When to Stack, When to Spread
Optimal Bitcoin Accumulation Strategy as a Function of Power Law Residuals
Figure 1: Lump sum win rate by trend multiple (top) with historical distribution of where Bitcoin actually trades (bottom). The crossover at 1.25× divides the lump sum zone from the DCA zone.
The Decision Rule
The Question
Lump sum or DCA? It is the most common question in Bitcoin investing. The standard answer—"DCA is always safer"—is wrong. The correct answer depends on a single number: the power law trend multiple at the time of purchase.
We tested every entry date from July 2010 to March 2026 (5,713 days). For each, we simulated both a lump sum investment and a 12-month DCA (12 equal monthly purchases). We measured which strategy produced higher returns at 1-year, 2-year, and 4-year horizons. Then we bucketed the results by the trend multiple at entry.
Results
| Entry Multiple | LS Win Rate (1yr) | LS Win Rate (4yr) | Days in Zone |
|---|---|---|---|
| < 0.3× | 100.0% | 100.0% | 2.6% |
| 0.3 – 0.5× | 100.0% | 100.0% | 12.7% |
| 0.5 – 0.75× | 97.6% | 99.7% | 28.8% |
| 0.75 – 1.0× | 89.4% | 90.1% | 14.0% |
| 1.0 – 1.3× | 58.5% | 51.0% | 12.4% |
| 1.3 – 1.6× | 40.1% | 45.0% | 7.6% |
| 1.6 – 2.0× | 50.0% | 50.7% | 5.3% |
| 2.0 – 2.7× | 36.5% | 36.5% | 6.8% |
| 2.7 – 4.0× | 6.8% | 6.8% | 5.4% |
| > 4.0× | 2.1% | 2.1% | 4.2% |
The highlighted row contains the crossover zone. Green = lump sum dominates. Purple/red = DCA dominates. "Days in Zone" shows how often Bitcoin historically trades at each valuation level.
Figure 2: Median returns at each valuation bucket. The magnitude difference at the extremes is enormous: at low valuations, lump sum returns exceed DCA by 200%+.
Robustness
Three robustness tests confirm the result is not an artifact of data mining.
Out-of-sample validation. We fit the power law using only 2010–2018 data, then tested the strategy on 2019–2026. The regime structure holds: lump sum dominates below trend, DCA dominates above it. The crossover shifts from 1.25× to 1.01× due to the steeper training-set exponent, but the qualitative conclusion is identical.
Bootstrap confidence interval. Resampling 5,000 times with replacement, the crossover was found in 100% of bootstrap samples. The 95% CI is [1.20×, 1.32×], a width of only 0.12×. This is a stable structural feature, not noise.
DCA window sensitivity. The crossover shifts monotonically with DCA duration: 0.95× for 3-month DCA, 1.03× for 6-month, 1.25× for 12-month, and 1.57× for 24-month. Shorter DCA windows are nearly equivalent to lump sum; longer windows provide more smoothing but require lower entry valuations to justify.
Figure 3: Left: Win rate curves by halving cycle showing the narrowing corridor. Right: Distribution of trend multiples per cycle, with Cycle 5 compressed almost entirely below 1.0×.
The Volatility Compression Effect
The crossover zone is shrinking. In earlier cycles, Bitcoin regularly traded at 3–8× trend, creating many entry points where DCA was strongly preferred. By Cycle 4, the distribution peaks below 1.0× and rarely exceeds 2.0×. In Cycle 5 so far, over 95% of days fall in the unambiguous lump sum zone.
This is consistent with the Observatory's volatility decay research: the price corridor compresses approximately 20% per halving cycle. As this continues, the extreme mispricings that make DCA most valuable will become rarer. The future of Bitcoin accumulation may not be "stack or spread" at all. It may simply be: stack.