Foundations
What Money Has To Be What Money Is For What Bitcoin Is The Bitcoin Synthesis Bitcoin Defined The Bitcoin Trilemma
The Arguments
The Bitcoin Migration The Half-Life Money Trees The Melting Ice Cube Is Bitcoin a Bubble? Bitcoin Spend and Replace
The Numbers
The Bitcoin Fixed Share BTC vs. Real Estate BTC vs. Rental Property Bitcoin & The Power Law Bitcoin vs. The Stock Market The Bitcoin Heatmap The Bitcoin Retirement Disciplined Rebalancing Borrowing Against Your Stack Living on Bitcoin Bitcoin-Backed Mortgages The Bitcoin Horizon The Gallery Calculators About
indicates pages with interactive tools

If you’re weighing bitcoin against a normal index-fund portfolio, the question that gates the decision is how bitcoin’s long-run trend compares against the S&P 500 and NASDAQ-100 over the horizons a typical investor actually holds. This page uses the Power Law as a structural reference for reading bitcoin’s position in real time, stress-tests historical cyclical-top entries against the equity comparators to show how strictly conservative the framework’s guidance is, and projects the trend forward over a typical investor’s 10-to-15 year decision window. Across every multi-year window the page tests, the answer is decisive.

Framework

Reading bitcoin through the Power Law

Why this isn’t 2013 bitcoin — and why today’s price may be the most useful signal on the chart.

Every cyclical top in bitcoin’s history was visible as a top in real time. Every cycle floor was visible as a floor. The pattern isn’t subtle when you plot bitcoin’s price against its long-run Power Law trend — tops register as measurable deviations above trend; floors register as measurable deviations below it. The chart below plots both across 16 years of price history, plus today’s position.

Bitcoin price vs. Power Law trend, with cyclical-top and floor markers
Today’s bitcoin price: · —× trend (Power Law trend = )

Historical BTC price (white) vs. Power Law trend (dashed amber), log-scale Y axis. Numbers next to each marker are the cycle’s trend-deviation multiple. Top markers (rust) register at ≥1.0× trend; floor markers (sage) at ≤1.0× trend. Price line uses monthly close samples through mid-April 2026 with the latest spot appended; the “you are here” marker shows the live bitcoin price, fetched on page load. Use the time-range toggle above to zoom into the most recent cycle.

Two things are immediately visible in the chart that qualitative narratives about bitcoin tend to miss.

First, tops are getting smaller. Bitcoin’s cyclical peaks have compressed dramatically: 12.1× over trend in 2013, 6.4× in 2017, 2.8× in 2021, and just 1.1× in both the March 2024 top and the October 2025 all-time high. (The 12.1× in 2013 reflects early bitcoin’s pre-institutional regime, when retail-driven overshoots were far more violent than anything since — and the compression from 12× to 1.1× is the maturation evidence.) The euphoric overshoots that defined the early asset have faded every cycle. This is the maturation thesis — institutional capital, regulated ETF flows, roughly 6.4% of supply held in ETPs, treasury allocations at 49+ public companies, 23 nation-state holders — rendered as a single visual fact: tops aren’t what they used to be.

Second, floors have stayed structurally stable. Across four different cycles spanning a 90× range of absolute prices, the cycle bottoms have all registered between 0.41× and 0.66× trend — a tight band. The downside reference hasn’t moved while the upside has compressed toward it. The within-cycle entry-price spread has gone from 22× (2013 top vs. 2015 floor) to 1.7× (2024 March top vs. 2024 August dip). Timing matters less now than it used to; the boundaries are tighter on both sides.

By the framework’s own logic, low-channel readings have historically been structurally favorable entry territory: bitcoin’s trend-relative discount tends to compress over multi-year horizons (mean reversion plus continued absolute trend growth). The October 2025 all-time high only managed 12% above trend, and bitcoin has spent more “distance” below trend than above it in this cycle. The relationship inverts when bitcoin trades above trend — at upper-channel positions the prudent read is the same framework running in the opposite direction.

The chart isn’t a forecast — the Power Law is a central-tendency expectation, not a prediction, and the asset can stay below or above trend for extended periods. The point is that you have a structural reference for reading entry quality in real time. The scenarios below stress-test that reference against entries the framework itself would flag as upper-channel: what would have happened if you’d actually bought at cyclical tops like these? The answer rhymes across every cycle — and it isn’t what the “what if I’d bought the top” objection assumes.

Looking back

What if you bought at the worst time?

The worst-case stress test — pick a cyclical top, then choose between a lump sum held to today or weekly DCA from that day forward.

