The rate you were quoted, and the money that arrived monthly

The calculator is on a fund house’s website and it takes three inputs. ₹10,000 a month. Ten years. Expected return, twelve per cent. It returns ₹23,00,387, and that number goes onto a sheet, into a message to a spouse, and into the sentence "by 2036 we will have twenty-three lakh". Ten years later the fund has in fact returned almost exactly twelve per cent a year and the account holds something else entirely, in one direction or the other. Nothing went wrong, nobody misled anybody, and the fund’s own reporting is accurate. The number on the sheet was the answer to a question that had not been asked.

Think of it like this

The bus that averaged forty kilometres an hour

A bus covers a route and its average speed for the trip works out at forty kilometres an hour. Two passengers were on it. One boarded at the depot and rode the whole way. The other got on forty minutes in, at the point where the road opens up, and got off before the town traffic. The bus’s average speed is a fact about the bus and it is the right number for the driver’s logbook. Quoting it to the second passenger answers a question about the vehicle rather than about the journey she took, and hers could easily have been faster or slower.

In the market

A fund’s ten-year return is a fact about the fund between two dates, and it is the right number for judging the manager, who does not decide when money arrives. Your return depends on when each rupee got on and how much of it there was. When money arrives in a hundred and twenty instalments, the fund’s number and yours are answers to two different questions, and they can differ enormously — in either direction.

Two returns, and what each one is a fact about

	The fund’s number	Your number
What it is called	A time-weighted return. On a factsheet it appears as the 1-year, 3-year, 5-year and since-inception figures, and as a CAGR	A money-weighted return. On a platform statement it appears as XIRR, and in a spreadsheet as the function of the same name
What it measures	What one rupee, present throughout the whole period, would have earned	What the actual stream of rupees earned — each instalment weighted by how large it was and how long it was present
Who it is the correct measure for	The fund manager, who chooses the holdings and does not choose when money arrives or leaves	You, who choose almost nothing else
What it ignores	The size and timing of every contribution and withdrawal, deliberately — that is what makes it comparable between funds	Nothing. That is the point of it, and it is why it cannot be compared between people
Where the two agree	Only where a single amount went in at the start and nothing was added or taken out	Which is not how anybody with a salary invests

Two paths, one ten-year fund return of zero

The cleanest way to see the size of the gap is to hold the fund’s number completely still and move only the path. Take a fund whose net asset value is 100 today and was 100 ten years ago. Its ten-year return is zero, on any path whatsoever, and every report it publishes will say so. Now run ₹10,000 a month through it for the whole hundred and twenty months — ₹12,00,000 invested — on two different paths between those two fixed points.

Worked example

The V and the inverted V

A fund at NAV 100 both ten years ago and today, with a ₹10,000 monthly instalment throughout

Path A — the VTen-year return: zero. Average NAV across the period: 75NAV slides steadily to 50 over five years, then climbs back to 100

Units bought on path AA fixed rupee amount buys more units when the NAV is low, so most of the units were bought in the cheap middle of the periodAbout 16,636

Value at the end, at NAV 100The average price paid works out at about ₹72 a unit, against an average NAV of 75 and a closing NAV of 100About ₹16,63,600 on ₹12,00,000 invested

The investor’s return on path AOn a fund that returned zero over the same ten years and described itself, accurately, as flatAn XIRR of about +6.5% a year

Path B — the inverted VTen-year return: also zero. Average NAV across the period: 150NAV climbs steadily to 200 over five years, then slides back to 100

Units bought on path BAverage price paid about ₹144 a unit — still below the average NAV of 150, because the averaging worked here tooAbout 8,318

Value at the end, at NAV 100The closing NAV of 100 is far below the ₹144 average price paid, so the averaging lowered the price and the investor still lostAbout ₹8,31,800 on ₹12,00,000 invested

The investor’s return on path BSame fund return, same amount invested, same number of instalmentsAn XIRR of about −7.6% a year

