Investor Summary – SPY (S&P 500 ETF) Outlook (April 2025)

Abstract

SPY has shown a mild rebound in spot price recently, but our quantum-inspired modelling suggests caution. The first derivative (Ψₚ′(t)) remains negative, indicating that price momentum is still downward. While the second derivative (Ψₚ″(t)) is less negative, implying a slowing rate of decline, it has not yet crossed into positive territory—so there’s no confirmation of a true reversal. At the same time, ACI(t) has breached the 95th percentile threshold, indicating intense crowd focus. Historically, such spikes precede turning points, but in this case, the signal lacks confirmation from internal price dynamics. Investors should hold off on fresh allocations until both momentum (Ψₚ′(t)) and acceleration (Ψₚ″(t)) approach or exceed zero.

Details

SPY Outlook: Four-Chart Quantum Analysis (Feb–Apr 2025)

Prepared by Claremont Partners, April 2025

Disclaimer: This is not investment advice. Interpretations below are for educational and theoretical research purposes only. Please consult a licensed financial advisor before making any decisions.

Summary:

SPY (S&P 500 ETF) has exhibited crowd-induced volatility through March 2025, but recent spot price action has rebounded. Using our quantum-inspired modelling based on our patent-pending Modified Schrodinger Equation, we plot the normalized price Ψₚ(t), its first and second derivatives (Ψₚ′(t), Ψₚ″(t)), and the crowd-sensitive Attention Collapse Index ACI(t) to guide investor behaviour.

Chart 1: Ψₚ(t) Normalized Price

Despite an upward rebound in the spot price recently, the normalized Ψₚ(t) trend has moved downward since mid-February. This mismatch highlights how market internal momentum is lagging the spot recovery—a potential warning sign that the bounce may lack structural support.

Chart 2: Ψₚ′(t) Velocity

The first derivative (velocity) of Ψₚ(t) remains in negative territory, although its magnitude is declining. This suggests that while prices are falling slower than before, the system has not yet reversed direction. Investors should interpret this as a “neutral-to-cautious” signal—there’s no definitive sign of bullish reversal yet.

Chart 3: Ψₚ″(t) Acceleration (Curvature)

Curvature turned positive briefly before dipping again. Acceleration patterns are noisy but no longer as extreme as late March. The lack of consistent positive curvature tells us that a sustained reversal in investor sentiment has not yet taken root.

Chart 4: ACI(t) vs Collapse Threshold

ACI(t) recently spiked above the 95th percentile threshold—a classic sign of crowd attention, fear, or reflexive trading behaviour. While previously such spikes were tied to bearish collapses, we are now seeing positive price response. This confirms our insight: high ACI(t) could signal crowd attention without necessarily being negative. But caution is still warranted—this alert must coincide with a rise in Ψₚ′(t) before buying conviction can be justified.

Investment Interpretation (April 2025)

Current signals suggest:

• Do not buy yet.

• SPY is under crowd attention (high ACI), but the velocity Ψₚ′(t) and acceleration Ψₚ″(t) are not yet supportive of a sustained rally.

• If Ψₚ′(t) flattens to zero and then turns positive, and Ψₚ″(t) holds above zero, we may witness a turning point.

• The critical signal is a convergence of three events:

1. Ψₚ′(t) = 0 (inflection point),

2. Ψₚ″(t) > 0 (rising momentum),

3. ACI(t) > threshold (crowd shift with participation).

Until then, investors should hold off, stay alert, and observe the next 5–7 sessions for signs of confluence.