Dollar-Cost Averaging Calculator
Should you invest all at once or spread it over time? Calculate your DCA schedule, compare strategies, and discover how volatility works in your favour.
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How to Use This Calculator
Tab "DCA Schedule"
Enter your amount per purchase, purchase interval (weekly, bi-weekly, monthly, or quarterly), number of purchases, starting share price, and an assumed annual return. The calculator generates a realistic price path and shows total shares acquired, your average cost per share (harmonic mean), and how it compares to the arithmetic average price.
Tab "DCA vs Lump Sum"
Enter a total investment amount, how many months to spread the DCA, a starting price, expected return, and price volatility. The calculator shows what happens if you invest the full amount on day one (lump sum) vs spreading it monthly. You will see which strategy wins in the modelled scenario, and by how much.
Tab "Volatility Benefit"
Model the pure volatility effect. Set price volatility to 0% and you will see minimal DCA advantage. Increase volatility to 30–50% and watch the gap between your average cost and the average price widen significantly. Hover over the bar chart to see individual purchase prices and share counts.
The Formulas
Avg cost = Total invested ÷ Total shares
= (n × A) ÷ Σ(A ÷ pᵢ)
= n ÷ Σ(1 ÷ pᵢ)
where n = number of purchases, A = fixed amount, pᵢ = price at purchase i
Arithmetic average price (always ≥ DCA avg cost):
Avg price = Σpᵢ ÷ n
Total shares acquired:
Total shares = Σ(A ÷ pᵢ)
Key inequality (Jensen's inequality):
Harmonic mean ≤ Arithmetic mean
DCA avg cost ≤ Simple avg price (always, for any price sequence)
Cost saving per share:
Saving = Arithmetic avg price − Harmonic avg cost > 0
Lump sum comparison:
LS shares = Total amount ÷ Initial price
DCA shares = Σ(Monthly amount ÷ monthly price)
Final value = Shares × Final price
All calculations use standard financial mathematics. Prices are modelled using Geometric Brownian Motion with user-specified return and volatility. No country-specific tax rates are applied. Results are pre-tax estimates.
Worked Examples
Example 1 — DCA Advantage: $1,000/month for 12 months, prices $40–$60
An investor puts $1,000 into a stock each month for 12 months. Prices fluctuate between $40 and $60 with an average (arithmetic) of $50. How does DCA affect the average cost?
At $50 simple average, you might expect to buy $12,000 ÷ $50 = 240 shares. DCA's harmonic mean effect delivers 247 shares instead — 7 extra shares at no extra cost. The lower your average cost, the higher your profit when prices rise.
Example 2 — Volatile Market: DCA wins over lump sum
An investor has $12,000 to deploy. Lump sum option: invest all $12,000 at $50/share on day 1. DCA option: invest $1,000/month over 12 months. Prices are volatile, ending back at $50 after swings to $35 and $65.
When prices end where they started but experienced significant swings along the way, DCA wins. The deep dips allowed monthly buyers to accumulate extra shares cheaply, leading to a better outcome than the single up-front investment.
Example 3 — Rising Market: Lump sum wins
Same $12,000 total. Now prices rise steadily: $50, $52, $54, $56, $58, $60, $62, $64, $66, $68, $70, $72 (no dips). Final price: $72.
| Strategy | Avg cost | Shares | Final value |
|---|---|---|---|
| Lump Sum ★ | $50.00 | 240.00 | $17,280.00 |
| DCA (12 months) | $60.49 | 198.37 | $14,282.64 |
In a continuously rising market, lump sum wins decisively — by nearly $3,000 in this example. The earlier money goes in, the longer it benefits from price appreciation. This is why lump sum outperforms DCA approximately 67% of the time historically: markets trend upward more often than they fall. DCA's role is risk reduction, not return maximisation.
Understanding DCA: Key Concepts
What is Dollar-Cost Averaging?
Dollar-cost averaging means investing a fixed amount of money at regular intervals — regardless of market conditions. You might invest $500 every month into an index fund, or $200 every week into a stock. The key is that the amount is fixed in currency terms, not in share quantities. This is distinct from investing a fixed number of shares each period, which has no mathematical advantage.
The Harmonic Mean Advantage
When you invest a fixed dollar amount, you buy more shares when prices are low and fewer when prices are high. Your average cost per share is the harmonic mean of the prices you paid, while the simple average of those prices is the arithmetic mean. The harmonic mean is always less than or equal to the arithmetic mean — this is Jensen's inequality in action. This means DCA structurally guarantees your average cost is at or below the average price, regardless of the price sequence.
Lump Sum vs DCA: The ~67% Rule
Research by Vanguard (2012) examined 10-year rolling periods across the US, UK, and Australian markets from 1926 to 2011 and found that lump sum investing outperformed DCA approximately two-thirds of the time. The intuition: markets spend more time rising than falling. If you have the money available, investing it immediately puts it to work longer. DCA introduces cash drag — the portion not yet invested earns less than the market in trending periods.
However, DCA wins in the remaining one-third of scenarios — precisely those where markets fall or remain volatile during the investment window. And crucially, DCA wins on psychology: an investor who uses DCA is far more likely to stay the course than one who invested a large lump sum just before a 30% drawdown.
When DCA Makes Most Sense
DCA is the right strategy when: (1) You receive income regularly and invest as it arrives — this is natural, automatic DCA. (2) You have a lump sum but are too anxious to invest it all at once — spreading it reduces emotional risk. (3) Markets are highly volatile and you lack confidence in timing. (4) You want to build discipline and automate investing. It is less optimal when you have confirmed access to a lump sum and markets have strong upward momentum.
DCA Does Not Eliminate Risk
DCA does not guarantee a profit. If the asset you buy steadily declines throughout your investment window, every purchase is at a higher price than needed — and you lose money. DCA reduces timing risk but not fundamental investment risk. Choosing what to buy remains more important than how to buy it.
Frequently Asked Questions
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