Context-Aware RSI: Integrating Global M2 Money Supply and News Sentiment

A Design Proposal for Adaptive Technical Analysis

Version: 2.1

Author: Martin Russmann (mrussmann@proton.me)

Updated: December 2025

Prototype: https://e-rsi.anassumption.com

1. Executive Summary

This design proposal presents a comprehensive framework for enhancing the Relative Strength Index (RSI) by incorporating macroeconomic liquidity conditions and market sentiment. The traditional RSI, while widely used, suffers from well-documented limitations including false signals during trending markets and fixed thresholds that fail to adapt to changing market conditions.

Our core design principle is to preserve the canonical RSI scale $[0,100]$ while adapting interpretation through dynamic thresholds and conditional normalization. This approach maintains interpretability for practitioners familiar with traditional RSI while systematically accounting for external factors that influence asset prices.

Key contributions of this proposal:

• A canonical design that preserves RSI's bounded nature while enabling context-awareness
• An explicit, GDP-weighted definition of global M2 money supply
• NEW in v2.1: Monetary transmission lag analysis to find optimal delay between M2 changes and market effects
• A regularized calibration framework with overfitting safeguards
• Operational specifications for real-time implementation
• A working prototype for practitioner validation

A working prototype implementing this framework is available at https://e-rsi.anassumption.com.

Keywords: Relative Strength Index, Global M2 Money Supply, News Sentiment Analysis, Adaptive Technical Indicators, Liquidity-Aware Trading, Technical Analysis Enhancement

2. Introduction

2.1 Background and Motivation

The Relative Strength Index (RSI), introduced by J. Welles Wilder in his seminal 1978 work New Concepts in Technical Trading Systems [1], has become one of the most widely used momentum oscillators in technical analysis. The indicator measures the speed and magnitude of price movements on a bounded scale from 0 to 100, with readings above 70 traditionally interpreted as "overbought" and readings below 30 as "oversold."

Despite its enduring popularity among traders and analysts, the RSI suffers from several well-documented limitations:

1. False signals in trending markets: During sustained bull markets, RSI frequently signals overbought conditions while prices continue rising, leading to premature exits or missed opportunities [2].

2. Static threshold assumptions: The 70/30 boundaries assume stationary market conditions, yet market dynamics vary substantially across liquidity regimes and sentiment environments.

3. Price-only calculation: RSI ignores fundamental drivers of price movements, including macroeconomic liquidity conditions and market psychology.

4. Arbitrary parameterization: The standard 14-period lookback lacks theoretical justification and may not be optimal across different assets and timeframes.

These limitations motivate the central question of this proposal: Can we enhance RSI to account for external market conditions while preserving its interpretability and bounded nature?

2.2 The Case for M2 Money Supply

Global money supply, particularly the broad M2 aggregate, serves as a fundamental driver of asset prices across multiple channels:

Portfolio rebalancing channel: When central banks expand money supply, the additional liquidity flows into financial assets as investors seek returns, pushing up prices [3].

Discount rate channel: Monetary expansion typically accompanies lower interest rates, reducing the discount rate applied to future cash flows and increasing present values [4].

Risk appetite channel: Abundant liquidity tends to compress risk premiums and encourage risk-taking behavior, amplifying price movements [5].

Empirical research consistently documents significant relationships between M2 growth and equity returns. Bernanke and Kuttner [6] find that a surprise 25-basis-point cut in the federal funds rate is associated with approximately a 1% increase in broad stock indices. Thorbecke [3] demonstrates that expansionary monetary policy reliably increases stock returns across multiple identification strategies.

Why M2 over other macro aggregates? We choose M2 over alternatives for several reasons:

• Breadth: M2 captures a wider range of liquid assets than M1, including savings deposits and money market funds
• Observability: Unlike credit conditions or real rates, M2 is directly measured and consistently reported across major economies
• Leading indicator properties: M2 changes often precede asset price movements, providing predictive value
• Cross-country comparability: Central banks report M2 using relatively standardized definitions

2.3 The Role of Market Sentiment

News sentiment captures the collective psychological state of market participants and serves as a distinct information source from price data alone. Tetlock's foundational work [7] demonstrates that media pessimism predicts downward pressure on market prices, while Engelberg and Parsons [8] provide causal evidence that local media coverage directly influences local trading activity.

Sentiment affects markets through several mechanisms:

Attention channel: News coverage directs investor attention to specific assets or themes, influencing trading activity [8].

Belief updating channel: Investors update their expectations based on news content, affecting demand and supply [7].

Coordination channel: Public information serves as a focal point for coordinating beliefs and actions across dispersed market participants.

By incorporating sentiment, we can potentially anticipate shifts in market direction before they fully manifest in price-based indicators like RSI.

2.4 Design Philosophy

A critical challenge in enhancing RSI is maintaining its bounded, interpretable nature. Many proposed modifications—including simple multiplicative adjustments—break the fundamental property that RSI lies in $[0, 100]$. An "enhanced RSI" of 85 or 120 loses intuitive meaning and comparability with historical readings.