The gap between the two outcomesProduced entirely by the route the path took between two identical endpoints, on a fund whose own reported number was the same in both cases. Note which pair of numbers this fourteen belongs to: it is the spread between the two investors, not the distance from either of them to the fund’s noughtAbout ₹8,31,800, and about 14 percentage points a year

Two things are going on and it is worth keeping them apart. A fixed rupee amount buys more units at a low price than at a high one, which pulls the average price paid below the average price of the period — ₹72 against 75 on path A, ₹144 against 150 on path B. Note that this happened on both paths, so it is not the explanation on its own. What decides the outcome is the second thing, and it comes down to two numbers: the average price you actually paid, against the price on the day the money is valued. Path A paid about 72 and was valued at 100; path B paid about 144 and was valued at the same 100. Said the other way round, with money arriving monthly the balance is at its largest towards the end, so a path that recovers late lands the recovery on the biggest amount and a path that falls late lands the fall there. Both favour a path that is cheap while the instalments are going in and dear on the day you are valued, and both punish the reverse — which is why path A wins despite being dear at both ends and cheap only in the middle. Nobody knows in advance which path they are on, which is the actual finding here: the number you were quoted has a spread around it that your contribution pattern amplifies, and the direction of the amplification is unknowable. These two paths are straight lines chosen so the arithmetic can be checked by hand; a real path wanders. The conclusion does not depend on the shape, only on the two quantities it turns on: what the units cost on average, and what they are worth on the day the money is needed.

Which is why averaging is only half a rule

Rupee cost averaging is usually presented as a benefit you obtain by investing monthly. Path A appears to confirm it and path B refutes it, and the honest version has to account for both.

For money that arrives monthly there is nothing to compare against. A salary arrives in instalments, so it is invested in instalments. The averaging is a consequence of how you are paid rather than a strategy anybody selected, and there is no alternative version of the decision in which the same money went in as a lump.
For a lump that already exists, splitting it is a decision to hold cash. A bonus, a maturity, a property sale. Dividing ₹9,00,000 into twelve instalments means most of it sits outside the market for some months. On an asset that rises more often than it falls, that lowers the expected outcome; it also narrows the range of outcomes, which is a real benefit to somebody who could not survive the worst case. Both halves are true. The honest statement is that it trades expected return for a smaller spread — not that it produces a better return.
The averaging is not a source of return. Path A’s +6.5% did not come from the instalments being clever; it came from the fund being cheap in the middle of the period. The identical mechanism on path B produced −7.6%. Anything that behaves like that in both directions is not an edge.
A step-up changes the weighting again. Contributions that rise each year push even more of the total towards the end of the period, so the final years matter even more than they already did. That is not an argument against a step-up, which does other useful things. It is a reason not to read a ten-year fund return as a forecast of what a rising contribution will produce.
None of this makes the fund’s number dishonest. It is the right measure of the manager, who is being judged on the decisions they actually took. Asking it to describe your outcome is asking it to include information it was specifically constructed to exclude.

What the calculator on the website is actually computing

It applies one constant monthly rate to every instalment, which is the arithmetic of a path that has never existed — no market delivers one per cent a month for a hundred and twenty months in a row. So the output is not a forecast and does not pretend to be. It is the answer to "what would this be if the volatility were zero", and it is useful as a check on the order of magnitude rather than as a target.

Worked example

The same calculator, honestly used

₹10,000 a month for ten years, at three assumed rates

At 12% a yearThe number that went onto the sheet, and the only one of the three anybody ranAbout ₹23,00,000

At 10% a yearTwo percentage points is ₹2,52,000 of the answerAbout ₹20,48,000

At 8% a yearThe spread across a perfectly ordinary range of assumptions is about ₹4,71,000 — on ₹12,00,000 put inAbout ₹18,29,000

The same ₹23,00,000, in today’s moneyAt 6% inflation over ten years, ₹23,00,000 in 2036 buys roughly what ₹12,85,000 buys now. The goal, if it is a school fee or a down payment, is priced in the second kind of rupeeAbout ₹12,85,000

