Annualised return
A 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.
In plain language
Suppose one investment says it has returned 5 per cent since it started and another says 3 per cent. Which did better? You cannot tell until you know how long each took. If the first has existed for 6 months and the second for 4 months, the raw numbers are, as the workbook says, obviously not comparable.
Annualisation fixes that by asking: at this pace, what would the return be over a full year? The first investment's 5 per cent in 6 months becomes 10 per cent a year; the second's 3 per cent in 4 months becomes 9 per cent a year. Now the comparison is fair, and the first is ahead.
The method is a straight-line scaling of the simple return — the change in value over the period with no adjustment for time. It is the second of the three return measures the workbook builds up: simple, annualised and compounded.
How it works
Annualised return scales the simple return by how many such periods fit into a year:
| Investment | Simple return | Period | Annualised |
|---|---|---|---|
| 1 | 5% | 6 months | 5% × 12/6 = 10% |
| 2 | 3% | 4 months | 3% × 12/4 = 9% |
Its limit is compounding. The workbook is explicit that if the two investments had instead existed for 6 years and 4 years, it would not be possible to use this formula, because it does not consider compounding. For multi-year periods you move to the compounded return, (Later Value ÷ Initial Value)^(1/n) − 1.
Two more limits come from how NAV-based returns are calculated:
- The simple, annualised and compounded formulas capture only change in NAV. They apply to growth options, or to IDCW options that paid no distribution in the period. Where a distribution was paid, the SEBI-prescribed CAGR technique — reinvesting the payout at the ex-dividend NAV — is used.
- They measure the scheme return. Investor return uses the price actually paid and received, so loads and taxes pull it lower.
The workbook's holding-period convention matches: returns for periods over one year are calculated using CAGR, and simple absolute returns are used for periods of less than one year.
The formula
Simple return = (Later Value − Initial Value) ÷ Initial Value
Annualised return = Simple return × (12 ÷ holding period in months)
= Simple return × (365 ÷ holding period in days)
A worked example
A liquid fund. An investor parks Rs 5,00,000 when the NAV is Rs 3,000.00, and redeems after 73 days at Rs 3,030.00. Figures are illustrative.
Simple return = (3,030 − 3,000) ÷ 3,000 = 1.00%
Rupee gain = 5,00,000 × 1% = Rs 5,000
Annualised return = 1.00% × 365 ÷ 73 = 5.00% a year
The 5 per cent figure lets her compare this with a savings account or a 3-month deposit on equal terms.
An equity fund over one quarter. NAV moves from Rs 50.00 to Rs 53.00 in 3 months.
Simple return = 3 ÷ 50 = 6.00%
Annualised return = 6.00% × 12 ÷ 3 = 24.00% a year
That 24 per cent is arithmetic, not a forecast. One strong quarter in an equity fund says almost nothing about the next three, and scaling it up magnifies the noise.
Notice too what the simple scaling leaves out. Four successive quarters of 6 per cent, compounded, would be 1.06⁴ − 1 = 26.25 per cent, not 24. The gap is the compounding that annualisation ignores — and it widens the longer the period, which is why the workbook switches to compounded return beyond a year.
Why NISM asks about it
Chapter 10 (Risk, Return and Performance of Funds), section 10.4, introduces simple, annualised and compounded return in sequence, using the 5 per cent / 6 months and 3 per cent / 4 months comparison, and then the CAGR method for schemes that paid distributions. Expect a computation of annualised return from a short-period return, and a conceptual question on why annualised return cannot be used for multi-year periods.
Common exam traps
- Annualised return ignores compounding. For multi-year periods the workbook says the formula cannot be used — use compounded return or CAGR.
- Scale by the period, not by the return. 3 per cent in 4 months is 9 per cent a year, not 12.
- Holding-period returns: CAGR above one year, simple absolute return below one year.
- These formulas ignore distributions. If IDCW was paid in the period, use the CAGR (reinvestment) method.
- Scheme return ≠ investor return. Loads and taxes reduce what the investor actually earns.
- An annualised figure from a short period is not a prediction, least of all for equity.
Where this is taught
- Series V-A · Chapter 10: Risk, Return and Performance of Fundsintroduced here
- Series XV · Chapter 12: Fundamentals of Risk and Returnintroduced here
- Series V-D · Chapter 10: Risk, Return and Performance of Fundsintroduced here
- Series XVII · Chapter 5: Evaluating Fund Performance & Fund Selectionintroduced here
Related terms
- 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.
- Entry loadThe former mark-up of a mutual fund's sale price over NAV, charged when an investor bought units. SEBI has banned it, so units are now sold at NAV, subject only to stamp duty.
- Compounded returnThe 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.
- Price Return IndexThe variant of a market index that captures only the price movement — the capital gains — of its constituents, leaving out dividends and interest. Mutual funds were benchmarked to it until 1 February 2018.
- 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.
- VarianceA measure of how widely a scheme's periodic returns fluctuate around its own average return — the square of standard deviation, and a risk measure relevant to both debt and equity schemes.
- Wealth relativeThe ending value of one unit of money over a period — 1 plus the period's return in decimals. Multiplying wealth relatives chain-links sub-period returns into TWRR or geometric return.