DCA or lump-sum Bitcoin and Ethereum: an equal-capital study

The question: what happens to the same available money?

Imagine having 12,000.00 USD before buying any cryptocurrency. Lump sum uses the whole budget at the first scheduled price. Dollar-cost averaging, or DCA, divides that same budget into scheduled purchases. In our main test, it buys 1,000.00 USD per month for 12 months, starting on the same day as lump sum.

The experiment is separate for Bitcoin and Ethereum. It is not a combined BTC–ETH portfolio, a comparison of different budgets or a simulation of money arriving from future salaries. Each historical window starts with a fresh hypothetical investor and the same available capital.

Across the full set of horizons there are 910 strategy comparisons. For the main 12-month horizon, each asset has 113 start dates. The purpose is to show how timing and price paths changed the outcome, rather than nominate a method that should always be used.

Two purchase methods, one capital base

Lump sum turns the available budget into the asset at one reference price, less the purchase fee. DCA keeps the unspent part as USD cash and buys at successive monthly reference prices. That cash is part of the investor's wealth throughout the test.

Both methods hold their acquired asset until the same final valuation date. Neither borrows, trades with leverage, sells early, reinvests staking rewards or switches the schedule because a price has moved. The comparison below describes mechanics, not a ranking of investment choices.

Why comparing only the crypto is incomplete

At the first purchase, DCA spends 1,000.00 USD, pays a fee equivalent to 1.00 USD, and receives crypto worth 999.00 USD at the benchmark. It also still owns 11,000.00 USD. Its total portfolio value is therefore 11,999.00 USD. Lump sum has crypto worth 11,988.00 USD and no remaining cash after its fee of 12.00 USD.

Comparing 999.00 USD of crypto with 11,988.00 USD of crypto would conceal the reserve. Conversely, describing cash as a return-free loss would also be wrong: it is still capital, with a different exposure. Our primary measure at every valuation is crypto value plus all remaining cash.

At the end of the zero-yield baseline, all scheduled purchases have occurred and the remaining cash is zero. Crypto-only and total value then coincide. The cash distinction is still essential for the path to that endpoint, and they differ again when reserve interest is retained in the sensitivity test.

Data coverage fixed before reading the outcomes

We use Coin Metrics Community PriceUSD for BTC and ETH from a preserved snapshot, with the same provider and price field throughout. PriceUSD is a USD daily closing reference rate. Its calendar-date label represents that UTC day's close; it must not be mistaken for a market order filled at midnight at the start of the day.

The retrieved archive has prices through 2026-05-23. The latest complete shared month therefore ends on 2026-04-30. We do not invent later prices or extend a window with an incomplete month. Testing starts on 2016-01-01, at the beginning of the first complete calendar year after ETH's available 2015 price history.

Both assets have 3,918 continuous daily observations in the preserved data from 2015-09-01 to 2026-05-23, including the warm-up history needed for trailing classifications. Every used price was compared with a separately retrieved snapshot. No price was replaced with zero, interpolated or forward-filled.

This verifies the data we used, not every exchange trade behind the provider's reference rate. It is a retrieved historical series, not a record of the exact benchmark vintage available to an investor in real time. The snapshot and its fingerprints are included in the research files.

The calendar rules and completed horizons

A new test starts on every first calendar day of the month. Both methods use that day's closing benchmark for their first purchase. DCA then buys on the first day of each remaining scheduled month. Final valuation uses the last calendar day's closing benchmark in the last scheduled month.

For example, the 2022-01-01 test buys monthly from January through December 2022 and values both portfolios on 2022-12-31. These are 12 scheduled purchases, not twelve months of additional contributions after an initial purchase. Buying at the close is a benchmark model, not a promise that an order could obtain that price.

The 3, 6, 12 and 24-month tests use the same capital and cost rules for both assets. Their monthly allocations are 4,000.00 USD, 2,000.00 USD, 1,000.00 USD and 500.00 USD. Longer completed horizons have fewer eligible starts because they need more future data.

All eligible calendar starts are included, including bad outcomes. No required purchase or final date is missing, so no window is excluded. For the main horizon, starts run from 2016-01-01 to 2025-05-01. Monthly windows overlap: they are different starting decisions, but they are not statistically independent observations.

Fees come from the budget, not extra money

The baseline charges 0.10% on each buy, deducted from the acquired asset. A gross allocation A at price P therefore adds A × (1 − f) ÷ P net units. The allocation leaves cash in full; the fee reduces the units received. Nothing is funded outside the initial budget.