The instalment conventionThe same calculator gives one or the other depending on whether it applies the month’s growth to an instalment paid at the start or the end of the month. A ₹23,000 difference nobody has ever noticed, and it is worth knowing only because it shows how little of this figure is a forecast₹23,00,387 or ₹23,23,391

Three rates and one deflation, four minutes of work, and the plan now carries a range in today’s money rather than a single figure in 2036 rupees. The rates and the inflation assumption here are illustrative and the point does not depend on them: the output moves by roughly a fifth across an ordinary range of inputs, which is a statement about how much of the answer was ever in the calculator’s hands. Two things it still cannot tell you. It cannot tell you your XIRR, because that depends on a path nobody has. And it cannot tell you whether the contribution is large enough, because that requires the goal, the date and the two questions the previous lessons in this module were about.

Check yourself

A fund’s NAV is 100 today and was 100 ten years ago, so its ten-year return is zero. A ₹10,000 monthly instalment ran for the whole period. What was the investor’s return?

◆ Checkpoint

Module checkpoint: the shape the question arrived in

5 questions. Answers are revealed once you submit all of them.

1.A household needs ₹30,00,000 on a date fixed by an agreement five years away, has ₹8,00,000 saved, and can add ₹25,000 a month — which together need about 8% a year. A profiling form places them at 70% equity. Which of the three tests decides the allocation, and why?

2.Two people hold the identical fund over the identical six years; one checks daily and one twice a year. On ordinary assumptions, what is the difference between them?

3.A household holding ₹11,20,000 against a cost of ₹9,00,000 moves ₹2,20,000 of it into a single smallcap because "only the profit is at risk". What is the accurate description of what happened?

4.A fund’s NAV was 100 ten years ago and is 100 today. What can be said about a ₹10,000 monthly instalment that ran throughout?

5.A ₹9,00,000 maturity has landed, and the plan is for it to sit in equity for the next twenty years. Somebody suggests splitting it into twelve monthly instalments "to get the benefit of rupee cost averaging". What is the accurate reading?

0 of 5 answered

Simple bhasha mein

Ek baar ka bhaav, roz ke saudе pe

Dukaandaar ne bola "chawal ₹60 kilo" — aapne saal bhar mein thoda-thoda 200 kilo liya, kabhi ₹52 pe, kabhi ₹71 pe. Saal ke aakhir mein aapka asli bhaav ₹60 nahi hai, aur woh sirf tab pata chalta hai jab kab kitna liya woh bhi ginno. Calculator ne ₹10,000 mahina aur "12%" daal ke ₹23,00,000 nikaal diya, aur woh number dus saal se ghar ke plan pe chipka hai. Woh kisi ne poocha hi nahi tha us sawaal ka jawab hai. 12% fund ka return hai — ek hi baar daale hue paise pe naapa gaya. Aapka paisa har mahine gaya, yaani har instalment ne alag safar kiya: pehla dus saal chala, aakhri ek mahina. Isiliye do ghar, jinke fund ka dus-saal ka return bilkul ek jaisa hai, apne liye +6.5% aur −7.6% kama sakte hain — farak sirf isme hai ki bada paisa kab pada aur bura daur kab aaya. Jo number aapke liye sach hai use XIRR kehte hain: tareekh ke saath jama-nikaasi daalo, tab jawab milta hai. Fund ka return fund ka record hai; aapka return aapka record hai — aur do alag cheezein hain. Plan pe wahi likho jo aapne kamaya, aur quote wale number ko target maano, guarantee nahi.

What to remember

A fund’s reported return is time-weighted — what one rupee present throughout would have earned — and it deliberately excludes the size and timing of your contributions.
Your return is money-weighted, arrives as XIRR, and cannot be compared with anybody else’s.
On a fund with a ten-year return of exactly zero, the same monthly instalment produces about +6.5% a year on one path and about −7.6% on another.
With money arriving monthly the balance is largest at the end, so the final years land on the biggest amount — and a step-up sharpens that further.
A SIP calculator computes a path with no volatility in it: run it at three rates and convert the answer into today’s money before writing it anywhere.

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