We therefore adopt the following canonical design principle:

Design Choice: The base RSI calculation remains unchanged, preserving the $[0,100]$ scale. External factors (M2, sentiment, volatility) influence interpretation exclusively through dynamic thresholds and conditional normalization, never by direct transformation of the RSI value itself.

This design ensures that:

• RSI values remain directly comparable across time periods and assets
• Practitioners retain intuitive understanding of the indicator
• Context-awareness is achieved without breaking mathematical bounds
• The enhancement is additive to existing workflows rather than disruptive

3. Literature Review

3.1 RSI Limitations and Extensions

The academic and practitioner literature has long recognized RSI's limitations. Cardwell [2] pioneered the concept of "positive and negative reversals," demonstrating that RSI behavior differs systematically in bull versus bear markets. This work implicitly suggests that interpretation should be conditioned on market regime—an insight we formalize in this proposal.

Murphy's comprehensive treatment [9] notes that RSI tends to oscillate between 40 and 80 during bull markets, rarely reaching the traditional 30 oversold level. Conversely, during bear markets, RSI typically ranges between 20 and 60. This regime-dependent behavior motivates our conditional normalization approach.

3.2 Monetary Policy and Asset Prices

The relationship between monetary policy and asset prices has been extensively studied. Key findings relevant to our framework include:

Thorbecke (1997) [3]: Using multiple identification strategies (VAR innovations, narrative indicators, event studies), this seminal paper establishes that expansionary monetary policy reliably increases stock returns. The effect operates through both expected cash flows and discount rates.

Rigobon and Sack (2004) [5]: Employing heteroskedasticity-based identification, this study finds that a 25-basis-point increase in short-term rates leads to a decline in stock prices of approximately 1.7%. The methodology addresses endogeneity concerns that plague earlier studies.

Bernanke and Kuttner (2005) [6]: This paper decomposes the stock market's response to monetary policy into effects on expected dividends, real interest rates, and equity premiums. Most of the response operates through the equity premium channel, suggesting that liquidity conditions affect risk appetites.

Pícha (2017) [10]: Examining the long-run relationship between money supply and stock indices across multiple countries, this study confirms positive cointegration for several major markets including the US, UK, and emerging economies.

3.3 Sentiment Analysis in Finance

The application of sentiment analysis to financial markets has evolved rapidly:

Lexicon-based approaches: Early work relied on word lists such as the Harvard General Inquirer or finance-specific dictionaries. Loughran and McDonald [11] demonstrate that general-purpose sentiment dictionaries perform poorly in financial contexts, motivating domain-specific lexicons.

VADER: Hutto and Gilbert [12] develop VADER (Valence Aware Dictionary and sEntiment Reasoner), which incorporates grammatical and syntactical conventions for improved accuracy. VADER provides compound sentiment scores in $[-1, 1]$ and is computationally efficient for real-time applications.

Transformer models: Recent advances in NLP enable more nuanced sentiment analysis. FinBERT [13] fine-tunes BERT on financial text, achieving state-of-the-art performance on financial sentiment classification tasks.

Commercial solutions: Providers like RavenPack [14] offer institutional-grade sentiment feeds aggregated from thousands of news sources with low latency, suitable for systematic trading applications.

3.4 Adaptive Technical Indicators

Recent work has explored conditioning technical indicators on external factors:

Mostafavi and Hooman [15] examine which technical indicators provide the most predictive value when combined with machine learning models, finding that adaptive indicators outperform static versions.

Kim and Enke [16] integrate macroeconomic indicators with technical signals using data-driven approaches, demonstrating improved forecasting accuracy for stock market direction.

Gerunov [17] applies machine learning to combine macroeconomic, technical, and sentiment features for market forecasting, providing a template for multi-factor integration.

However, few studies specifically address enhancing RSI with macroeconomic and sentiment conditioning—a gap this proposal aims to fill.

4. Standard RSI: Calculation and Limitations

4.1 Traditional RSI Formula

The RSI compares the magnitude of recent gains to recent losses over a specified lookback period $n$ (typically 14 periods). The calculation proceeds as follows:

Step 1: Compute price changes

$$\delta_t = \text{Close}_t - \text{Close}_{t-1}$$

Step 2: Separate gains and losses

$$G_t = \max(\delta_t, 0)$$

$$L_t = \max(-\delta_t, 0)$$

Step 3: Compute smoothed averages using Wilder's exponential moving average

$$\overline{G}_t = \frac{\overline{G}_{t-1} \times (n-1) + G_t}{n}$$

$$\overline{L}_t = \frac{\overline{L}_{t-1} \times (n-1) + L_t}{n}$$

Step 4: Calculate Relative Strength

$$RS_t = \frac{\overline{G}_t}{\overline{L}_t}$$

Step 5: Normalize to [0, 100]

$$\text{RSI}_t = 100 - \frac{100}{1 + RS_t} = \frac{100 \cdot RS_t}{1 + RS_t}$$

The RSI is bounded by construction: when $\overline{L}_t \to 0$ (all gains), $RS_t \to \infty$ and $\text{RSI}_t \to 100$; when $\overline{G}_t \to 0$ (all losses), $RS_t \to 0$ and $\text{RSI}_t \to 0$.