With 12 allocations of 1,000.00 USD, DCA pays 1.00 USD per buy and 12.00 USD in total USD equivalents. Lump sum pays 12.00 USD once. A constant percentage of the same total amount does not become larger merely because there are more orders. The asset units used to pay commission differ with purchase prices, and the timing of the charges differs.

The 0.10% assumption is anchored to Binance's published regular-user standard spot rate, checked 2026-10-03. It is not a reconstruction of that exchange's history, not a claim that it operated in every tested year, and not the fee for every account, pair, discount or retail purchase service. The price source and fee illustration are different inputs.

Daily reference prices do not supply a full historical bid–ask series. We do not fabricate spreads or fills. The baseline excludes spread, slippage, deposit, withdrawal and network charges; later sensitivity tests add explicitly hypothetical costs. Valuation marks the holdings to the benchmark without selling them, so it is not cash received after an exit fee.

The formulas that keep the comparison honest

Let C be initial capital, H the number of monthly buys, A = C ÷ H, f the buy-fee fraction, Pᵢ the price at purchase i, and Pₜ the price at valuation. After k purchases, Q is the sum of net units actually acquired; unspent cash is C − kA in the zero-yield baseline.

Lump sum: Q = C(1 − f) ÷ P₀. DCA: Qₖ = Σ A(1 − f) ÷ Pᵢ over the k completed purchases. At any date, V = Q × Pₜ + cash. Portfolio return is (V ÷ C − 1) × 100. The denominator stays the same initial capital for both methods.

The paired difference is V_DCA − V_LS. Dividing it by C and multiplying by 100 expresses a difference in percentage points of the initial budget. It is not the percentage by which DCA exceeds the other portfolio. A difference within 0.01 USD is classified as a tie.

The downloadable files retain each purchase, net holdings, cash balance, daily portfolio value and final result. The arithmetic was independently reconstructed from the archived prices with exact rational calculations, rather than accepted because the authoring script completed without an error.

Bitcoin: all twelve-month starts

For BTC, DCA finished higher in 33 of 113 windows, or 29.20%. Lump sum finished higher in 80, or 70.80%. There were 0 ties under the one-cent rule. These are descriptive shares of this historical sample, not probabilities assigned to a future purchase.

The mean paired difference was −9,770.62 USD; the median was −4,998.22 USD. Expressed against the initial capital, those differences are −81.42 percentage points and −41.65 percentage points. The full table also shows each strategy's own mean, median, minimum and maximum, so the comparison is not reduced to one average.

The most negative paired difference was −83,628.08 USD, for the start 2016-12-01; the most positive was 7,698.87 USD, for 2022-04-01. A negative difference means lump sum ended with more capital. A positive one can occur even when both portfolios lost money.

Ethereum: its own prices and results

For ETH, DCA finished higher in 37 of 113 windows, or 32.74%. Lump sum finished higher in 76, or 67.26%, with 0 ties. These figures come from ETH purchases and ETH prices; they are not Bitcoin's result relabelled.

The mean paired difference was −38,220.41 USD, while the median was −2,716.15 USD, or −318.50 percentage points and −22.63 percentage points of initial capital. The large gap between mean and median reflects a strongly uneven sample. Early ETH growth windows create very large values, which remain in the calculation instead of being removed for a tidier result.

The paired range runs from −996,450.47 USD at 2017-02-01 to 12,932.90 USD at 2016-06-01. That range is part of the finding. It does not establish what prices, liquidity or investable returns will be available in the future.

What the result distributions actually measure

The start-date chart shows the paired portfolio difference for each new hypothetical investor. It is not the balance history of one investor who kept adding money. The histogram counts those differences in fixed intervals, with open-ended tails so that extreme outcomes are not clipped or discarded.

A mean is sensitive to very large gains or losses. A median is the middle observation after sorting. The median paired difference is calculated from the differences for the same starts; subtracting the two strategies' separate medians generally gives a different answer.

Nor does a high historical win share prove a superior future choice. The windows reuse many of the same market days, BTC and ETH were selected as surviving assets, and one time period is represented. We report no confidence interval or future success probability as if these were independent draws.

A paired gap can be less than −100.00 percentage points because lump sum's gain can exceed the initial budget many times. That is a gap between returns, not a claim that an unleveraged crypto portfolio lost more than all its capital. The chart's extreme ETH differences must be read in that sense.

The complete horizon comparison

The table includes every completed 3, 6, 12 and 24-month window for each asset. The capital is always 12,000.00 USD; changing the duration changes the allocation per buy and the time spent in cash. All differences retain the DCA-minus-lump-sum sign convention.

