The Relative Strength Index (RSI), developed by J. Welles Wilder Jr., is a bounded momentum oscillator that quantifies the speed and size of recent price changes. Rather than comparing a security to a sector or index benchmark, RSI evaluates an asset solely against its own price history over a rolling N-period window.
RSI cannot leave the 0 to 100 band, which is what makes 70 and 30 usable as fixed reference points. The line is built only from the stock's own gains and losses over the lookback window.
The Standard 14-Period Formula
The classic RSI utilizes a 14-period lookback window. It computes a smoothed average of daily positive price changes (gains) versus daily negative price changes (losses):
RS = Smoothed Average Gain ÷ Smoothed Average Loss
RSI = 100 − (100 ÷ (1 + RS)) = (100 × Smoothed Average Gain) ÷ (Smoothed Average Gain + Smoothed Average Loss)
Where smoothed averages are updated using Wilder's Smoothing Technique (t = current session, N = 14):
Average Gaint = ((Average Gaint−1 × 13) + Current Gaint) ÷ 14
Average Losst = ((Average Losst−1 × 13) + Current Losst) ÷ 14
Boundary Conditions & Sensitivity
Because gains and losses are both non-negative values, RS ranges from 0 to +∞, constraining RSI strictly between 0 and 100:
Today's closing price is the 14th input of today's RSI calculation. A large single-session move shifts the current RSI reading immediately by approximately 1/14th (~7.1%) of the total smoothed gain/loss denominator.
Unlike zero-line oscillators, RSI operates across a fixed scale without a zero axis. Analysts set arbitrary horizontal threshold levels to classify market states.
Preset Threshold
Regime Description
Share of Total Sessions
Avg Stretch Duration
RSI ≤ 30
Oversold Territory
1.8% of Sessions
1.9 Days
RSI ≥ 50
Bullish Midpoint
68.1% of Sessions
12.3 Days (Above)
RSI ≥ 70
Overbought Territory
7.9% of Sessions
3.3 Days
SPY RSI Distribution Across Traditional Presets (Historical Benchmark)
Asymmetry in Index Benchmarks
In long-term upward-trending equity indices like SPY, oversold (RSI ≤ 30) and overbought (RSI ≥ 70) are not symmetrical conditions.
Regime
Share
RSI ≤ 30 (Oversold)
1.8%
RSI ≥ 50 (Midpoint)
68.1%
RSI ≥ 70 (Overbought)
7.9%
Historical SPY Session Distribution
Extreme Scarcity at RSI ≤ 30: SPY spends less than 2% of its trading life below 30. When it drops into this zone, panic selling quickly attracts buyers, causing stretches to end in under 2 days on average.
Persistence at RSI ≥ 70: Overbought states occur more than four times as often (7.9%) as oversold states, driven by steady equity market drift.
Methodological Tip
When viewing RSI statistics, first check the Session Share. Metrics generated from a 1.8% sample reflect rare, tail-event market conditions rather than everyday baseline dynamics.
Chapter 3
Market Conditions at Each RSI Level
Classifying market sessions by their RSI level reveals clear differences in returns, win rates, and volatility metrics.
Quantitative Environment Matrix
RSI Threshold Regime
Session Share
Green-Day Odds
Avg Daily Return
Avg VIX
Below RSI 30
1.8%
7.0% Green
−1.94%
32.9
Below RSI 50
31.9%
38.0% Green
−0.38%
25.1
Above RSI 50
68.1%
63.0% Green
+0.24%
17.1
Above RSI 70
7.9%
82.0% Green
+0.36%
14.2
Market Environment Characteristics by RSI Level (SPY Benchmark)
The Volatility Gradient
Evaluating the Average Volatility Index (VIX) across RSI tiers demonstrates a clean inverse relationship:
RSI momentum and option volatility are inversely linked: sharp equity drawdowns drag 14-day RSI down while simultaneously spiking option demand (elevating VIX).
Chapter 4
The Circularity Problem in Same-Session Data
The statistical table in Chapter 3 shows striking numbers: SPY closes green only 7% of the time when RSI is below 30, but 82% of the time when RSI is above 70. However, these figures must be interpreted carefully due to a bias in same-session metrics.
Mathematical Proof of Same-Session Bias
When a model classifies a trading session by today's closing RSI and evaluates today's return, the dependent variable is built directly into the independent classifier:
Closet ⇒ Δ Pricet ⇒ RSIt ⇒ Bucket Classificationt
Today's close updates today's RSI, which places the session in a regime bucket that is then scored with that same day's return. The classifier and the outcome share an input.
Filtering Out Up Days: For an index ETF like SPY to drop below RSI 30, it requires a sequence of severe declines. If session t closes green, that positive move immediately lifts RSIt, removing the session from the RSI < 30 bucket.
Inherent Selection Bias: The 7% win rate under RSI 30 does not mean "low RSI causes down days." Rather, it reflects the fact that a session must typically be a severe down day to pull the 14-day RSI into that low zone.
Clean Metrics: Time in Regime, Average Stretch Duration, VIX & RSI Averages.
Chapter 5
The Crosses View: Measuring Forward Transitions
To eliminate circular measurement bias, analysts evaluate forward returns after a boundary transition occurs.
Forward evaluation starts after the transition session, so the measured returns are independent of the RSI reading that classified the event.
Transition Alternation Rule
Because RSI is a continuous oscillator, directional crosses across any threshold must alternate:
Crosses AboveN ≈ Crosses BelowN (Difference ≤ 1)
Forward Performance Analysis
Threshold & Event Direction
Occurrences
5-Day Green %
10-Day Green %
20-Day Green %
RSI 70: Cross Above (Entry)
120
62.0%
68.0%
68.0%
RSI 70: Cross Below (Exit)
121
63.0%
69.0%
70.0%
RSI 30: Cross Below (Entry)
46
61.0%
70.0%
76.0%
RSI 30: Cross Above (Exit)
46
54.0%
61.0%
67.0%
Forward Performance Following RSI Threshold Crosses (SPY Benchmark)
Key Statistical Takeaways
The RSI 70 Neutrality Problem
Crossing above 70 (entering overbought) and crossing below 70 (exiting overbought) show nearly identical forward win rates across 5-, 10-, and 20-day time frames. The direction of a cross at 70 provides almost no directional edge on SPY.
Counter-Intuitive RSI 30 Dynamics
Traditional technical analysis suggests buying when RSI crosses up out of oversold (RSI > 30). However, historical performance on SPY shows that crossing down into oversold (RSI < 30) yielded higher forward win rates across every window (76% vs. 67% at 20 days).
Contextualizing the Drift Bias
SPY maintains a natural long-term upward drift, closing green on ~55% of all 20-day windows. Both RSI 30 transition triggers outperform this baseline, showing that extreme selling pressure historically creates strong mean-reversion buying opportunities.