Four of the cyclical tops marked on the §1 chart are reflected in the calculator below as preset entries — three obvious above-trend overshoots (2013 at 12.1× trend, 2017 at 6.4×, 2021 at 2.8×) plus the most recent local high (2025 ATH at 1.12×). The 2024 March top is omitted from the preset row: at 1.14× trend it’s barely above trend, normal cycle behavior rather than a stress test worth running in isolation. The calculator runs two scenarios per entry: a single lump sum held to today, or weekly DCA from that day forward. Compare against the same dollar amount or weekly cadence in the S&P 500 (total return, with dividends reinvested) and the NASDAQ-100 (total return). What’s being tested is the framework’s strict-conservatism claim: even at entries the Power Law would flag as upper-channel — entries you wouldn’t make if you were using the framework — the horizons that matter still produced wealth.

DCA mode smooths the worst-timing risk because most of the dollars get deployed at prices other than the peak. Lump-sum mode shows the rawest version of the stress test: a single buy on the worst day. The verdict text below each result calls out where the page’s argument depends on long-enough holding periods — particularly for the most recent 2025 ATH preset, where the hold has only had a handful of months to play out. The pattern stabilizes at horizons longer than ~3 years, and decisively at horizons longer than ~5; the older the entry, the more the pattern has had time to assert itself.

Lump sum at the cyclical top

Bought at:
Start date?The date the position begins. Use the preset buttons above to jump to a cyclical top, or drag the slider for any date from 2010 onwards. In lump-sum mode this is the day the single investment is made; in weekly DCA mode it’s the day the weekly buys start. Nov 30, 2013
Lump-sum amount?The hypothetical dollar amount invested as a single lump sum on the start date. The calculation tracks what that amount would have become in each asset class through today. $10,000
Wealth-over-time — lump sum invested at the chosen start date

Log-scale Y-axis. All three series start at the same dollar amount on the start date and track their respective asset’s value through today.

Bitcoin

Value today

S&P 500

Value today (total return)

NASDAQ-100

Value today (total return)

The 2025 ATH preset deserves a specific caveat in either mode. It’s the most recent cyclical high covered here and has had the least time to play out — bitcoin reached its all-time high of approximately $126K on October 6, 2025, and as of this writing in mid-2026 the price sits roughly 35% below that level. If you started from that scenario in lump-sum mode, your hold has been less than a year and you may currently be underwater on the comparison against the S&P 500. The page’s argument depends on long-enough holding periods. The 2017-top and 2021-top presets show what the same scenario tends to look like after five-plus years of patience.

A note on DCA versus lump-sum, since the page is being fair to the reader who’d ease in: Vanguard’s research on this question — across decades of equity-market history — finds that lump-sum investing beats dollar-cost averaging in roughly two-thirds of historical 12-month windows. The mechanism is simple: markets spend more time going up than down, so deploying capital later (on average) means buying at higher prices. DCA’s value is real, but it’s primarily a regret-minimization tool that prevents the worst single-day-entry outcome, not a return-maximization strategy. The page leads with the lump-sum-at-the-top scenarios precisely because they’re the most-feared outcome — if the historical record handles even those cases at the horizons that matter, the case for DCA-as-a-better-alternative gets weaker, not stronger.

Looking back · all entries

Across every entry, every horizon

The aggregate stress test — every monthly entry, every common horizon, in one grid.

The calculator above runs one scenario at a time. The grid below runs every scenario at once: every monthly start date from January 2010 through today, against every common holding horizon. Each cell is one window — one entry, one horizon — and the color shows whether bitcoin outperformed the chosen comparator over that window, and by how much.

Two patterns surface immediately. At short horizons (six months, one year) there are real losses to find — visible red pockets that line up with cyclical-top entries. At long horizons (seven years and up) every cell is amber: there is no historical window over which a 7+ year holder failed to outperform the index. The page's argument across the prose chapters above is the same argument the heatmap makes visually — the horizons that matter still produced wealth, even from the worst entries.

Bitcoin compared to:
Bitcoin mode:
View:
Holding period
Entry month →
<−50% −50% to −10% ±10% +10% to 2× 2× to 5× >5×
Color = bitcoin’s outperformance multiple over the comparator. Click any cell to load that start date in the calculator above. View toggle above: Period return reads each cell as the return over the cell’s specific window. Held to today reads each cell as the return from that entry date to today, for someone who held through.
Looking forward

How long does the bitcoin advantage last?

The forward projection — what the Power Law trend says about the next 10 to 30 years.

The retrospective evidence above answers the question for someone considering a position who would have started at any of the dates the page covers. The forward question for someone deciding right now is: over the horizon I’ll actually hold this, where is the trend headed?

