Rolling Returns in Mutual Funds, Stocks, Indices, and Other Assets – India

What is Rolling Return, and how do you calculate it manually?

Rolling return (RR) is basically the arithmetic average (mean) of all annualised returns (CAGR) for a fixed period (say 2 years of RA over 5 years) across multiple overlapping time frames. Say an annual return of MF or any stock is:

• Year 1: +35%
• Year 2: -15%
• Year 3: +28%
• Year 4: +5%
• Year 5: +18%

Manual Step-by-Step Calculation of 2YAARR (2Y average annualised return ratio) using simple average:

• 2YRA1 = 10% – Mean – Y1:Y2 = (35-15)/2 and so on: RA1 = 10.0%; RA2 = 6.5%; RA3 = 16.5%; RA4 = 11.5%
• Now 2Y-ARR (2Y Average Rolling Return) over 5 years  = (RA1+RA2+RA3+RA4)/4 = (10.0+6.5+16.5+11.5)/4 = 11.1%

Calculation of 2YAARR (2-year average annualised return ratio) using CAGR (true meaning after 1+ decimal compounding)

• Year 1: +35%=1.35 (1.00+0.35)
• Year 2: -15%=0.85 (1.00-0.85)
• Year 3: +28%=1.28 (1.00+0.28)
• Year 4: +5%=1.05 (1.00+0.05)
• Year 5: +18%=1.18 (1.00+0.18)

Now the true 2-year rolling CAGRs:

• Years 1–2: (1.35 × 0.85)^(1/2) - 1 = (1.1475)^(0.5) - 1 ≈ +7.12%
• Years 2–3: (0.85 × 1.28)^(1/2) - 1 = (1.088)^(0.5) - 1 ≈ +4.31%
• Years 3–4: (1.28 × 1.05)^(1/2) - 1 = (1.344)^(0.5) - 1 ≈ +15.93%
• Years 4–5: (1.05 × 1.18)^(1/2) - 1 = (1.239)^(0.5) - 1 ≈ +11.31%

2-Year ARR over 5-years (average of these rolling CAGRs) = (7.12% + 4.31% + 15.93% + 11.31%) / 4 ≈ 9.67%
Notes

• 2-year returns (simple averages): 10.0%, 6.5%, 16.5%, 11.5%; average 11.13%
• True 2-year rolling CAGRs: 7.12%, 4.31%, 15.93%, 11.31%; average 9.67%
• Simple arithmetic average of the five annual returns: (35 - 15 + 28 + 5 + 18)/5 = 14.2%

Key Observations from this Example

• True ARR 9.67% is significantly lower than the simple average of annual returns, 14.2%
• The approximate method (11.13%) is closer to reality than the simple annual average, but still higher than the true ARR

Manual step-by-step calculation of the Standard Deviation (SD) for the 2-year rolling returns (ARR) from the above example: Like RR/ARR, SD is also an important metric in the calculation of the return of any financial asset—it gives an idea about potential deviation from expectations of returns in the future.

Given Data (True 2-Year Rolling CAGRs)—These are the four individual 2-year rolling returns (already calculated correctly using compounding):

• Rolling period 1 (Y1–Y2): 7.12%  
• Rolling period 2 (Y2–Y3): 4.31%  
• Rolling period 3 (Y3–Y4): 15.93%  
• Rolling period 4 (Y4–Y5): 11.31%
• 2-Year ARR (average of these) = 9.67%  
• Number of observations (N) = 4

Calculate the Mean (already known):  Mean = 9.67% Mean = 9.67%

1. Calculate the deviation of each value from the mean

• 7.12 − 9.67 = −2.55            
• 4.31 − 9.67 = −5.36            
• 15.93 − 9.67 = +6.26           
• 11.31 − 9.67 = +1.64

2. Square each deviation

• (−2.55)² = 6.5025 
• (−5.36)² = 28.7296
• (6.26)²  = 39.1876
• (1.64)²  = 2.6896 

3. Sum of squared deviations = 6.5025 + 28.7296 + 39.1876 + 2.6896 = 77.1093
4. Calculate Variance

• Population variance (most commonly used in rolling returns reporting):  

               Variance = Sum of squared deviations ÷ N = 77.1093 ÷ 4 = 19.277325

• Sample variance (used when estimating from a sample):  

               Variance = Sum of squared deviations ÷ (N − 1)  = 77.1093 ÷ 3 ≈ 25.7031

Final Result: Standard Deviation of the 2-Year Rolling Returns:

• Population SD = 4.39% ─ this is the value most mutual fund platforms, like Value Research, PrimeInvestor, AdvisorKhoj, etc., report when they show SD alongside rolling returns.  
• Sample SD = 5.07%

Summary of the Example: 2Y ARR over 5 years and SD:

• 2-Year ARR = 9.67%  
• Population Standard Deviation = 4.39% 
• Sample Standard Deviation = 5.07%    
• Minimum 2Y rolling return = 4.31%
• Maximum 2Y rolling return = 15.93%  
• Simple average of annual returns = 14.20%    

The population SD of 4.39% means the 2-year rolling returns varied moderately around the average — showing that entry timing had a noticeable (but not extreme) impact on 2-year outcomes in this period. Averaging two annual returns arithmetically is a quick approximation, but it overestimates when returns vary (especially when one is negative or very high). The true CAGR is always the mathematically correct annualised figure. This gap (9.67% vs 14.20%) is meaningful in financial markets. Investors who rely on simple averages often overestimate expected returns and underestimate risk. This is very common in volatile series. The simple arithmetic average overstates long-term compounded growth because it ignores the mathematical drag from negative returns and volatility.

Thus, Rolling Return is one of the most insightful calculations to evaluate the true average performance of any long-term financial assets like Mutual Funds (MFs), stocks, or indices. It provides a more comprehensive and unbiased snapshot than traditional trailing returns (annualised returns from a fixed past date to today), point-to-point returns (between two fixed dates, annualised), absolute return (simple percentage) or annual average return (AAR) over 5 or 10-years. 

This RR/ARR methodology produces a distribution of outcomes, revealing consistency, downside protection, and performance across diverse market phases—bull runs, corrections, and sideways amid various market cycles. A fund or stock that has appeared exceptional over the last few years may have underperformed in earlier periods, while a seemingly average performer might demonstrate remarkable consistency across cycles over the long term.

The RR methodology creates a distribution of returns, showing:

• The average rolling return
• The minimum (worst-case scenario)
• The maximum (best-case scenario)
• The range or standard deviation (indicating consistency)
• How often the return beat a benchmark or exceeded a certain level (e.g., 10–12%)

Why Rolling Returns Are Considered Superior for Long-Term Evaluation

• Removes timing
• Ensures consistency
• Ensures Risk Assessment
• For Realistic Expectations

Conclusions

The Rolling Returns (RR/ARR) method delivers a more distribution-based and cyclical perspective than traditional metrics.  The ARR metric averages annualised, or simply annual, CAGR returns across overlapping periods (like 2 years) over a longer period (say 5 years). This ensures consistency & reliability across diverse asset classes (MFs, Equities, etc.) and market cycles & macroeconomic conditions. In summary, the ARR & SD are essential for any modern capital market, including India, where volatility is normal and always an opportunity. Embracing this Rolling Return approach, Indian investors can navigate volatility with greater confidence and clarity across Mutual Funds, Equities, and other financial asset classes.