring

Choosing Between 13612U and 13612W

The unweighted composite (13612U) is better suited for asset ranking and selection, where stability and consistency matter more than speed. Its equal weighting across timeframes produces rankings that change gradually, reducing unnecessary turnover.

The weighted composite (13612W) is better suited for danger detection, where speed matters more than stability. Its heavy emphasis on recent returns allows it to detect momentum breakdowns within one to two months — fast enough to exit before the majority of a decline occurs, at the cost of occasional false alarms during volatile but ultimately non-threatening market conditions.