3-Period RSI

In algorithmic trading, one of the most widely used technical indicators for quantifying the momentum of asset prices is the Relative Strength Index (RSI). The RSI was introduced by J. Welles Wilder in his 1978 book “New Concepts in Technical Trading Systems.” The RSI is a momentum oscillator that measures the speed and change of price movements. It oscillates between 0 and 100 and is typically used to identify overbought or oversold conditions in a market. While the standard RSI calculation uses a 14-period timeframe, shorter period RSIs, such as the 3-period RSI, are also commonly employed, particularly in short-term trading strategies.

Calculation of the 3-Period RSI

Standard RSI Formula

To understand the 3-period RSI, it is crucial first to grasp the standard calculation of the RSI. The RSI is calculated using the following formula:

[ RSI = 100 - \left( \frac{100}{1 + RS} \right) ]

where RS (Relative Strength) is the average of ‘N’ days’ up closes divided by the average of ‘N’ days’ down closes:

[ RS = \frac{\text{Average Gain over } N \text{ periods}}{\text{Average Loss over } N \text{ periods}} ]

Calculation Steps for the 3-Period RSI

1. Determine the Up and Down Days:
   • Calculate the daily price changes for the asset over the past 3 periods.
   • A day is considered an “up day” if the closing price is higher than the previous day’s close. Conversely, it is a “down day” if the closing price is lower.
2. Calculate the Average Gain and Average Loss:
   • The average gain over the last 3 periods is the sum of all up day changes divided by 3.
   • The average loss over the last 3 periods is the sum of all down day changes divided by 3.
3. Compute the Relative Strength (RS):
   • RS is calculated as the ratio of the average gain to the average loss over the 3 periods.
4. Calculate the RSI:
   • Plug the RS value into the RSI formula to compute the 3-period RSI.

Example Calculation

Suppose we have the following closing prices for an asset over four days: $50, $52, $51, and $53.

1. Calculate the daily price changes:
   • Day 1 to Day 2: $52 - $50 = +2 (Up Day)
   • Day 2 to Day 3: $51 - $52 = -1 (Down Day)
   • Day 3 to Day 4: $53 - $51 = +2 (Up Day)
2. Calculate the average gain and average loss:
   • Average Gain = (2 + 2) / 3 = 1.33
   • Average Loss = 1 / 3 = 0.33
3. Compute the Relative Strength (RS):
   • RS = 1.33 / 0.33 ≈ 4.03
4. Calculate the RSI:
   • RSI = 100 - (100 / (1 + 4.03)) ≈ 80.1

Thus, the 3-period RSI in this example is approximately 80.1.

Application in Algorithmic Trading

Trading Signals

The 3-period RSI can be used to generate trading signals in a variety of ways:

1. Overbought/Oversold Conditions:
   • An RSI above 70 is typically considered “overbought,” suggesting that the asset might be overvalued and due for a pullback.
   • An RSI below 30 is considered “oversold,” indicating that the asset might be undervalued and ripe for a potential rally.
2. Divergence:
   • Bullish Divergence: Occurs when the price makes a new low, but the RSI makes a higher low. This divergence may indicate a potential upward reversal.
   • Bearish Divergence: Occurs when the price makes a new high, but the RSI makes a lower high. This divergence could signal a potential downward reversal.
3. Swing Rejections:
   • Bullish Rejection: RSI falls below 30 (oversold), rises above 30, falls again but stays above 30, and then rises above its previous high.
   • Bearish Rejection: RSI rises above 70 (overbought), falls below 70, rises again but stays below 70, and then falls below its previous low.

Algorithmic Implementation

Pseudocode for 3-Period RSI Calculation

Below is a pseudocode example for integrating the 3-period RSI into an algorithmic trading system:

function calculate3PeriodRSI(prices):
    N = 3
    gains = []
    losses = []

    for i from 1 to N:
        change = prices[i] - prices[i-1]
        if change > 0:
            gains.append(change)
            losses.append(0)
        else:
            gains.append(0)
            losses.append(abs(change))

    averageGain = sum(gains) / N
    averageLoss = sum(losses) / N

    if averageLoss == 0:
        [return](../r/return.html) 100  # Prevent division by zero and resulting in undefined RSI

    RS = averageGain / averageLoss
    RSI = 100 - (100 / (1 + RS))
  
    [return](../r/return.html) RSI

This pseudocode calculates the 3-period RSI of a given series of prices. In a real algorithmic trading system, this function would be incorporated into a broader strategy, where buy and sell signals could be generated and acted upon.