The available start counts are 122, 119, 113 and 101 per asset. Each pair of strategies and each pair of assets uses the same eligible dates within its horizon. Different horizons end with different last eligible starts, so comparing their average rows does not isolate the effect of duration alone.

None of these rows represents a return compounded across all starts, or an investor who held hundreds of portfolios simultaneously. They are repeated equal-budget counterfactual comparisons. A longer schedule is not automatically a safer or more profitable purchase method.

Calendar examples, not a showcase of winning entries

We fixed a simple illustrative rule: the first day of each year from 2018 through 2023, with a 12-month schedule and valuation on the last day of that year. This includes different price paths without selecting examples because one method won. These examples supplement the full sample; they do not replace it.

In the tables, prices are the same historical benchmarks used in the calculations. Units are net of buy fees. Both portfolios spend 12,000.00 USD, pay 12.00 USD in total purchase-fee equivalents and finish with zero cash in the baseline. Dates show the shared start and final valuation.

Bitcoin examples across different years

Compare the start and end prices with both final holdings. DCA's final quantity depends on all intervening purchase prices. Lump sum's quantity is fixed by its first price. The difference column compares the complete portfolios on the same date, even when both results are negative.

A rising final price alone does not determine which method wins: the path between the endpoints also matters. A declining final price does not prove that gradual buying avoided a loss. The full individual ledgers and daily paths are available in the research files.

Ethereum examples across the same years

ETH uses exactly the same dates, initial capital and schedule as BTC, but its own prices. Keeping the dates fixed makes it possible to see where the two assets followed different paths. ETH's results must therefore be assessed independently.

The regime label is a description of the price change observed after the window ended. It is not information that was available when the first purchase was made. Detailed rules for these labels appear later in the study.

A full Bitcoin ledger: starting in 2022

On 2022-01-01, BTC's reference price was 47,560.00938165 USD. Lump sum bought 0.25206051 BTC after a fee equivalent to 12.00 USD. DCA's first 1,000.00 USD allocation bought 0.02100504 BTC after 1.00 USD in fees and left 11,000.00 USD as cash.

The ledger records all 12 DCA buys. Each row shows that month's price, gross allocation, fee equivalent, net units bought, cumulative net holdings and remaining cash. The budget includes the fees, so the remaining cash falls by the gross allocation, not by the allocation plus an extra fee.

At the common final price of 16,524.21780245 USD on 2022-12-31, DCA held 0.45391738 BTC worth 7,500.63 USD; lump sum held 0.25206051 BTC worth 4,165.10 USD. With zero remaining cash, these are also their total portfolio values.

DCA ended 3,335.53 USD higher, but its loss from the initial budget was 4,499.37 USD, or −37.49%. Lump sum's loss was 7,834.90 USD, or −65.29%. A relative win is not the same thing as an investment profit.

A full Ethereum ledger under the same conditions

On the same start date, ETH's reference price was 3,761.05964027 USD. Lump sum acquired 3.18739960 ETH. DCA's first allocation acquired 0.26561663 ETH and left the same 11,000.00 USD reserve. The fee rate and dollar-equivalent fee totals are unchanged.

After the 12 scheduled buys, DCA held 6.50361942 ETH. At 1,195.33087931 USD on 2022-12-31, its total portfolio was worth 7,773.98 USD, compared with 3,810.00 USD for lump sum. Both had zero cash left.

The paired advantage for DCA was 3,963.98 USD. It nevertheless lost 4,226.02 USD, or −35.22%, from the initial capital. Lump sum lost 8,190.00 USD, or −68.25%. These are ETH calculations, with no staking rewards added.

Watch the cash during the year

For the 2022 BTC example, the first month-end shows why the denominator matters. On 2022-01-31, DCA's crypto alone was worth 807.91 USD, alongside 11,000.00 USD of cash. Its full portfolio was 11,807.91 USD. Lump sum's portfolio was 9,694.92 USD on that same date.

Looking only at the crypto would describe a very different comparison. The reserve was still owned and could fund the remaining scheduled purchases. By the third month-end, DCA had 9,000.00 USD left; by the sixth, 6,000.00 USD; after the eleventh, 1,000.00 USD; and after the twelfth, zero.

The table separates crypto-only value from total portfolio value for both assets at five shared checkpoints. The files contain every daily valuation, not just these dates. Cash is ordinary USD in the model, not a stablecoin holding, a lending account or an assumed bank product.