4.2 Detailed Analysis of Limitations

4.2.1 False Signals in Trending Markets

Consider a persistent uptrend accompanied by monetary expansion. As prices rise consistently, RSI will naturally trend toward overbought territory. Under traditional interpretation, this signals a sell—yet the underlying liquidity conditions support continued price appreciation.

Illustrative scenario: During 2020-2021, global M2 expanded by approximately 25% as central banks responded to the pandemic. Equity markets rose substantially, with the S&P 500 gaining over 40% from March 2020 lows. Throughout this period, RSI frequently exceeded 70, generating repeated overbought signals that would have resulted in premature exits from a profitable trend.

The fundamental issue is that traditional RSI interpretation assumes mean-reverting price behavior, but liquidity-driven trends can persist far longer than price-only analysis suggests.

4.2.2 Static Threshold Problem

The 70/30 thresholds are essentially arbitrary conventions without theoretical foundation. Empirically, optimal thresholds vary across:

• Asset classes: Highly volatile assets like cryptocurrencies may require wider thresholds (e.g., 80/20)
• Market regimes: Bull markets exhibit higher average RSI than bear markets
• Liquidity conditions: Expansionary environments support higher sustainable RSI levels
• Volatility regimes: High volatility produces more extreme RSI readings

4.2.3 Lack of External Context

RSI's exclusive reliance on price data means it cannot distinguish between:

• Price rises driven by fundamental liquidity expansion (sustainable)
• Price rises driven by speculative excess without fundamental support (unsustainable)
• Price declines during temporary sentiment shocks (buying opportunity)
• Price declines reflecting fundamental deterioration (continued risk)

By incorporating M2 and sentiment, we aim to provide this missing context.

5. Global M2 Money Supply: Definition and Construction

5.1 Formal Definition

We define Global M2 as a GDP-weighted aggregate of national M2 measures from the five largest economies by money supply:

$$M2^{global}_t = \sum_{i \in \mathcal{C}} w_i \cdot M2^{(i)}_t$$

where the constituent set $\mathcal{C} = \{\text{US, Eurozone, China, Japan, UK}\}$ represents approximately 75% of global economic output, and weights $w_i$ are proportional to nominal GDP:

$$w_i = \frac{\text{GDP}_i}{\sum_{j \in \mathcal{C}} \text{GDP}_j}$$

Table 1: Global M2 composition. Weights are approximate and should be updated annually based on IMF World Economic Outlook GDP data.

5.2 Currency Considerations

National M2 figures are reported in local currencies. For aggregation, we convert to a common currency (USD) using end-of-month exchange rates:

$$M2^{global,USD}_t = \sum_{i \in \mathcal{C}} w_i \cdot M2^{(i)}_t \cdot FX^{(i)}_t$$

where $FX^{(i)}_t$ is the exchange rate of currency $i$ per USD.

Robustness consideration: Exchange rate movements can introduce noise into the global M2 measure. An alternative approach uses constant exchange rates (e.g., PPP rates) for more stable aggregation. In practice, the growth rate $\Delta M2^{global}_t$ is less sensitive to exchange rate choices than the level.

5.3 Growth Rate and Regime Classification

We compute the year-over-year growth rate to capture the liquidity expansion or contraction trend:

$$\Delta M2_t = \frac{M2^{global}_t - M2^{global}_{t-252}}{M2^{global}_{t-252}}$$

where 252 represents the number of trading days in a year. For monthly data, replace 252 with 12.

Regime classification uses rolling percentiles over a 5-year lookback to establish context-relative thresholds:

$$R^{M2}_t = \text{Percentile}(\Delta M2_t, \text{lookback}=1260 \text{ days})$$

We partition the percentile distribution into four regimes:

Table 2: M2 regime definitions with interpretive guidance

Minimum sample size requirement: Each regime bin must contain at least 63 observations (approximately one quarter of trading days) for stable statistical estimation. If this threshold is not met, adjacent bins should be merged.

5.4 US-Centric Proxies and Their Limitations

For real-time applications, official M2 data arrives with 2-4 week delays. We can estimate current US M2 using high-frequency proxies:

Table 3: High-frequency proxies for US M2 nowcasting

Important limitation: These proxies are US-centric and may not capture global liquidity dynamics. For non-US assets, particularly emerging market equities or local currency bonds, consider:

• Using lagged official global M2 data (accepting the delay)
• Weighting local M2 alongside global M2
• Using asset-class-specific liquidity measures (e.g., FX reserves for EM)

6. Sentiment Quantification

6.1 Sentiment Score Construction

We aggregate news sentiment using a recency-weighted average that gives greater influence to recent articles:

$$S_t = \frac{\sum_{i=1}^{N} e^{-\lambda(t - t_i)} \cdot s_i}{\sum_{i=1}^{N} e^{-\lambda(t - t_i)}}$$

where:

• $s_i \in [-1, 1]$ is the sentiment score of article $i$
• $t_i$ is the publication timestamp of article $i$
• $N$ is the number of articles in the lookback window
• $\lambda$ controls recency decay (higher $\lambda$ = faster decay)

Recommended parameter: $\lambda = 0.1$ per day, implying a half-life of approximately 7 days.

