Calculating the Investment Clock

Overview

The Merrill Lynch Investment Clock maps macroeconomic cycles into a two-dimensional continuous phase plane defined by Growth and Inflation momentum relative to trend.

This guide details the mathematical formulas, FRED data pipeline, Exponential Moving Average (EMA) rolling Z-score normalization, and phase-angle calculations used in SOPHIE's real-time engine.

1. FRED Data Pipeline & Indicator Weightings

Ten underlying indicators from the St. Louis Federal Reserve (FRED) feed the dual composite indices:

Growth Composite ($Z_{\text{growth}}$)

Inflation Composite ($Z_{\text{inflation}}$)

2. Exponential Rolling Z-Score Normalization

To eliminate lookahead bias while adapting quickly to regime shifts, each raw indicator $x_t$ is normalized using an Exponential Weighted Moving Average (EWMA) with a 24-month span ($\alpha = \frac{2}{\text{span} + 1} = \frac{2}{25} = 0.08$):

$\mu_t = \alpha x_t + (1 - \alpha) \mu_{t-1}$

$\sigma_t^2 = \alpha (x_t - \mu_t)^2 + (1 - \alpha) \sigma_{t-1}^2$

$z_{i,t} = \frac{x_{i,t} - \mu_{i,t}}{\sigma_{i,t}}$

The aggregate composite score for each dimension is the weighted sum:

$Z_{\text{growth},t} = \sum_{i \in \text{Growth}} w_i \cdot z_{i,t}$

$Z_{\text{inflation},t} = \sum_{j \in \text{Inflation}} w_j \cdot z_{j,t}$

3. Phase Angle & Quadrant Classification

The economy's exact position on the clock face is computed via the four-quadrant arctangent in degrees:

$\theta_t = \operatorname{atan2}(Z_{\text{inflation},t}, Z_{\text{growth},t}) \times \frac{180}{\pi}$

Normalizing $\theta \in [0^\circ, 360^\circ)$ mapped clockwise where 12:00 corresponds to peak inflation ($\theta = 90^\circ$):

• Phase I: Reflation (6:00 to 9:00, Bottom-Left): $Z_{\text{growth}} < 0 \land Z_{\text{inflation}} < 0 \implies \textbf{Optimal Asset: Government Bonds}$
• Phase II: Recovery (9:00 to 12:00, Top-Left): $Z_{\text{growth}} \ge 0 \land Z_{\text{inflation}} < 0 \implies \textbf{Optimal Asset: Equities}$
• Phase III: Overheat (12:00 to 3:00, Top-Right): $Z_{\text{growth}} \ge 0 \land Z_{\text{inflation}} \ge 0 \implies \textbf{Optimal Asset: Commodities}$
• Phase IV: Stagflation (3:00 to 6:00, Bottom-Right): $Z_{\text{growth}} < 0 \land Z_{\text{inflation}} \ge 0 \implies \textbf{Optimal Asset: Cash / T-Bills}$

4. Hysteresis Filtering (Noise Reduction)

To avoid whipsaw regime flips during cyclical consolidation, a $0.20\,\sigma$ Hysteresis Threshold is enforced:

A phase shift is only confirmed when the composite coordinate crosses the quadrant boundary by at least $\Delta Z \ge 0.20$.

Related Resources

• Live Merrill Lynch Investment Clock Tracker
• Article: A Quantitative Guide to Calculate The Investment Clock
• Wiki: The Investment Clock Framework
• Watch on YouTube