Endpoint returns do not describe the whole risk path

We also calculate maximum drawdown on the cash-inclusive daily portfolio. It is the largest fall from a prior portfolio peak to a later daily closing value within the window. The initial budget is included as the first peak, so purchase fees are not hidden.

The 12-month table gives the mean, median and worst observed drawdown for each strategy and asset. Holding cash early can reduce market exposure, but DCA still experienced substantial losses after buying. A lower historical average drawdown is not a guarantee for every window or a future investment.

For the 2022 example, BTC's maximum drawdown was 41.21% for DCA and 66.90% for lump sum; ETH's was 41.53% and 74.09%. These differ from the final returns because a portfolio may rise, fall and partially recover before the endpoint. Intraday losses, custody failures and cash-provider risk are not reconstructed.

The same endpoints can conceal different price sequences

The next table is deliberately hypothetical, not historical BTC or ETH data. It uses the same 12,000.00 USD capital but four buys of 3,000.00 USD, with the baseline 0.10% fee. Three paths start at 100.00 USD and end at 200.00 USD, while the intermediate purchase prices differ.

Lump sum gets the same quantity and final value in all three equal-endpoint paths. DCA buys different quantities because it divides the allocations by different prices. A temporary fall followed by recovery can lead to more units; buying later at higher prices can lead to fewer.

This is a mathematical illustration of price-sequence dependence, not evidence that one of those paths will occur. The fourth, continuously falling path has a different final price and illustrates that a relative DCA advantage can coexist with a substantial loss.

What fast growth does to the uninvested reserve

In the rising toy path, DCA's later allocations buy less as the price increases. Lump sum already has its full asset exposure. The final values are 17,782.20 USD for DCA and 23,976.00 USD for lump sum, a DCA-minus-lump-sum difference of −6,193.80 USD.

The cash has not vanished; it was deliberately kept out of the asset while prices rose, then used for later buys. That creates an opportunity cost in this path. It does not prove that immediate exposure is always rewarded or that the next market will rise.

What a fall after the first purchase changes

In the falling toy path, later DCA buys acquire more units at lower prices. Its final value is 8,866.13 USD, compared with 5,994.00 USD for lump sum. Both are below 12,000.00 USD. DCA's final return is −26.12%; lump sum's is −50.05%.

Gradual buying changes when the budget is exposed. It does not put a floor under BTC or ETH, prevent further falls or ensure that the final average entry price is below the market price. Once invested, those units remain exposed to the asset.

Average purchase price and time in the market

DCA's average purchase price, weighted by the net asset units bought, is the amount spent on crypto, excluding fees, divided by net units acquired. With equal net allocations, this is a harmonic mean of the purchase prices, not their arithmetic average. Including fees gives a separate all-in acquisition cost per net unit.

For BTC in 2022 those two prices were 26,410.09264416 USD and 26,436.52917334 USD. A lower average purchase price explains more units in that example, but does not measure the entire capital's return. Cash and the valuation date still belong in the comparison.

Under that calendar schedule, an allocation-weighted dollar of DCA purchase capital had 197.5 days of asset exposure before final valuation, versus 364 days for lump sum. This is a timing measure, not a measure of risk-adjusted performance. The later buys had less time exposed to both rises and falls.

Annualized returns in the files are shown only for 12 and 24-month windows, using all initially available capital and actual elapsed days. They are mathematical normalizations, not forecasts. We do not apply a contribution-based money-weighted return as if the DCA reserve had arrived from outside later.

Regimes with transparent, pre-set definitions

The main regime labels describe the completed benchmark price change: strong growth is at least 50.00%; decline is at most −30.00%; all remaining windows are grouped as mixed or intermediate. These three bins are exclusive and cover every main-horizon start for each asset.

Two separate context flags use the start benchmark and preceding prices: after a large fall means the start price is at least 30.00% below the highest close in the previous 90 days; high volatility means the previous 90 daily log returns have annualized sample volatility of at least 80.00%, using a 365-day scaling factor.

The trailing flags can overlap each other and the forward regime bins, so their counts must not be added into one total. The forward labels use hindsight and are not entry signals. Thresholds and example dates were fixed before reading strategy outcomes, not tuned to produce a desired winner.

The regime table shows that results can differ across price environments. It cannot establish a usable prediction rule: choosing the growth or decline bin before buying would require knowing the future price path. Even a large observed advantage within a descriptive group is not a forecast.

Sensitivity: which assumptions change the comparison?