6.2 Sentiment Scoring Methods

Table 4: Sentiment scoring methods with tradeoffs

6.3 Sentiment Regime Classification

Analogous to M2, we classify sentiment into regimes using rolling percentiles:

$$R^{S}_t = \text{Percentile}(S_t, \text{lookback}=252 \text{ days})$$

The shorter lookback (1 year vs. 5 years for M2) reflects sentiment's higher frequency dynamics.

6.4 Event-Time vs. Clock-Time Aggregation

Two approaches exist for sentiment aggregation:

Clock-time: Aggregate all articles within fixed time windows (e.g., daily). Simple but may miss intraday sentiment shifts around major events.

Event-time: Weight articles by proximity to significant events (earnings, Fed announcements, economic releases). More responsive but requires event calendar integration.

For most applications, daily clock-time aggregation with recency weighting provides a reasonable balance of simplicity and responsiveness.

7. The Canonical Design: Dynamic Thresholds with Conditional Normalization

7.1 Design Rationale

We deliberately reject approaches that directly transform RSI values (e.g., multiplicative scaling) because they:

1. Break the $[0, 100]$ bound, destroying comparability
2. Can produce negative or $>100$ values without clear interpretation
3. Mix conceptually distinct adjustments in a single number

Instead, we adapt RSI interpretation through two complementary mechanisms:

• Method 1: Adjust the thresholds that define overbought/oversold
• Method 2: Normalize RSI relative to regime-conditional distributions

Both methods preserve the original RSI value while providing context-aware signals.

7.2 Method 1: Regime-Conditional Dynamic Thresholds

The overbought and oversold thresholds adjust based on the joint regime state:

$$\theta^{OB}_t = \theta^{OB}_{base} + \alpha_{M2} \cdot (R^{M2}_t - 50) + \alpha_S \cdot (R^{S}_t - 50) + \alpha_\sigma \cdot (R^{\sigma}_t - 50)$$

$$\theta^{OS}_t = \theta^{OS}_{base} - \alpha_{M2} \cdot (R^{M2}_t - 50) - \alpha_S \cdot (R^{S}_t - 50) - \alpha_\sigma \cdot (R^{\sigma}_t - 50)$$

where:

• $\theta^{OB}_{base} = 70$, $\theta^{OS}_{base} = 30$ (standard thresholds)
• $R^{M2}_t, R^{S}_t, R^{\sigma}_t \in [0, 100]$ are regime percentiles
• $\alpha_{M2}, \alpha_S, \alpha_\sigma > 0$ are sensitivity parameters (threshold points per percentile deviation from median)

Example: Suppose $R^{M2}_t = 80$ (strong expansion), $R^{S}_t = 60$ (mildly positive sentiment), $R^{\sigma}_t = 40$ (below-average volatility), and $\alpha_{M2} = \alpha_S = \alpha_\sigma = 0.1$.

$$\theta^{OB}_t = 70 + 0.1 \cdot (80 - 50) + 0.1 \cdot (60 - 50) + 0.1 \cdot (40 - 50)$$

$$= 70 + 3 + 1 - 1 = 73$$

The overbought threshold rises from 70 to 73, reflecting that higher RSI values are sustainable given supportive liquidity and sentiment conditions.

7.3 Method 2: Conditional Z-Score Normalization (Recommended Primary Method)

This method normalizes RSI readings relative to the historical distribution conditional on the current regime:

$$Z^{RSI}_t = \frac{\text{RSI}_t - \mu_{RSI|R}}{\sigma_{RSI|R}}$$

where $\mu_{RSI|R}$ and $\sigma_{RSI|R}$ are the mean and standard deviation of RSI conditional on regime $R = (R^{M2}, R^{S}, R^{\sigma})$.

Practical implementation: Rather than conditioning on the full joint distribution (which may have sparse cells), we use a simplified additive adjustment:

$$\mu_{RSI|R} = \mu_{RSI} + \beta_{M2} \cdot (R^{M2}_t - 50) + \beta_S \cdot (R^{S}_t - 50) + \beta_\sigma \cdot (R^{\sigma}_t - 50)$$

$$\sigma_{RSI|R} = \sigma_{RSI} \cdot \left(1 + \gamma \cdot \frac{R^{\sigma}_t - 50}{100}\right)$$

where $\mu_{RSI}$ and $\sigma_{RSI}$ are unconditional RSI statistics, and $\beta_{M2}, \beta_S, \beta_\sigma, \gamma$ are estimated coefficients.

Signal generation:

• $Z^{RSI}_t > 2.0$: Strongly overbought relative to current conditions
• $Z^{RSI}_t > 1.0$: Moderately overbought
• $-1.0 < Z^{RSI}_t < 1.0$: Normal for current regime
• $Z^{RSI}_t < -1.0$: Moderately oversold
• $Z^{RSI}_t < -2.0$: Strongly oversold relative to current conditions

Why we recommend this method: The Z-score approach:

1. Preserves the original RSI for direct inspection
2. Provides a statistically grounded measure of extremity
3. Automatically adapts to regime-specific RSI distributions
4. Produces standardized signals comparable across assets

7.4 Volatility Integration

Market volatility affects RSI reliability: high volatility produces more extreme readings that may not represent true overbought/oversold conditions. We compute annualized realized volatility:

$$\sigma_t = \sqrt{\frac{252}{n} \sum_{i=1}^{n} (r_{t-i} - \bar{r})^2}$$

where $r_t = \ln(\text{Close}_t / \text{Close}_{t-1})$ are log returns and $n$ is the lookback (typically 20 days).

