What it means
The mechanics are multiplicative rather than additive. Each period's return is expressed as a growth factor, one plus the return, and the factors are multiplied together to give the total growth factor for the whole period.
This matters because averaging returns arithmetically overstates what an investor experienced, and the overstatement grows with volatility. A portfolio that gains 50% then loses 50% has an arithmetic average of 0% but a compound return of -25%, because the loss applies to a larger base than the gain did.
Investors and finance teams therefore distinguish between the arithmetic mean return, which is useful for estimating a single expected period, and the geometric or compound return, which is the right measure of realised performance. Fund performance tables and investment mandates almost always quote the compound figure.
Compound return is also the basis for annualising performance over an uneven period. Taking the total growth factor and raising it to the power of one divided by the number of years gives the constant annual rate that would have produced the same ending balance.
The nuance worth carrying into meetings is that compound return says nothing about the path or the risk taken to get there. Two investments with identical compound returns can have wildly different volatility, and the more volatile one is harder to hold and harder to fund from, so the return should always be read alongside a measure of variability.
In practice
Real-world examples.
Example
A pension trustee compares two funds that both advertise an average annual return of 8%. On a compound basis over ten years the smoother fund has delivered 8.0% a year while the volatile one has delivered 6.9%, a gap worth roughly $210,000 on a $1,000,000 holding.
Example
A family business reinvests its profits rather than distributing them, achieving a compound return on retained earnings of about 12% a year. Over twelve years that turns $2,000,000 of retained profit into roughly $7,800,000 of accumulated value.
Example
A finance director evaluating a five-year supplier contract with escalating rebates converts the uneven yearly savings into a single compound return figure. That makes the deal directly comparable with a capital project quoted as an annual percentage return.
Think of it
“Compound return is your true growth rate when gains are reinvested-interest earning interest.
Formula
Calculation
Compound return over n periods = [(1 + r1) x (1 + r2) x ... x (1 + rn)] - 1. Annualised compound return = the same product raised to the power of (1 / number of years), minus 1.
Suppose a $100,000 portfolio returns 10% in year one, loses 5% in year two, and gains 20% in year three. The growth factors are 1.10, 0.95 and 1.20, and multiplying them gives 1.10 x 0.95 = 1.045, then 1.045 x 1.20 = 1.254.
The compound return over the three years is 1.254 - 1 = 0.254, or 25.4%, so the portfolio is worth $100,000 x 1.254 = $125,400. Note that simply adding the three returns gives 10% - 5% + 20% = 25%, which is close but wrong. The annualised compound return is 1.254 raised to the power of one third, minus 1, which is about 7.8% a year.Case study
Seen in the real world.
Marlowe Endowment Trust is a fictional charitable fund used here as an illustrative example. Its investment committee reported average annual returns of 9% over six years and used that figure when setting an annual grant-making budget.
A new treasurer recalculated on a compound basis. The yearly returns had been 28%, -14%, 19%, -6%, 22% and 5%, which multiply out to a total growth factor of about 1.58, an annualised compound return of roughly 7.9% rather than the 9% arithmetic average being quoted.
In the illustrative outcome, the 1.1 percentage point difference mattered a great deal: on a $30,000,000 fund it meant the trust had been budgeting to spend around $330,000 a year more than the portfolio was genuinely generating. The committee moved to reporting compound returns only, and reset the spending rule to a three-year rolling average.
Watch out
Common mistakes.
- Adding or averaging yearly returns arithmetically, which always overstates the realised outcome whenever returns vary.
- Comparing a compound return from one investment with an arithmetic average from another, producing a comparison that favours the more volatile option.
- Ignoring fees and taxes, since a 1% annual charge compounds against the investor just as returns compound for them.
Questions
People also ask.
Why is compound return lower than the average return?
Because losses reduce the base that later gains apply to, and the gap widens as returns become more volatile.
Is compound return the same as CAGR?
Annualised compound return and CAGR are the same calculation, though CAGR is more often used for business metrics such as revenue and compound return for investment performance.
Does compound return work for negative overall performance?
Yes, the multiplication handles losses naturally, and the result is simply a negative percentage showing how much of the original capital was lost.
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