The set-up
Take a fund whose NAV, on seven consecutive SIP dates, reads 100, 90, 80, 70, 80, 90 and 100. It starts at ₹100 and ends at ₹100, with a dip in between. The numbers are made up so the arithmetic can be checked by hand; they are not any particular fund. You invest ₹10,000 on each date.
| SIP date | NAV (₹) | Amount (₹) | Units bought |
|---|---|---|---|
| 1 | 100 | 10,000 | 100.00 |
| 2 | 90 | 10,000 | 111.11 |
| 3 | 80 | 10,000 | 125.00 |
| 4 | 70 | 10,000 | 142.86 |
| 5 | 80 | 10,000 | 125.00 |
| 6 | 90 | 10,000 | 111.11 |
| 7 | 100 | 10,000 | 100.00 |
| Total | 70,000 | 815.08 |
What the totals say
You put in ₹70,000 and hold about 815.08 units. Your average cost per unit is 70,000 ÷ 815.08 = ₹85.88.
The plain average of the seven NAVs is (100 + 90 + 80 + 70 + 80 + 90 + 100) ÷ 7 = 610 ÷ 7 = ₹87.14. So you paid less per unit than the average price on offer, simply because the same rupees bought 142.86 units at ₹70 and only 100 units at ₹100.
Now look at the value. The NAV is back at ₹100, so the 815.08 units are worth about ₹81,508. Against ₹70,000 invested, that is a gain of about ₹11,508, or 16.4%, even though the fund finished exactly where it started.
Compare that with a single ₹70,000 lump sum put in on date 1 at ₹100: it buys 700 units, worth ₹70,000 at the end. Zero gain. The SIP earned its 16.4% only because it kept buying through the dip. That is the whole mechanism, and it is arithmetic, not magic: a fixed amount automatically buys more at low prices.
Why the average cost is a harmonic mean
Average cost = total rupees ÷ total units = n × amount ÷ (amount × (1/P₁ + 1/P₂ + …)) = n ÷ (1/P₁ + 1/P₂ + …). That is the harmonic mean of the prices. For any set of prices that are not all equal, the harmonic mean is lower than the ordinary average. The wider the swings, the bigger the gap, which is why volatile funds can show a bigger averaging benefit than steady ones.
The case where it does not rescue you
Now change only the last four dates and let the NAV keep falling: 100, 90, 80, 70, 60, 50, 40. The units are 100.00, 111.11, 125.00, 142.86, 166.67, 200.00 and 250.00, a total of 1,095.64 for ₹70,000. The average cost falls to about ₹63.89, which is again below the ordinary average of 70. But the NAV ended at ₹40, so the holding is worth about ₹43,825, a loss of around 37%.
Averaging lowered the cost, and the loss was still large, because the price kept going down and never came back. Rupee cost averaging protects you from the timing of your entries. It does not protect you from a fund that stays down, and it cannot make a bad fund good.
What this means in practice
- Staying invested through a fall is when a SIP does its work. The units bought at the low are the ones that lift the final value. Stopping the SIP in a fall removes exactly those purchases; see should you stop a SIP in a market crash.
- The benefit depends on the NAV recovering. In the first path the gain arrives because the price returned to ₹100. Averaging buys cheaper units; recovery is what makes them valuable.
- A SIP is not always better than a lump sum. If the NAV only rises, the lump sum put in on day one wins, because every rupee has been invested longer. The comparison is worked through in lump sum or SIP: how to decide.
- Compare returns with XIRR, not a simple gain. Each instalment has been invested for a different time; portfolio XIRR vs gain explains why.
To test your own numbers, use the SIP calculator, or backtest a real fund with the SIP and lump sum backtest on any fund page.
Reading this
- The NAV paths above are invented for illustration. They show how the arithmetic behaves, not what any fund has done or will do.
- Costs, taxes and exit loads are left out to keep the unit counts checkable.
- This describes how fixed-amount buying works. It is not a recommendation for or against any fund.
Frequently asked questions
What is rupee cost averaging?
Investing a fixed rupee amount at regular intervals. The same amount buys more units when the NAV is low and fewer when it is high, so the average cost per unit ends up below the simple average of the NAVs you paid.
Does rupee cost averaging guarantee a profit?
No. It lowers your average cost relative to the prices you paid, but if the NAV ends below that average cost you still have a loss. It is a feature of fixed-amount buying, not a return guarantee.
Why is the average cost lower than the average NAV?
Because the average cost is a harmonic mean of the NAVs, which is always at or below the ordinary average whenever the NAVs differ. Equal rupees buy more units at the cheap prices, so those prices carry more weight.
This is commentary on published data, not investment advice. WealthTicker is not a SEBI-registered adviser or distributor. Figures are as of the dates stated and can be revised by their source.
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