The volatility regime percentile $R^{\sigma}_t$ enters both the threshold adjustment and conditional distribution estimation.

7.5 Combined Signal Generation

The complete signal generation process is:

Algorithm: Context-Aware RSI Signal Generation

Input: Price series, M2 data, sentiment data

1. Compute standard RSI_t using Wilder's formula
2. Compute regime percentiles: R^M2_t, R^S_t, R^σ_t
3. Calculate conditional statistics: μ_RSI|R, σ_RSI|R
4. Compute Z-score: Z^RSI_t = (RSI_t - μ_RSI|R) / σ_RSI|R
5. Calculate dynamic thresholds: θ^OB_t, θ^OS_t

Output: RSI_t, Z^RSI_t, θ^OB_t, θ^OS_t

Signal:
  if Z^RSI_t > 2 OR RSI_t > θ^OB_t:
    Overbought signal
  else if Z^RSI_t < -2 OR RSI_t < θ^OS_t:
    Oversold signal
  else:
    Neutral

8. Calibration and Regularization

8.1 Parameter Space

The framework requires estimation of the following parameters:

Table 5: Calibration parameters and typical ranges

8.2 Objective Function

Parameters are optimized to maximize regularized risk-adjusted returns:

$$\hat{\boldsymbol{\theta}} = \arg\max_{\boldsymbol{\theta}} \left[ \frac{E[R_p(\boldsymbol{\theta})] - R_f}{\sigma_p(\boldsymbol{\theta})} - \lambda_{reg} \|\boldsymbol{\theta}\|_2^2 \right]$$

where:

• $R_p(\boldsymbol{\theta})$ is the strategy return under parameter vector $\boldsymbol{\theta}$
• $R_f$ is the risk-free rate
• $\sigma_p(\boldsymbol{\theta})$ is strategy volatility
• $\lambda_{reg}$ is the regularization strength

Recommended: $\lambda_{reg} = 0.01$, which penalizes extreme parameter values without overly constraining the optimization.

8.3 Overfitting Mitigation Strategies

Given the multi-dimensional parameter space, overfitting is a significant concern. We employ several safeguards:

8.3.1 Nested Cross-Validation

1. Outer loop: 5-fold time-series cross-validation for performance estimation
2. Inner loop: 3-fold cross-validation within each training fold for hyperparameter selection

This ensures that reported performance is estimated on data not used for parameter selection.

8.3.2 Walk-Forward Optimization

• Training window: Rolling 3-year (756 trading days)
• Test window: 1-year (252 trading days)
• Re-estimation frequency: Quarterly (63 trading days)

Parameters are re-optimized at each step using only past data, simulating realistic implementation conditions.

8.3.3 Parameter Count Constraint

To limit model complexity, we impose a maximum of 5 free parameters in any single specification. If using all parameters in Table 5, some should be fixed at theoretically motivated values or constrained to equal each other.

8.3.4 Multiple Testing Correction

When evaluating across multiple assets, apply Bonferroni or Benjamini-Hochberg FDR correction to p-values. For $n$ assets tested, the adjusted significance threshold becomes $\alpha / n$ (Bonferroni) or uses the BH procedure for FDR control.

8.4 Re-estimation Protocol

Table 6: Recommended re-estimation schedule

9. M2 Nowcasting for Real-Time Applications

9.1 The Data Lag Problem

Official M2 data from central banks is typically released with a 2-4 week lag, creating challenges for real-time trading applications. For example, US M2 for month $t$ is usually released in the third week of month $t+1$.

9.2 Nowcasting Model

We estimate current US M2 using observable high-frequency proxies:

$$\widehat{M2}^{US}_t = \beta_0 + \sum_{i=1}^{k} \beta_i X_{i,t} + \epsilon_t$$

Estimation approach:

• Static OLS: Estimate coefficients on a rolling 2-year window. Simple but may miss structural changes.
• Kalman filter: Allow dynamic coefficient evolution. More adaptive but requires state-space specification.

Model validation: Assess out-of-sample nowcast accuracy using RMSE and directional accuracy metrics. The nowcast should correctly predict M2 growth direction at least 70% of the time to add value.

9.3 Interpolation for Daily Values

Since M2 is reported monthly, we need daily values for indicator calculation. Options include:

• Step function: Hold monthly value constant until next release (simplest)
• Linear interpolation: Smooth transition between monthly values
• Spline interpolation: Smoother curves but risk of overfitting

For regime classification, the choice matters less than for level estimation, as percentile ranks are relatively robust to interpolation method.

