When investors look at the performance of a stock, mutual fund or portfolio over several periods or years, one of the first numbers they look at is the average return. This is easy to calculate. Add the returns earned in each period and divide by the number of periods.
But there’s a catch. An average return is not necessarily the rate at which money actually grows (Chart 1 shows how Funds A and B with same arithmetic average return of 5% deliver very different outcomes).
A loss is harder to recover
Losses are particularly damaging because recovering from them requires a disproportionately larger gain. A 20% fall does not require a 20% gain to recover. If Rs.100 falls by 20%, it becomes Rs.80. To get back to Rs.100, the investment needs to rise by (Rs.20 ÷ Rs.80) X 100 = 25% (Chart 2). This asymmetry is one of the key reasons why volatile returns can leave investors with much less wealth than the arithmetic average might suggest.
Unlike the arithmetic average, the geometric average takes compounding into account. It answers what constant annual return would have turned the starting investment into the ending investment? The calculation may look slightly complicated, but the idea is straightforward. Add 1 to each periodic return, multiply them together, and then take the ‘n’ root, where ‘n’ is the number of periods.
Geometric average For Fund A: [(1 - 15%) × (1 + 25%) × (1 - 20%) × (1 + 30%)] ^ (1/4) - 1 = 2.53%. (Chart 1)
Although Fund A has an arithmetic average return of 5%, its actual compounded annual growth rate is only about 2.5%. This highlights why relying only on the arithmetic average can give investors an overly optimistic picture of returns. Generally, more volatile the returns, wider the gap between the arithmetic and geometric averages.
Geometric average & CAGR: Two routes, same destination
CAGR, or compounded annual growth rate, is another number investors frequently use. CAGR and geometric return are essentially two ways of looking at the same compounded growth rate when the same investment period is considered. Geometric average uses periodic returns. CAGR needs the starting value, ending value and number of years.
For Fund A, NAV rises from Rs.12 to Rs.13.26 over four years. CAGR = [(13.26 ÷ 12)^(1/4) - 1] × 100 = 2.53% (Chart 1).
That is the same as the geometric average of the four annual returns. There is, however, an important limitation to CAGR. While it tells the annualised rate at which an investment grew between two points, it says nothing about what happened along the way. Since the calculation considers only the starting and ending values, it does not reveal how volatile the investment was during the period.
For instance, two investments can have the same CAGR but take very different paths to get there. One may have delivered relatively steady returns year after year, while the other may have experienced sharp gains and losses before reaching the same final value.
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Their CAGR would be identical, but the risks investors experienced along the way could be very different.
CHART 1
Two funds, same average return, very different wealth
Both funds had a 5% arithmetic average return. However, the investment of Rs.1 lakh grew to Rs.1,10,500 in Fund A, while Rs.1,21,551 in Fund B at the end of 2025.
What led to two different outcomes?
*Both funds have an arithmetic average return of 5%. Yet Rs.1 lakh invested in Fund A grew to Rs.1,10,500 by 2025, while the same amount in Fund B grew to Rs.1,21,551.
*The difference comes from volatility. Each year’s return is earned on whatever is left from the previous year, not on the original investment. So a loss shrinks the base on which the next gain is earned.
*Fund B’s path was smooth: +5% every year, taking Rs.1 lakh to Rs.1,05,000, Rs.1,10,250, Rs.1,15,763 and finally Rs.1,21,551.
*Fund A’s path was bumpy:-15%, +25%, -20%, +30%. Rs.1 lakh fell to Rs.85,000, rose to Rs.1,06,250, fell back to Rs. 85,000, and ended at Rs.1,10,500.
*Note that Fund A’s 25% gain came on just Rs.85,000, and its 20% loss hit a larger Rs.1,06,250. The losses did more damage than the gains could repair. This is called volatility drag, and the arithmetic average hides it completely.
An investment of Rs.1 lakh each was made in 2021 in two funds (Funds A & B). Both funds have a NAV of Rs.12.
CHART 2
CHART 3
Portfolio return depends on portfolio weight
Note
Three averages investors should not confuse
ARITHMETIC AVERAGE
Average of periodic returns
Useful for: Understanding the average return across individual periods
Limitation: Does not account for compounding
GEOMETRIC AVERAGE
Compounded annual rate implied by a series of periodic returns
Useful for: Understanding how a series of returns compounds.
Limitation: Requires the periodic return series
WEIGHTED AVERAGE
Portfolio return after accounting for the amount invested in each asset
Useful for: Calculating portfolio-level returns when allocations differ
Limitation: Sensitive to changes in weights.
Portfolio return: Weights matter
Suppose an investor has Rs.50,000 in equity, Rs.20,000 in debt and Rs.10,000 in gold. Total investment is Rs.80,000. If equity earns 5%, debt 8% and gold 12%, a simple average gives 8.33%. (Chart 3) But the portfolio did not earn 8.33% because the investor did not invest the same amount in each asset.
The larger the allocation to an asset, the greater its influence on the portfolio’s return. Equity has the lowest return in this example, but because it accounts for 62.5% of the portfolio, it has the largest impact.
ET Wealth’s Trendmap on portfolio allocation uses the concept of weighted average returns while analysing the annual performance of seven different portfolio allocations. All numbers and returns used in illustrations are hypothetical.
