Compounded return
Also written Compound return · Compounded returns · Compounded rate of return · Compound growth rate
The single yearly rate at which an investment's starting value would have to grow, each year's growth earned on the year before, to reach its ending value over a stated number of years.
In plain language
Money left alone earns on its own earnings. That is compounding.
Take the workbook's own case. Rs 10,000 goes into a cumulative bank deposit at 10 per cent for 3 years. Year one pays Rs 1,000. Year two pays 10 per cent on Rs 11,000, which is Rs 1,100. Year three pays Rs 1,210. You end with Rs 13,310.
Simple interest would have paid Rs 1,000 every year. You would have ended with Rs 13,000. The extra Rs 310 is compounding, and the gap widens the longer you hold.
A compounded return runs the same idea backwards. You know what you put in. You know what it is worth now. You know how many years passed. The compounded return is the steady yearly rate that links the two.
Use it when the holding is longer than a year. For shorter periods the workbook uses a simple return or an annualised return instead, because neither of those allows for compounding.
How it works
Chapter 10 builds three return measures in order: simple return (section 10.4.1), annualised return (10.4.2) and compounded return (10.4.3).
The first two break down over long periods. Annualisation is a straight-line scaling — it compares a 5 per cent return earned in 6 months with a 3 per cent return earned in 4 months by turning them into 10 per cent and 9 per cent a year. That works for months. Stretch the same two investments to 6 years and 4 years and the formula fails, because, in the workbook's words, it does not consider the effect of compounding.
The compounded return formula fixes that. Feed it the workbook's test case: Rs 1,000 grows to Rs 4,000 in 2 years. The answer is 1, or 100 per cent a year — and it checks out, because Rs 1,000 doubling to Rs 2,000 and doubling again reaches Rs 4,000.
For a scheme, the NAV at the beginning of the period is the Initial Value and the NAV at the end is the Later Value.
There is one limit, and it is the most examinable line in the section. All three formulae work only for growth schemes, or for an IDCW scheme that paid no dividend during the period. Once a dividend has been paid and compounding has to be counted, SEBI prescribes the CAGR technique — the reinvestment method — which reinvests each payout at the ex-dividend NAV and so shows up as extra units rather than extra rupees. Chapter 10 section 10.4.4 works that example to 43.65 per cent over 1.51 years (551 days divided by 365).
The formula
Compounded return = (Later Value ÷ Initial Value) raised to the power (1 ÷ n), minus 1
where n is the holding period in years.
| Symbol | For a bank deposit | For a mutual fund scheme |
|---|---|---|
| Initial Value | amount invested | NAV at the beginning of the period |
| Later Value | amount at the end | NAV at the end of the period |
| n | years held | years held |
A worked example
Ms Meera Iyer invests Rs 2,00,000 in the growth option of a flexi cap scheme at an NAV of Rs 50.00, so she gets 4,000 units. Five years later the NAV is Rs 100.00 and her units are worth Rs 4,00,000.
| Input | Value |
|---|---|
| Initial Value | Rs 2,00,000 |
| Later Value | Rs 4,00,000 |
| n | 5 years |
Compounded return = (4,00,000 ÷ 2,00,000) to the power (1 ÷ 5), minus 1 = 14.87 per cent a year.
Now do it the lazy way. Her money doubled, so the simple return is 100 per cent; divide by 5 and you get 20 per cent a year. That is wrong, and it is wrong by a lot. Rs 2,00,000 compounding at 20 per cent for five years would have reached about Rs 4,97,700, not Rs 4,00,000.
The workbook then separates the scheme return from the investor return. Suppose an exit load of 1 per cent applies when Ms Iyer redeems. She receives 99 per cent of Rs 100, which is Rs 99, so her proceeds are Rs 3,96,000 and her own compounded return falls to about 14.64 per cent. Same portfolio, same five years, 0.23 percentage points less — because loads and taxes drag the investor's return below the scheme's. A scheme advertisement shows the number before any load.
(The NAVs and the load here are illustrative; the Rs 10,000 deposit, the Rs 1,000-to-Rs 4,000 case and the 43.65 per cent CAGR are the workbook's own.)
Why NISM asks about it
Chapter 10 (Risk, Return and Performance of Funds), section 10.4.3, sitting between annualised return in 10.4.2 and CAGR in 10.4.4. Expect a straight formula question, a question on why an annualised return cannot be used beyond a year, and the boundary question — which measure applies when the scheme has paid a dividend during the period. Section 10.4 also supplies the holding-period rule that is easy marks: CAGR for holding periods over one year, simple absolute return for less than one year.
Common exam traps
- A compounded return is not a simple return divided by the number of years. The workbook's own case is Rs 1,000 to Rs 4,000 in 2 years at 100 per cent a year, not 150 per cent.
- Annualised return ignores compounding. It is fine for 6 months; it is wrong for 6 years.
- n is in years. Chapter 10 converts 551 days to 1.51 years by dividing by 365 before applying the formula.
- If a dividend was paid in the period, none of the three formulae apply. Use CAGR, the reinvestment method, which reinvests each payout at the ex-dividend NAV.
- Holding period returns: CAGR above one year, simple absolute return below one year.
- Scheme return is not investor return. Entry load (now banned), exit load and tax all pull the investor's figure down, and advertised returns are shown without load.
Check yourself
1.Two schemes report returns since inception of 5% over 6 months and 3% over 4 months. Which has performed better on an annualised basis?
- a)The first, at 10% annualised against 9%
- b)The second, at 9% annualised against 10%
- c)They are equal once annualised
- d)They cannot be compared at all
Show the answer
Answer: (a) The first, at 10% annualised against 9%
Annualised return = simple return × (12 ÷ months)
- Scheme 1: 5% × (12 ÷ 6) = 10%
- Scheme 2: 3% × (12 ÷ 4) = 9%
The first scheme performs better — but note how much the raw figures misled. A headline of 5% versus 3% looked like a comfortable win; annualised, the gap narrows to 10% versus 9%.
That is exactly why annualisation exists: the two returns are obviously not comparable across different periods, and annualisation helps us compare the returns of two different time periods.
One limit to remember: this simple annualisation works for periods under a year. Beyond that it ignores compounding, and the compounded return formula must be used instead.
Where this is taught
Free preparation for NISM Series V-ARelated terms
- Annualised returnA return scaled up or down to a one-year basis so that investments held for different lengths of time can be compared — a simple scaling that, unlike CAGR, ignores compounding.
- CAGRThe single smoothed annual rate at which a starting value would have to grow, compounding each year, to reach the ending value over a given period.
- Net Asset ValueThe net assets of a mutual fund scheme divided by the number of units outstanding — what one unit of the scheme is worth on a given day, after every liability except the unitholders' own.
- Exit loadA charge levied when an investor redeems units, calculated as a percentage of NAV and deducted from it, usually only if the units are sold within a stated holding period.
- Rolling returnsThe average annualised return over many consecutive holding periods inside an evaluation period — say every one-year return in three years — used to remove the distortion of an unusually high or low start or end point.
- Simple returnThe plain percentage change in the value of an investment over a period — (ending value minus beginning value) divided by beginning value — with no adjustment for time or compounding.
- Total Return IndexThe variant of a market index that adds the dividends and interest paid by its constituents to their price movement — the only variant a mutual fund scheme may be benchmarked against since 1 February 2018.