10. Monetary Transmission Lag Analysis (NEW in v2.1)

10.1 The Transmission Lag Problem

A critical but often overlooked aspect of incorporating M2 money supply into technical analysis is the time delay between monetary changes and their manifestation in asset prices. When central banks expand or contract money supply, the effects do not appear instantaneously in market prices. This delay—the monetary transmission lag—varies based on:

• Transmission channels: Different channels (portfolio rebalancing, discount rate, risk appetite) operate at different speeds
• Asset class: Highly liquid assets may respond faster than illiquid ones
• Market conditions: The lag may compress during crisis periods when attention to monetary policy is heightened
• Information diffusion: Market participants need time to observe, interpret, and act on M2 data

Using M2 data without accounting for this lag can lead to suboptimal signals—either too early (before the market effect materializes) or misaligned with actual price dynamics.

10.2 Statistical Framework for Lag Discovery

We employ two complementary statistical methods to identify the optimal monetary lag:

10.2.1 Cross-Correlation Analysis

Cross-correlation measures the relationship between M2 changes at time $t$ and market returns at time $t + \tau$:

$$\rho(\tau) = \text{Corr}(\Delta M2_t, R_{t+\tau})$$

where:
- $\Delta M2_t$ is the year-over-year M2 growth rate
- $R_{t+\tau}$ is the forward market return over a specified window (e.g., 5 days)
- $\tau$ is the lag in trading days (typically tested from 0 to 60 days)

The optimal lag $\tau^*$ maximizes the absolute correlation:

$$\tau^*_{corr} = \arg\max_{\tau} |\rho(\tau)|$$

Statistical significance testing: For each lag, we compute the p-value using a t-test:

$$t = \frac{r \sqrt{n-2}}{\sqrt{1-r^2}}$$

where $r$ is the sample correlation and $n$ is the number of observations. To account for multiple testing (testing many lags), we apply Bonferroni correction:

$$\alpha_{adjusted} = \frac{\alpha}{k}$$

where $k$ is the number of lags tested and $\alpha$ is the desired significance level (typically 0.05).

10.2.2 Granger Causality Testing

While correlation identifies association, Granger causality tests whether M2 changes have predictive power for market returns beyond what past returns alone provide. The test compares two models:

Restricted model (autoregressive only):
$$R_t = \alpha + \sum_{i=1}^{p} \beta_i R_{t-i} + \epsilon_t$$

Unrestricted model (includes lagged M2):
$$R_t = \alpha + \sum_{i=1}^{p} \beta_i R_{t-i} + \sum_{j=1}^{q} \gamma_j \Delta M2_{t-j} + \epsilon_t$$

The null hypothesis $H_0: \gamma_1 = \gamma_2 = ... = \gamma_q = 0$ is tested using an F-statistic:

$$F = \frac{(RSS_R - RSS_U) / q}{RSS_U / (n - p - q - 1)}$$

where $RSS_R$ and $RSS_U$ are the residual sum of squares for restricted and unrestricted models.

Interpretation: A significant F-statistic (low p-value) indicates that M2 changes Granger-cause market returns at the tested lag.

10.3 Optimal Lag Determination Algorithm

The algorithm combines cross-correlation and Granger causality results:

Algorithm: Monetary Lag Discovery

Input: M2 growth series, Market return series
Parameters: max_lag (default: 60), significance_level (default: 0.05)

1. For each lag τ in [0, max_lag]:
   a. Compute cross-correlation ρ(τ) and p-value
   b. Apply Bonferroni correction to p-value

2. Identify significant lags: S_corr = {τ : p(τ) < α_adjusted}

3. For each lag q in [1, min(max_lag, 10)]:
   a. Run Granger causality test
   b. Record F-statistic and p-value

4. Identify Granger-significant lags: S_granger = {q : p(q) < α_adjusted}

5. Determine optimal lag:
   if S_corr is not empty:
       τ* = argmax_{τ ∈ S_corr} |ρ(τ)|
   else:
       τ* = argmax_τ |ρ(τ)|  # Use highest correlation even if not significant

6. Compute bootstrap confidence interval for τ*

Output: τ*, confidence_interval, correlation_profile, granger_results

10.4 Bootstrap Confidence Intervals

To quantify uncertainty in the optimal lag estimate, we compute bootstrap confidence intervals:

Algorithm: Bootstrap CI for Optimal Lag

Input: M2 series, Returns series, optimal_lag τ*, n_bootstrap (default: 1000)

1. For b = 1 to n_bootstrap:
   a. Resample (M2, Returns) pairs with replacement
   b. Compute correlation at lag τ*
   c. Store correlation in bootstrap_correlations[]

2. Sort bootstrap_correlations
3. CI_lower = percentile(bootstrap_correlations, 2.5)
4. CI_upper = percentile(bootstrap_correlations, 97.5)

Output: (CI_lower, CI_upper)

10.5 Empirical Findings

Based on analysis of S&P 500 (SPY) and M2 data from 2010-2024:

Table 8: Typical monetary lag values by asset class

Key observations:
- Most equity markets show significant M2 effects at lags of 5-15 trading days
- More liquid/speculative assets (crypto) respond faster
- Safe-haven assets (gold) show longer lags
- The lag is not constant—it varies with market conditions

10.6 Integration with RSI Framework

The discovered optimal lag $\tau^*$ is integrated into the E-RSI calculation:

Before (v2.0): M2 regime percentile used contemporaneously
$$R^{M2}_t = \text{Percentile}(\Delta M2_t, \text{lookback})$$

After (v2.1): M2 regime percentile uses lagged M2 data
$$R^{M2}_t = \text{Percentile}(\Delta M2_{t-\tau^*}, \text{lookback})$$

This shift ensures that the M2 signal aligns with when its effects actually manifest in prices, improving signal accuracy.

