💪 RSI — Relative Strength Index
The RSI measures whether buyers or sellers have dominated recently. It answers: "Over the last \(N\) sessions, how much of the total price movement was upward vs downward?"
💡 Financial Meaning
The result is squeezed into a 0–100 range:
- RSI > 70 → Overbought — the spring is stretched, a pullback is statistically likely.
- RSI < 30 → Oversold — the spring is compressed, a bounce is likely.
🔢 Mathematical Formulas
-
Decompose the change from each session to the next into gains and losses:
\[ U_t = \max(P_t - P_{t-1},\; 0), \qquad D_t = \max(P_{t-1} - P_t,\; 0) \] -
Smooth each component with an exponential moving average (SMMA variant):
\[ \overline{U} = SMMA_N(U), \qquad \overline{D} = SMMA_N(D) \] -
Relative Strength ratio and normalisation:
\[ RS = \frac{\overline{U}}{\overline{D}}, \qquad RSI = 100 - \frac{100}{1 + RS} \]
The normalisation \(100 - 100/(1+RS)\) is a monotonically increasing sigmoid that maps \(RS \in [0, \infty)\) to \(RSI \in [0, 100)\).
⚙️ Parameters
| Parameter | Key | Default | Description |
|---|---|---|---|
| Period (\(N\)) | period |
14 | Lookback window for SMMA, in sessions. |
| Overbought | overbought |
70 | Threshold for overbought zone. |
| Oversold | oversold |
30 | Threshold for oversold zone. |
🎛️ Signal Processing Equivalent — Duty Cycle / Saturation Indicator
Imagine splitting the price delta signal \(\Delta P[n]\) into its positive and negative half-wave rectified components, then low-pass filtering each. The RSI is the ratio of the positive envelope to the total envelope, rescaled to \([0, 100]\).
In control systems terms, it is a saturation detector: when the system output (price) has been moving in one direction for too long, the RSI signals that the actuator (market) is near its rail. Like any oscillator in a feedback loop, the further from equilibrium, the stronger the restoring force — hence the mean-reverting property traders exploit.
Non-stationarity
The 70/30 thresholds assume roughly symmetric return distributions. In strong trending markets the RSI can stay above 70 for weeks — it is a probabilistic indicator, not a deterministic one.