Rolling Returns

Rolling returns is a technique in quantitative finance that calculates returns for a portfolio or security over a set of time periods, typically moving windows of time. This method allows investors to assess the performance of an asset or portfolio over different time horizons and provides a more dynamic view of its returns.

Methodology:

1. Divide the time series: Divide the time series of returns into overlapping time periods, typically of equal length.
2. Calculate returns for each period: Calculate the return for each time period by taking the difference between the closing price at the end of the period and the closing price at the beginning of the period, divided by the closing price at the beginning of the period.
3. Calculate rolling returns: Use the returns for each time period to calculate rolling returns, which are the average returns over the specified time window.

Advantages:

• Provides a more complete picture of returns: Rolling returns account for the changing market conditions over time, providing a more comprehensive view of an asset or portfolio’s performance.
• Allows for comparison across different time horizons: Rolling returns allow for comparisons of performance across different time periods, enabling investors to evaluate the consistency and stability of an asset or portfolio.
• Informs investment decisions: Rolling returns can be used to guide investment decisions by identifying periods of high or low performance.

Disadvantages:

• Can be computationally intensive: Calculating rolling returns for large datasets can be computationally intensive.
• May not be suitable for all assets: Rolling returns may not be appropriate for assets with high transaction costs or significant events that can distort historical returns.
• Can be noisy: Rolling returns can be noisy, especially for short time windows.

Examples:

• Calculating rolling returns for a stock portfolio over a 5-year period.
• Analyzing the rolling returns of an index fund to assess its consistency and stability.
• Comparing the rolling returns of two different investment strategies.

Conclusion:

Rolling returns is a valuable technique in quantitative finance that provides a more dynamic and comprehensive view of asset or portfolio returns. While it has advantages over traditional returns calculations, it is important to consider the potential disadvantages and limitations when interpreting rolling returns.