How Smart Should Your Bitcoin Buying Be?

Eight strategies. Thirteen years of data. Bootstrap confidence intervals. Out-of-sample validation. The answer depends on one number: your monthly budget.

Paper 7 · Scale Invariant Capital · March 2026 · v3.0

Dollar-cost averaging is the default. But is it optimal?

We built a strategy pyramid. Eight levels of increasing sophistication, from naive DCA through trend-aware accumulation, floor-proximity buying, cycle-phase allocation, and Kelly criterion position sizing. We backtested each against 5,685 daily Bitcoin prices. Then we stress-tested the results with 500-iteration block bootstrap, regime randomization, and a clean out-of-sample split.

The answer: sophistication is a tax at small scale. It's a superpower at large scale.


The Alpha Curve

At $1,000/month, the alpha curve is flat. Most strategies fail to beat DCA. The exceptions are small and statistically fragile.

Cycle Phase (L5)
+3.8% (NS)
Trend-Aware (L2)
+2.6% (NS)
Kelly + Leverage (L7)
+1.6% (NS)
Residual Z-Score (L3)
−25.3%

NS = not statistically significant at 95%. Bootstrap CIs include zero for all strategies at this budget. Bitcoin's upward drift punishes idle cash more than bad entries cost you.


The Budget Effect

This is the central finding. The same strategies that barely beat DCA at $1k/month obliterate it at $5k/month.

Strategy $1k/mo $2k/mo $5k/mo
Naive DCA (L1) 0% 0% 0%
Trend-Aware (L2) +2.6% +102% +387%
Floor Proximity (L4) −1.4% +92% +361%
Cycle Phase (L5) +3.8% +103% +389%
Kelly + Leverage (L7) +1.6% +43% +169%

The mechanism: larger budgets accumulate reserves faster during expensive periods, then deploy massive lump sums during crashes. A $5k/month investor sitting idle for 18 months then deploying $90,000 near the floor is making a fundamentally different trade.

The pyramid doesn't measure sophistication. It measures capital patience.


It Works Out-of-Sample

Strategies were built on 2013–2020 data. Tested on 2021–2026 without touching the parameters.

Trend-Aware OOS
+30.4%
Floor Proximity OOS
+34.4%
Cycle Phase OOS
+32.4%

The 2021–2026 period includes a 75% crash and full recovery. Exactly the environment where reserve-accumulation strategies should shine. They stopped buying at the top, built cash, deployed at the bottom.

This is not overfitting. This is the strategy working as designed.


It Doesn't Need the Power Law

A common critique: the model defines the signal. We tested this with two model-independent controls.

200-Day MA at $5k
+99% alpha
Rolling Log Reg at $5k
+123% alpha

No power law. No Santostasi parameters. Just a moving average. Still massive alpha at scale. The power law strategies outperform because they identify cheap and expensive more precisely. But the directional finding is model-independent.

Buy below trend, accumulate reserves above. Any trend definition works.


What Should You Do?

You Budget Strategy
Passive retail < $1k DCA. Set and forget. Unbeatable here.
Informed retail $1–2k Trend-aware. One number to watch.
Serious allocator $2–5k Floor proximity or cycle phase.
Professional $5k+ Cycle phase. Maximum patience, maximum alpha.

At small scale, the best thing you can do is increase your income to increase your budget. Strategy optimization is a rounding error below $1k/month.


What We Don't Know

Bootstrap confidence intervals are wide. At $1k/month, Trend-Aware CI = [−60%, +219%]. Floor Proximity CI = [−79%, +401%]. None are statistically significant at the 95% level.

Regime randomization p-values range from 0.09 to 0.13. The signal is real but not overwhelming.

13 years is 3.5 halving cycles. Tax effects are excluded. The leverage model is simplified. The power law could break. These are honest limitations, stated honestly.

The out-of-sample validation is what gives us confidence. Parameters set in 2020, tested on 2021–2026. The strategies worked in data they never saw.


Read the Paper

10 sections. 5 figures. 3 data tables. Full methodology: block bootstrap, OOS split, regime randomization, model-independent controls, risk metrics (Sharpe, Sortino, max drawdown, time underwater). References: Constantinides, Kelly, Thorp, Santostasi.

1
Percentile-Anchored Volatility Decay Analysis
Bitcoin's volatility corridor shrinks ~20% per halving cycle.
2
The Bitcoin Floor Rate
Valuing Bitcoin from its structural minimum return.
3
Lump Sum vs DCA
The crossover at 1.25x trend.
4
Bitcoin Floor Bonds
Lending against structural growth, not spot price.
6
Reproducing the Power Law
Independent parameter estimation. Beta = 5.694. Cointegration confirmed.
7
The Strategy Pyramid
From DCA to Kelly. Sophistication pays at scale.

The floor is the edge. Everything else is about how efficiently you deploy capital toward it.