How DCA builds an average cost
Dollar-cost averaging (DCA) invests a fixed amount in the same asset every period, whatever the price. A high price buys fewer units, a low price buys more.
The DCA average cost is therefore the harmonic mean of the prices, which is never above the arithmetic mean of those same prices. That does not mean DCA beats a single purchase on cost or return: the outcome depends entirely on the price path.
Formula
- Units bought in period i = Amount per period ÷ Price in period i
- Average cost = Total invested ÷ Total units
- Average of period prices = (Price 1 + … + Price n) ÷ n
- Value at final price = Total units × Price n
Assumptions
- The amount per period is fixed; each period buys once at exactly the price you enter.
- The price path is your input, not market data or a forecast.
- Fractional units are allowed; exchange lot sizes are ignored.
- Trading fees, taxes, dividends and the opportunity cost of cash waiting to be invested are ignored.
- DCA does not guarantee a profit or a lower cost than a single purchase.