A systematic investment plan buys a fixed rupee amount at a fixed interval, so it buys more units when the price is low and fewer when it is high. The average cost per unit that results is the harmonic mean of the prices, which is always at or below the arithmetic mean.
Worked Example 5 runs the arithmetic on three paths. On a rising path from 100 to 155 the average cost is 125.13 against an arithmetic mean price of 127.50, an advantage of 1.89 percent. On a falling path from 100 to 45 the average cost is 68.19 against an arithmetic mean of 72.50, an advantage of 6.32 percent. The advantage is larger when prices are more dispersed, which is the mathematical content of the claim that the method "benefits from volatility".
Does a SIP beat a lump sum?
Now the comparison that gets used to sell the method, and its honest answer. Against deploying the same 120,000 rupees at the first month's price, the plan loses badly on a rising path and wins handsomely on a falling one. Rising: 148,647 against 186,000, a shortfall of 37,353. Falling: 79,189 against 54,000, an advantage of 25,189. Add interest on the cash awaiting deployment at 6.5 percent and the rising-path shortfall narrows to 33,778 and the falling-path advantage widens.
Since markets rise more often than they fall, the expected value favours the lump sum. Under a stated model of 0.90 percent expected monthly total return, a rupee invested at the start grows to 1.1135 over twelve months while the average rupee in the plan is invested for only 6.5 months and grows to 1.0605, a shortfall of 4.76 percent. Interest on the idle cash recovers most of it, leaving 2.09 percent. Both numbers are small and both point the same way.
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Why is a SIP still worth using?
Here is why that entire comparison is usually irrelevant. A salaried investor has no lump to sum. Money arrives monthly, and the only choice is whether to invest it on arrival or hold it and wait for a better price. Against that alternative the systematic plan wins on an argument nobody disputes: a waiting rule requires a trigger, and triggers do not fire. Run a rule that waits for a 10 percent fall from the running peak across the illustrative rising path and it fires in zero of twelve months, deploying zero rupees while the price rises 55 percent.
So the plan's real justification is not a return advantage. It is that it converts an allocation decision into a default, removes twelve opportunities a year to talk yourself out of investing, and lands each contribution automatically at whatever price exists. Sell it on that and the claim is true. Sell it as a way to beat a lump sum and the claim is false in expectation, as the arithmetic above shows.
One structural point connects the plan to the band. A systematic plan is how the floor gets defended in practice. In a long decline, contributions arriving at falling prices push the equity weight up mechanically, so an investor who keeps contributing rarely reaches the floor at all, and one who stops contributing reaches it fast.