Rolling Returns

Introduction

Rolling returns, also known as rolling period returns or time period returns, is a method used in the evaluation of the performance of an investment over various time frames. Instead of relying on point-to-point return analysis, which can sometimes offer a limited view, rolling returns provide a more comprehensive picture by accounting for the changing risk and return profile over time. This method is instrumental in understanding the consistency of returns, the investment’s behavior in varying market conditions, and in comparing multiple investments.

Key Definitions

• Rolling Period: The time frame over which the return is calculated. Typical rolling periods include one month, three months, six months, one year, three years, and five years.
• Window Size: The length of the period for which returns are calculated. For instance, a 3-year rolling return might be calculated monthly over a 5-year span.
• Overlap: In rolling returns, periods often overlap, unlike fixed-period returns, offering a more granular view.

Calculation of Rolling Returns

The calculation involves several steps:

1. Choosing the Rolling Period: Decide on the time frame for which the rolling return will be calculated.
2. Setting the Window Size: Define how frequently the returns need to be calculated within the chosen rolling period.
3. Algorithm: Implement the rolling function that recalculates returns for each period:
   • For example, to calculate a 1-year rolling return on a monthly basis over a 5-year span, returns are calculated in 5-year windows that roll forward each month.

The formula for rolling returns relatively remains the same as the general return formula: [ \text{Return} = \frac{(P_{end} - P_{start}) + D}{P_{start}} ] Where:

• ( P_{end} ) = Ending price
• ( P_{start} ) = Starting price
• ( D ) = Dividends received during the period

Practical Example

Consider an investment with monthly return data over a 5-year span. To calculate a 1-year rolling return:

1. Start with the first 12 months and calculate the return.
2. Move forward one month and calculate the return for the next 12 months.
3. Repeat this process until the end of the available data.

Assuming we are calculating returns for an investment in stock XYZ:

• January 2020 to January 2021 returns
• February 2020 to February 2021 returns
• Continue this pattern until the last 12-month period within the data.

Tools and Software

Several tools can be employed to calculate and visualize rolling returns:

• Excel: Use formulas and pivot tables to perform rolling return calculations.
• Python: Libraries like pandas and matplotlib make it easy to calculate and plot rolling returns.
• MATLAB: Provides functions like movmean or custom scripts for rolling return calculations.
• R: Libraries like zoo and xts are specifically designed for handling time series analysis.

Companies Using Rolling Returns

Rolling returns are widely used by various financial institutions, investment firms, and analysis companies. Some of the notable companies include:

• Morningstar, a leading provider of independent investment research (morningstar.com)
• Vanguard, a significant player in mutual funds and ETFs (vanguard.com)
• BlackRock, a global investment management corporation (blackrock.com)

Each of these companies uses rolling returns to present comprehensive performance analysis of funds and investment strategies to their clients.

Advantages of Rolling Returns

• Consistency: By smoothing out short-term volatility, rolling returns can demonstrate the consistency of an investment’s performance over different periods.
• Comparative Analysis: They allow for better comparison of different assets or funds over identical time frames.
• Risk Assessment: Rolling returns help in understanding the risk and volatility associated with an investment over time.

Challenges and Limitations

• Complexity: Calculating and interpreting rolling returns can be more complex compared to simple point-to-point returns.
• Data Requirements: Continuous data over long periods is required to compute rolling returns effectively.
• Overlap Influence: Since the periods overlap, similar market events may influence multiple rolling periods, potentially skewing the results.

Conclusion

Rolling returns provide a dynamic and robust method for evaluating an investment’s performance. By offering insights into consistency, risk, and comparative performance, they are an invaluable tool for investors and analysts. While there are challenges associated with their complexity and data requirements, the advantages far outweigh these drawbacks.

For further details, you can explore resources and tools provided by leading firms like Morningstar at morningstar.com, Vanguard at vanguard.com, and BlackRock at blackrock.com.

References

• Morningstar. (n.d.). Retrieved from morningstar.com
• Vanguard. (n.d.). Retrieved from vanguard.com
• BlackRock. (n.d.). Retrieved from blackrock.com