Dynamic CAGR Line

Indicator: Dynamic CAGR Line

Overview
This Pine Script (version 6) creates a custom indicator called "Dynamic CAGR Moving Line," designed to calculate and display the Compound Annual Growth Rate (CAGR) in percentage terms for a financial instrument, such as a stock or cryptocurrency, based on a user-defined lookback period (default: 5 years). Unlike traditional overlays that plot directly on the price chart, this indicator appears in a separate pane below the chart, providing a clear visual of how the CAGR evolves over time with each new candle.
Purpose
The indicator helps traders and investors analyze the annualized growth rate of an asset’s price over a specified historical period. By plotting the CAGR as a percentage in a separate pane, users can easily track how the growth rate changes as new price data is added, offering insights into long-term performance trends without cluttering the price chart.
How It Works
User Input:
The script begins with an input parameter, lookback_years, allowing users to define the number of years (e.g., 5) to look back for the CAGR calculation. This is a floating-point value with a minimum of 1 and a step of 0.5, adjustable via the indicator’s settings in TradingView.

Timeframe Conversion:
Assuming a daily chart, the script converts the lookback years into a number of bars using bars_per_year = 252 (the average number of trading days in a year). The total lookback period in bars is calculated as lookback_bars = math.round(lookback_years * bars_per_year). For example, 5 years equals approximately 1260 bars.

Price Data:
For each candle, the start_price is fetched from the closing price lookback_bars ago (e.g., the close price from 5 years prior), using close[lookback_bars].

The end_price is the current candle’s closing price, accessed via close.

CAGR Calculation:
The total return is computed as (end_price - start_price) / start_price, measuring the percentage change from the start price to the current price.

To avoid division-by-zero errors, a conditional check ensures start_price != 0; if it is, the return defaults to 0.

The CAGR is then calculated using the formula: math.pow(1 + total_return, 1 / lookback_years) - 1, which annualizes the total return over the lookback period.

The result is converted to a percentage by multiplying by 100 (cagr_percent = cagr * 100).

Plotting:
The CAGR percentage is plotted as a blue line in a separate pane using plot(). The line only appears after enough data exists (bar_index >= lookback_bars), otherwise it plots na (not available).

A label is added for each candle, displaying the current CAGR percentage (e.g., "CAGR: 5.23%") near the plotted value, styled with a blue background and white text.

Usage
Chart Setup: Apply the indicator to a daily chart with sufficient historical data (e.g., more than 5 years for the default setting). It’s designed for daily timeframes but can be adapted for others by adjusting bars_per_year (e.g., 52 for weekly).

Interpretation: A positive CAGR (e.g., 5%) indicates annualized growth, while a negative value (e.g., -2%) shows an annualized decline. A flat line at 0% suggests no net change over the lookback period.

Customization: Adjust lookback_years in the settings to analyze different periods (e.g., 3 or 10 years).

Notes
Ensure your chart has enough data to cover the lookback period, or the line won’t appear until sufficient bars are available.

For debugging, you can temporarily plot start_price and end_price on the main chart to verify the calculation inputs.