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Measuring Average Returns over Multiple Periods ⏳🔁

When an investor holds an asset for several years, the return in each year affects the "base" amount for the next year. This creates a chain of returns. Calculating the average over these multiple periods requires a deep understanding of Compounding.

1. Single Period vs. Multi-Period Returns

How we look at time changes how we look at returns.

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2. The Compounding Effect

Compounding is the process where the value of an investment increases because the earnings on an investment, both the principal and the accrued interest, earn interest as time passes.

Important

Einstein on Compounding: Albert Einstein famously called compound interest the "Eighth Wonder of the World." He who understands it, earns it; he who doesn't, pays it.

In Portfolio Management, multiple periods (R1, R2, R3...) are combined into a single total return using the formula:

Total Value = (1 + R1) * (1 + R2) * ... * (1 + Rn)

3. Calculating Cumulative Multi-Period Return

If you want to know how much ₹100 became after 3 years of varying returns, you don't add the returns (10% + 20% + 10% = 40%); you multiply the growth factors.

Problem Scenario:

  • Year 1: +10%
  • Year 2: +20%
  • Year 3: -10%

Step 1: Convert to Growth Factors

  • 1.10, 1.20, 0.90

Step 2: Multiply

Total Growth = 1.10 * 1.20 * 0.90 = 1.188

Step 3: Convert back to percentage

Total Return = (1.188 - 1) * 100 = 18.8%
Tip

Notice that 10 + 20 - 10 would be 20%. But because of the compounding effect, the actual return is slightly different (18.8%).

4. Problems on Average Returns

Problem 1: Average Monthly Return

An investment grew by 15% over 6 months. What was the average compounded monthly return?

Solution: Total growth factor = 1.15 Number of periods (n) = 6 months

Monthly Average = (1.15) ^ (1/6) - 1
Monthly Average = 1.0235 - 1 = 2.35%

Summary

  • Multi-period returns are not additive; they are multiplicative (compounded).
  • The Compounding Effect significantly impacts total wealth over long horizons.
  • To find the average per period, we use the root of the total growth factor (Geometric Mean logic).
  • Precise calculation is vital for comparing managers or funds across different time windows.

Quiz Time! 🎯

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