10.7 Validation Run Configuration

The prototype at https://e-rsi.anassumption.com includes a Monetary Lag Analysis tool with the following options:

Table 9: Monetary Lag Analysis configuration parameters

10.8 Interpreting Results

The analysis produces:

1. Optimal Lag Value: The recommended delay in trading days
2. Correlation Chart: Bar chart showing correlation at each lag (significant lags highlighted)
3. Granger Causality Chart: F-statistics by lag with significance markers
4. Statistical Summary: Key metrics including p-values, confidence intervals
5. Interpretation Text: Plain-English explanation of findings

Example output interpretation:

"M2 money supply changes show a statistically significant positive correlation with SPY returns at a lag of 7 trading days. The correlation coefficient is 0.12 (p < 0.05 after Bonferroni correction). Granger causality tests also indicate that M2 changes help predict market returns at lags 5-8. This suggests monetary policy changes may take approximately 7 trading days (~1.5 weeks) to manifest in market prices."

10.9 Limitations and Considerations

1. Non-stationarity: M2 and price series may be non-stationary, potentially affecting Granger test validity. Differencing may be required.

2. Regime dependence: The optimal lag may differ between bull/bear markets or crisis/normal periods. Consider regime-specific lag estimation.

3. Sample size requirements: Reliable lag estimation requires substantial history (minimum 2 years, preferably 5+).

4. Spurious correlation: Even with significance testing, correlations may be spurious. Economic intuition should guide interpretation.

5. Changing dynamics: The monetary transmission mechanism may evolve over time. Periodic re-estimation is recommended (annually or semi-annually).

11. Implementation Architecture

11.1 Data Pipeline

┌─────────────────┐    ┌─────────────────┐    ┌─────────────────┐
│   Price Data    │    │    M2 Data      │    │   Sentiment     │
│  (Daily OHLC)   │    │   (Monthly)     │    │    (Daily)      │
└────────┬────────┘    └────────┬────────┘    └────────┬────────┘
         │                      │                      │
         ▼                      ▼                      ▼
┌─────────────────┐    ┌─────────────────┐    ┌─────────────────┐
│  Compute RSI    │    │ Compute Regimes │◄───│Compute Volatility│
│                 │    │ R^M2, R^S, R^σ  │    │                 │
└────────┬────────┘    └────────┬────────┘    └─────────────────┘
         │                      │
         └──────────┬───────────┘
                    ▼
         ┌─────────────────────┐
         │  Z-Score & Dynamic  │
         │     Thresholds      │
         └──────────┬──────────┘
                    ▼
         ┌─────────────────────┐
         │  Signal Generation  │
         └─────────────────────┘

Figure 1: Data pipeline architecture

11.2 Data Requirements

• Price data: Daily OHLC, minimum 252-day history for regime estimation, 1260 days preferred for full M2 regime lookback
• M2 data: Monthly releases from FRED (US), ECB (Eurozone), PBoC (China), BoJ (Japan), BoE (UK)
• Sentiment data: Daily aggregates from news APIs (NewsAPI, Polygon) or commercial providers (RavenPack, Bloomberg)
• Exchange rates: Daily rates for M2 currency conversion (available from FRED or central banks)

11.3 Computational Considerations

The indicator calculation is computationally lightweight:

• RSI calculation: $O(n)$ where $n$ is the lookback period
• Regime percentile: $O(T \log T)$ for sorting $T$ historical values (can be maintained incrementally)
• Conditional statistics: $O(1)$ lookup after initial computation
• Total per-bar computation: Sub-millisecond on modern hardware

The main computational cost is in the initial historical calculation and parameter optimization, not real-time signal generation.

12. Practical Trading Applications

12.1 Signal Integration

The context-aware RSI can be integrated into trading systems in several ways:

Standalone signals: Use Z-score thresholds ($\pm 2$) or dynamic threshold crossings as direct entry/exit signals.

Filter for other strategies: Require RSI confirmation (e.g., not overbought per dynamic threshold) before taking signals from other indicators.

Position sizing: Scale position size inversely with $|Z^{RSI}_t|$—larger positions when RSI is in normal range, smaller at extremes.

Regime overlay: Use M2/sentiment regime classification to select among multiple strategy variants.

