Notes

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This report presents the market index price together with two sets of sentiment-related indicators, covering the past 52 weeks and providing forecasts for the weeks ahead. Market index prices (e.g., S&P 500 Equal Weighted, DJIA) are shown on a logarithmic scale using weekly observations. For simplicity, the scale is omitted.

Our sentiment framework recognizes two broad forces shaping investor sentiment:

• Economic and market conditions. These factors influence investor views as they seek to maximize gains and minimize regret
• Natural forces. Naturally occurring forces have a meaningful impact on human emotion and investor sentiment, and this is our focus. A 2003 working paper by the Federal Reserve Bank of Atlanta concluded that solar energy variation has a significant effect on investor emotion and stock returns. Our research builds on this perspective. We refer to our measures of solar energy variation as Physics-Based Sentiment Drivers. Our findings show that these drivers are effective in predicting turning points in price momentum in the U.S. stock market.
   

This report shows two sets of sentiment indicators:

• Market Resilience Index® (MRI) series. Shown as solid lines, these indicators reflect broad investor sentiment, including both economic/market conditions and naturally occurring forces. Positive and negative sentiment related to these factors tends to build gradually over time.
• Physics-Based Sentiment Drivers. Shown as dashed lines, these drivers reflect only naturally occurring forces. We can forecast the drivers several months into the future. They do not predict specific news or events but instead estimate how investors are likely to respond to them. Elevated optimism amplifies positive reactions to good news, while natural pessimism intensifies responses to negative developments.
   

During times of economic and market stress, naturally occurring shifts exert a stronger influence on investor behavior, leading to emotion-driven trading. During such periods, the Macro MRI converges with and follows more closely the Macro Physics-Based Driver (Macro Driver), while the Micro MRI converges with and follows more closely the Micro Physics-Based Driver (Micro Driver).

The drivers forecast likely shifts in sentiment, while the MRI show how those shifts have actually influenced investor behavior. These two sets of indicators are calibrated to one another and tend to become more synchronized during periods of stress or crisis. When both develop a negative trend, this serves as an early warning signal, as discussed in Note 4.

The MRI series is derived solely from index price changes, measuring price acceleration over periods ranging from several weeks to multiple quarters. These indicators help identify sentiment inflection points, highlighting short- and long-term opportunities to enter or exit the market.

• Macro MRI (solid light blue line): Reflects long-term price trends lasting several quarters. Levels are normalized to range from 0 to 100, with the current score and slope (positive or negative) shown in the legend. 
• Exceptional Macro MRI (solid light blue spikes): Appears when the slope of the Macro MRI is likely to turn more positive, signaling rising market resilience. When present, it can offset pessimism associated with a declining Macro or Micro MRI. Its disappearance often precedes short-term market price weakness.
• Micro MRI (solid green): Captures shorter-term price trends lasting several weeks. A trough at a low level suggests a strong short-term buying opportunity, while a peak at a high level indicates a strong short-term selling opportunity.
   

In general, the market tends to recover quickly and move higher when at least two of the three MRI indicate resilience.

We identify four physics-based drivers that forecast periods of naturally occurring optimism and pessimism. These operate independently of economic and market factors but exert significant influence on investor behavior, especially during periods of stress. Convergence between MRI and their drivers is often an early sign of market vulnerability.

   Cyclic Drivers – Gradual changes:

• Macro Driver (dashed light blue line): Forecasts long-term shifts in sentiment that shape the Macro MRI. Low levels indicate natural pessimism, leaving markets vulnerable, particularly when combined with negative economic views. 
• Micro Driver (dashed green): Forecasts short-term shifts in sentiment that influence the Micro MRI and short-term price changes. Low levels indicate vulnerability. 

   Episodic Drivers – Abrupt changes:

• Flash Driver (dashed yellow): Identifies times when gradual sentiment trends are disrupted, often causing sudden market movements. Strong correlations exist between this driver and multi-week price disruptions.
• Minor Flash Driver (dashed gold): Detects brief bursts of optimism or pessimism. While not statistically significant over multi-decade tests, it is often associated with abrupt moves when investor views on economic factors are neutral or negative and/or consistent with other indicators.
   

Forecasts appear to the right of the vertical dashed blue line. The Macro, Micro, and Flash Drivers are the most important for assessing future resilience. If all three indicate pessimism, the market is naturally inclined to be vulnerable and slow to recover from declines. The episodic Flash Driver dominates cyclic drivers. 

Regarding accuracy, the Episodic Drivers are more accurate than the Cyclic Drivers, which can be off by +/- three weeks. 

To assess investor reactions to economic forces, we monitor the gap between actual and predicted sentiment metrics. This helps separate natural forces from economic and market influences.

• A small gap indicates neutral sentiment related to economic conditions. 
• A large positive gap suggests investors view economic and market conditions favorably.
• A large negative gap suggests investors hold negative views on economic and market conditions.
   

Key early warning signals of potential market declines include:

1. The Macro and Micro Drivers moving together in a negative trend during the forecast period. 
2. The MRI beginning to track their Drivers more closely. Since Drivers inevitably turn negative during their cycles, close alignment during an uptrend often foreshadows a downturn in the MRI and market prices.