We repeat every 12-month start for both assets with six cost and cash scenarios. The no-fee case, baseline 0.10%, and higher 1.00% rate apply the same percentage rule to both strategies. These proportional changes scale acquired units, so they do not automatically penalize the method with more buys.

The fixed-charge variant adds 1.00 USD per purchase from the same allocation before the percentage fee is deducted from the acquired asset. Total fee equivalents become 23.99 USD for DCA and 13.00 USD for lump sum. More orders now create a genuine extra charge, and that can change final wealth through the price path.

The reserve-yield variant assumes 4.00% effective annual USD cash growth, fixed as an illustrative input on 2026-10-03. It is not a historical deposit-rate series or a universal cash return. Interest compounds on the declining reserve with actual elapsed days divided by 365.25, stays in cash and does not increase scheduled allocations.

The execution-cost variant makes every buy price 0.10% higher than the benchmark. That is a uniform adverse-price stress assumption, not reconstructed spread or slippage. The table changes one input at a time and leaves dates, asset prices and capital unchanged; it does not search for a rate that makes a preferred strategy win.

With the illustrative reserve yield, DCA's higher-final-value count changes from 33 to 34 for BTC and from 37 to 38 for ETH. It improves DCA relative to its zero-yield version, because this schedule holds cash; it does not turn the sensitivity rate into an observed investment opportunity.

A decision schedule has a psychological dimension

Some investors may find smaller planned decisions easier to follow than committing the whole amount once. Others may prefer immediate exposure when they have already decided how much capital to allocate. These are characteristics of decision-making, not extra returns that can be added to the model.

Changing or stopping a schedule during a fall would create a different strategy. So would putting each new monthly salary into the market as soon as it arrives. That second case has no pre-existing full cash reserve, and should not be confused with delaying the investment of money already available.

The mechanism table at the start helps separate timing, cash, operations and exposure. Neither method removes the need to choose a budget, an asset, custody arrangements and a tolerable loss. A routine can help an individual follow a decision; it cannot guarantee the outcome.

Limits that stay visible with the results

The research covers two surviving assets and one reference-price provider over a fixed historical period. It does not represent failed cryptocurrencies or every exchange. Start windows overlap, the date rule is monthly, and changing the purchase day, duration or valuation endpoint may change the distribution.

Daily closing references cannot recreate actual order fills, historical bid–ask spreads, market impact, liquidity constraints, outages or intraday losses. We apply fixed comparative fees across history rather than reconstructing account-specific fees. The archive may contain provider revisions and is not a real-time vintage dataset.

The cash base case has zero yield. The sensitivity yield is hypothetical, without taxes, cash-account fees or credit events. Values are nominal USD, without inflation or currency conversion. ETH staking is not included: adding it would compare another income mechanism as well as purchase timing. Tax outcomes depend on jurisdiction and transaction rules, so no universal after-tax result is presented.

The final values mark assets to a reference price; no final sale, sale fee, withdrawal or conversion to a bank balance occurs. The experiment also assumes fractional purchases without minimum-order or rounding constraints. The mathematical precision of the calculation should not be mistaken for the precision of a real account simulation.

How to reproduce the research

The download contains the preserved daily prices, source attribution, model rules, calculation script, every start's result, every DCA purchase, daily cash-inclusive paths, sensitivity results and file fingerprints. Reproduction uses the snapshot, so a later provider revision does not silently change the published figures.

Source prices were checked for ordered unique dates and positive finite values, then compared with a second retrieval. Independent arithmetic checks covered all 910 baseline comparisons, 9,720 purchases, 295,840 daily portfolio records and 1,356 sensitivity comparisons, including statistics and drawdowns.

Figures and table values come from those same checked results. Means and medians use unrounded observations; only presentation is rounded. The underlying Coin Metrics Community data retains its CC BY-NC 4.0 licence and attribution; our selection of date ranges and research calculations is identified separately.

Read the whole-capital result before choosing a story

DCA and lump sum are two ways to distribute the same capital's exposure over time. Buying gradually changes entry prices and the time each allocation spends in the asset. Buying once concentrates the decision at the first price. Neither description supplies a guaranteed winner.

In this historical sample, lump sum more often ended higher, while DCA ended higher in other windows and both methods had losing cases. The full distribution, fees, reserve and dates matter more than a single attractive entry or one headline average.

For any comparison, first check whether the full budget was available, whether uninvested cash is included, whether costs come from that budget, and whether both portfolios use the same valuation date. Only then does a DCA-versus-lump-sum result answer the same question for both methods.