RSI (Relative Strength Index): Overbought, Oversold & Divergence

The Relative Strength Index compares average gains to average losses over N periods, producing a 0–100 bounded oscillator. RSI measures momentum exhaustion — not direction. It shows how fast price moved, not where it is going.

Section 1: Core Mechanics

RSI answers one question: is momentum exhausted in either direction? It divides average upward moves by average downward moves, then scales the result to 0–100.

Formula

Where N is the period (default 14).

Wilder Smoothing — applied after the first calculation:

The first average gain is a simple mean of the first N gains. Every subsequent value uses Wilder smoothing, which gives more weight to recent data without a sharp cutoff.

Inputs

• Price source: Close price (standard — do not change without reason)
• Period (N): Number of bars. Default 14. Shorter = more sensitive, more noise. Longer = smoother, fewer signals.

Parameters

Output

RSI outputs a single value between 0 and 100. Above 70 = overbought momentum. Below 30 = oversold momentum. The 50 line is the neutral centerline — above = net bullish momentum, below = net bearish.

Visual Behavior

RSI plots as a line in a separate panel below price. It oscillates between its extremes. In strong uptrends, RSI stays elevated (50–80) and rarely dips below 40. In downtrends, RSI stays suppressed (20–50). A shift in this pattern is an early warning sign.

Section 2: Interpretation & Signals

Signal Zones

Entry and Exit Rules

Overbought/Oversold Reversal:

• Entry: RSI crosses back below 70 (bearish) or above 30 (bullish)
• Exit: RSI reaches opposite extreme or crosses 50 against position

Centerline Cross:

• RSI crosses above 50 = momentum turning bullish — use as trend filter, not entry trigger
• RSI crosses below 50 = momentum turning bearish

Divergence — The Most Powerful RSI Signal

Divergence occurs when price and RSI disagree about momentum direction.

Bullish Divergence: Price makes a lower low. RSI makes a higher low. Momentum is recovering before price. This signals exhaustion of the downtrend.

Bearish Divergence: Price makes a higher high. RSI makes a lower high. Momentum is fading even as price climbs. This signals exhaustion of the uptrend.

RSI Failure Swings

A failure swing is a signal within the RSI itself — independent of price action.

Bullish failure swing: RSI dips below 30, bounces above 30, pulls back but holds above 30, then breaks above the prior bounce high. That break = the entry signal.

Bearish failure swing: RSI rises above 70, drops below 70, rallies but fails to reclaim 70, then breaks below the prior pullback low. That break = the entry signal.

Failure swings are J. Welles Wilder's original preferred signal — more selective than simple overbought/oversold crosses.

Best Market Conditions

RSI works best in ranging and mean-reverting markets. In trending markets, use RSI for divergence and failure swings only — not for overbought/oversold fade entries.

Section 3: Pass vs. Live — Real-Time Reliability

RSI on a live unclosed bar updates on every tick. The Wilder smoothing means sudden price moves shift RSI significantly. Wait for the bar to close before acting on any RSI signal. Once the bar closes, the value is permanent — there is no historical repaint.

Section 4: Practical Use Cases

Real example — AAPL 2022 bear market low: AAPL daily chart, October 2022. Price made a new 52-week low near $125. RSI(14) registered 28 on the first low, then 31 on the second lower price low — classic bullish divergence. RSI held above its prior RSI low even as AAPL printed a lower price. The recovery from that low drove AAPL from $125 to $177 over the next four months.

Section 5: Pseudo Code

INPUT: close_prices[], period=14, ob_level=70, os_level=30

PROCESS:
  Step 1: Calculate price changes: delta[i] = close[i] - close[i-1]
  Step 2: Separate gains and losses:
            gain[i] = delta[i] if delta[i] > 0 else 0
            loss[i] = abs(delta[i]) if delta[i] < 0 else 0
  Step 3: First avg gain = mean(gain[1:period+1])
          First avg loss = mean(loss[1:period+1])
  Step 4: For i > period, apply Wilder smoothing:
            avg_gain[i] = (avg_gain[i-1] * (period-1) + gain[i]) / period
            avg_loss[i] = (avg_loss[i-1] * (period-1) + loss[i]) / period
  Step 5: RS[i] = avg_gain[i] / avg_loss[i]  (if avg_loss == 0, RS = infinity)
  Step 6: RSI[i] = 100 - (100 / (1 + RS[i]))
          If avg_loss == 0: RSI[i] = 100

OUTPUT: rsi[] — array of RSI values (0 to 100)
EDGE CASES:
  - Period of all gains: avg_loss = 0, RSI = 100
  - Period of all losses: avg_gain = 0, RSI = 0
  - Fewer bars than period: return NaN until period bars available
  - NaN in close_prices: propagate NaN

Section 6: Parameters & Optimization

Standard Period Conventions

Parameter Impact

Section 7: Synergies & Conflicts

Section 8: Common Mistakes

Section 9: Cheat Sheet