Example in Python

[import](../i/import.html) numpy as np

def calculate_3_period_rsi(prices):
    n = 3
    changes = np.diff(prices)
    gains = np.maximum(changes, 0)
    losses = -np.minimum(changes, 0)

    average_gain = np.sum(gains[:n]) / n
    average_loss = np.sum(losses[:n]) / n

    if average_loss == 0:
        [return](../r/return.html) 100  # To [handle](../h/handle.html) the division by zero edge case
    
    rs = average_gain / average_loss
    rsi = 100 - (100 / (1 + rs))

    [return](../r/return.html) rsi

# Example usage
prices = [50, 52, 51, 53]
rsi = calculate_3_period_rsi(prices)
print(f"3-Period RSI: {rsi}")

In this Python example, the calculate_3_period_rsi function calculates the 3-period RSI for a given series of prices. The example usage demonstrates how to call the function and print the resulting RSI.

Benefits and Limitations

Benefits

1. Speed and Sensitivity:
   • The 3-period RSI responds more quickly to price changes compared to the standard 14-period RSI. This quick responsiveness is beneficial for short-term traders who need timely signals.
2. Detecting Short-Term Price Extremes:
   • Due to its high sensitivity, the 3-period RSI is adept at detecting short-term overbought and oversold conditions, which can lead to profitable contrarian trades.
3. Versatility:
   • The indicator can be used across different asset classes, including stocks, forex, and commodities. Its versatility makes it a valuable tool for various trading strategies.

Limitations

1. False Signals:
   • The increased sensitivity of the 3-period RSI can also be a double-edged sword, leading to more false signals. Short-term noise and market volatility can trigger premature buy or sell signals.
2. Dependency on Market Conditions:
   • In trending markets, the 3-period RSI may give numerous overbought or oversold signals without a resulting price reversal. This can lead to losses for traders relying solely on RSI signals.
3. Need for Confirmation:
   • To mitigate the risk of false signals, traders often combine the 3-period RSI with other technical indicators or analysis methods to confirm trading signals.

Practical Use Cases and Strategies

Mean Reversion Strategy

In a mean reversion strategy, the 3-period RSI can be used to identify when an asset is overbought or oversold. The idea is to buy when the RSI is below 30 and sell when the RSI is above 70.

Simple Mean Reversion Algorithm

1. Calculate the 3-period RSI for the asset.
2. Enter a long position when the RSI falls below 30.
3. Enter a short position when the RSI rises above 70.
4. Exit long positions when the RSI crosses above 50.
5. Exit short positions when the RSI crosses below 50.

Trend Following with RSI Confirmation

RSI can also be used in trend-following strategies, providing a confirmation signal for trend direction.

Simple Trend Following Algorithm

1. Calculate a longer-term moving average (e.g., 50-period) to determine the trend direction.
2. Calculate the 3-period RSI for the asset.
3. Enter a long position if the moving average indicates an uptrend and the RSI rises above 50 from below.
4. Enter a short position if the moving average indicates a downtrend and the RSI falls below 50 from above.
5. Exit positions based on opposite signals or predefined profit/loss targets.

Combining with Other Indicators

To increase the robustness of trading strategies, traders often combine the 3-period RSI with other technical indicators such as Moving Averages, MACD, or Bollinger Bands.

Example Strategy

1. Calculate the 3-period RSI and Moving Average Convergence Divergence (MACD).
2. Enter a long position when:
   • The 3-period RSI is below 30, indicating oversold conditions.
   • The MACD line crosses above the signal line, indicating bullish momentum.
3. Enter a short position when:
   • The 3-period RSI is above 70, indicating overbought conditions.
   • The MACD line crosses below the signal line, indicating bearish momentum.
4. Exit positions based on opposite signals or predefined profit/loss targets.

Conclusion

The 3-period RSI is a powerful tool in the arsenal of algorithmic traders. Its ability to provide timely insights into short-term market conditions makes it particularly useful for high-frequency trading and intraday strategies. However, like all technical indicators, it is not infallible and should be used in combination with other indicators and analysis techniques to improve accuracy and reduce the risk of false signals. By understanding its calculation, applications, and limitations, traders can effectively incorporate the 3-period RSI into their trading strategies to enhance their decision-making process and potentially increase profitability.