12.2 Risk Management Considerations

• Stop losses: Consider wider stops during high-volatility regimes when RSI readings are naturally more extreme
• Position limits: Reduce exposure when M2 is contracting, as liquidity-driven drawdowns can be severe
• Correlation awareness: M2 affects multiple assets simultaneously; diversification benefits may be reduced during liquidity-driven moves

12.3 Backtesting Considerations

When backtesting this framework:

1. Avoid lookahead bias: Use only data available at each historical point (especially for M2 releases)
2. Account for transaction costs: RSI signals can generate frequent trades; include realistic costs
3. Test across regimes: Ensure backtest period includes both M2 expansion and contraction phases
4. Out-of-sample validation: Reserve most recent data for final validation

13. Empirical Validation Framework

13.1 Prototype Tool

The prototype at https://e-rsi.anassumption.com implements this framework and allows users to:

1. Configure all sensitivity parameters ($\alpha$, $\beta$, $\gamma$, $\lambda$)
2. Select from multiple assets and asset classes
3. Define custom backtesting periods
4. Compare enhanced RSI signals against baseline RSI
5. Export performance metrics and signal history

13.2 Recommended Validation Protocol

For rigorous evaluation, we recommend:

Asset universe:

• US Equity: S&P 500 ETF (SPY)
• Cryptocurrency: Bitcoin (BTC/USD)
• Commodity: Gold ETF (GLD)
• Emerging Markets: EM Equity ETF (EEM)
• Foreign Exchange: EUR/USD

Time period: 2015-2024, which includes:

• Multiple M2 expansion phases (2015-2016, 2020-2021)
• M2 contraction (2022-2023)
• Various volatility regimes

Parameterization: Use a single, pre-specified parameter set across all assets to avoid in-sample optimization bias.

13.3 Performance Metrics

Table 7: Performance metrics for strategy evaluation

Statistical testing: Report Sharpe ratio differences with bootstrap confidence intervals (1000 replications). Apply Bonferroni correction when comparing across multiple assets.

14. Testable Hypotheses

Based on this design, we propose the following hypotheses for empirical validation:

1. H1 (False signal reduction): Regime-conditional Z-scores reduce false overbought signals during M2 expansion periods by at least 20% compared to fixed 70 threshold, without proportionally increasing missed signals.

2. H2 (Sentiment timing): Incorporating sentiment improves signal timing around major news events (earnings releases, Fed announcements), as measured by average trade P&L in event windows.

3. H3 (Volatility adaptation): Dynamic volatility thresholds reduce whipsaw trades (round-trip losses within 5 days) by at least 15% during high-volatility regimes.

4. H4 (Cross-asset heterogeneity): Liquidity-sensitive assets (crypto, EM) show greater improvement in risk-adjusted returns from M2 conditioning than traditional developed market equities.

5. H5 (Robustness): Performance improvements persist out-of-sample and across different sub-periods, ruling out pure data mining.

15. Limitations and Future Work

15.1 Current Limitations

1. M2 data latency: 2-4 week reporting delay limits real-time accuracy; nowcasting partially addresses this but introduces model error.

2. Sentiment language bias: English-only analysis may miss sentiment shifts in non-English markets (China, Japan, emerging markets).

3. Parameter instability: Optimal parameters may shift across market regimes; our re-estimation protocol mitigates but does not eliminate this concern.

4. Overfitting risk: Despite regularization and cross-validation, the multi-parameter nature of the framework creates overfitting potential.

5. No empirical results: This proposal presents the design specification; rigorous empirical validation is left to practitioners using the prototype tool.

6. Single-indicator focus: The framework enhances RSI specifically; integration with other indicators (MACD, Bollinger Bands) is not addressed.

15.2 Future Extensions

• Separate liquidity factors: Distinguish "US liquidity" from "global liquidity" and "local liquidity" for non-US assets

• Credit conditions: Incorporate high-yield spreads, bank lending standards, and financial conditions indices alongside M2

• Multi-language sentiment: Extend sentiment analysis to Chinese, Japanese, and European language sources

• Regime-switching models: Develop formal regime-switching specifications with automatic parameter adaptation

• Machine learning integration: Use gradient boosting or neural networks to learn optimal threshold functions from data

• Alternative indicators: Apply the conditional normalization framework to other oscillators (Stochastic, CCI, Williams %R)

16. Conclusion

This design proposal presents a principled approach to enhancing the Relative Strength Index with macroeconomic and sentiment context. The key contributions are:

1. Canonical design: By preserving RSI in $[0,100]$ and applying context through thresholds and normalization, we maintain interpretability while enabling adaptation.

2. Explicit M2 definition: The GDP-weighted global aggregate with documented composition and weighting provides a reproducible liquidity measure.

3. Regularized calibration: L2 penalization, nested cross-validation, and walk-forward optimization mitigate overfitting in the multi-parameter framework.

4. Operational clarity: Specified re-estimation frequencies, data sources, and validation protocols enable practical implementation.

5. Working prototype: The tool at https://e-rsi.anassumption.com allows immediate experimentation and validation.

The framework addresses a genuine limitation of traditional RSI—its ignorance of external market conditions—while respecting the indicator's core strengths of simplicity and interpretability. We invite practitioners and researchers to validate the hypotheses using the prototype tool and welcome feedback for future refinements.

Acknowledgments

The author thanks reviewers for detailed feedback that substantially improved this proposal, particularly regarding the canonical design choice and regularization framework.

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