The chart below plots two bitcoin trajectories against the long-run trend lines for the S&P 500 and the NASDAQ-100. The first is a trend-basis projection — it assumes today’s price sits at the Power Law trend value and projects forward at the trend’s growth rate; this is the conservative read. The second is a current-price projection — it anchors to today’s actual market price and projects forward at the same trend, which means the line starts above the trend-basis line when bitcoin is below trend (a discount) and below it when bitcoin is above trend (a premium, like a cycle top). The vertical gap between the two lines at year zero is the entry-quality signal: a positive gap means you’re entering at a discount and capture the mean-reversion on top of the trend; a negative gap means you’re paying a premium that trend says will fade. The Power Law itself is a central-tendency expectation, not a forecast — bitcoin spends roughly half its time above the trend and half below, and deviations within cycles can be very large in either direction.

Projection horizon?How many years forward from today to project. The Power Law trend continues to compound at its decreasing-CAGR rate; the comparator trends compound at their historical CAGRs. Marker dots indicate the projected value at the chosen horizon. 15 years
Investment today?A hypothetical amount invested today in each asset. Used to project the dollar value of that investment at the chosen horizon under each trend. $10,000
Projected wealth over the chosen horizon — trend lines only

Log-scale Y-axis. Two bitcoin lines: solid is the trend basis (assumes today is fair value), dashed is the current-price basis (captures the gap to trend). Both follow the canonical Power Law (P(d) = 1.6 × 10−17 × d5.77) forward. Comparator trends compound at their approximate historical nominal CAGRs (S&P 500 ~10.9%, NASDAQ-100 ~16.3%) — central-tendency expectations, not forecasts.

Bitcoin (trend basis)?The conservative projection. Assumes today’s bitcoin price sits at the Power Law trend value (whether or not it actually does) and projects forward at the trend’s growth rate. Use this as the central-case expectation if you don’t want to assume mean-reversion. At year zero this line equals the investment amount; at the chosen horizon it equals investment × trend growth over the period. conservative; trend forward from today
Bitcoin (current price)?Anchors to today’s actual market price and projects forward at the same Power Law growth rate. When bitcoin sits below trend (today’s case, ~35% below), this line starts above the trend-basis line — the gap is the additional gain you’d capture if today’s market price mean-reverts to trend over the horizon. When above trend at a cycle top, this line starts below the trend-basis line — the gap is the premium that trend says will fade. The two lines converge when the market is at trend. includes today’s discount/premium to trend
S&P 500 at 10.9% nominal CAGR
NASDAQ-100 at 16.3% nominal CAGR

For an investor with a typical decision horizon — 10 to 15 years — the Power Law trend keeps bitcoin meaningfully above all three comparators by a wide margin, with the gap measured in multiples rather than basis points. The convergence dates — where the Power Law trend eventually slope-matches each comparator’s trend line — sit decades or centuries in the future, with NASDAQ-100 the nearest at roughly 2066–2080 and the S&P 500 not until ~2139. Even at the 40-year horizon, bitcoin’s trendline expected returns remain substantially higher than any conventional stock-market comparator.

Takeaway

The long-horizon argument

Tying the historical evidence to the decision a reader is making today.

Volatility is a horizon-dependent concern. A 50% drawdown is terrifying at six-month horizons and noise at ten-year horizons. The historical record in §2 above is the empirical version of this claim: every worst-timed lump-sum entry the page tests at horizons of five years or longer produced more wealth than the S&P 500 over the same period. The horizon-dependence shows up sharply when the recent past is sliced at different windows. Through May 2026, at a one-year horizon — measuring from roughly the October 2025 cycle top — the S&P 500 has returned about +27% and bitcoin about −21%. At five years, bitcoin (+74%) trails the S&P 500 (+80%) modestly. At ten years, bitcoin’s roughly 17,000% total return dwarfs the S&P 500’s 264%. Same asset, same comparator, three completely different stories — the drama isn’t in the asset, it’s in the horizon you use to measure it.

Time in market applies differently at different CAGRs. A 10%-CAGR asset doubles in about seven years. A 25%-CAGR asset doubles in under three. Compounding advantage over long horizons is exponential, not linear — which is why a relatively small allocation to a high-trend asset, held across years, can materially shift a portfolio outcome even when most of the portfolio is in conventional assets. The relevant question isn’t whether bitcoin is volatile (it is) or risky (it is) or might fail (it might). It’s whether a small position, held long enough, with a clear understanding of the trend, compounds to something that materially changes the holder’s financial picture. The historical record says yes at every horizon the page tests.

Bitcoin vs. gold is its own argument. Gold has rallied strongly over recent years on central-bank buying and currency-debasement concerns — the same long-cycle store-of-value rotation bitcoiners argue eventually benefits bitcoin disproportionately, given gold’s ~$25T market cap versus bitcoin’s roughly an order of magnitude smaller. The mechanics, the relative cycles, the ETP-cost asymmetry (GLDM vs. GLD), and the structural overlap with bitcoin’s thesis all deserve a dedicated treatment rather than a sidebar here; see the forthcoming Bitcoin vs. Gold page. This page’s comparison set is bitcoin vs. the equity indexes a typical retail or institutional investor would otherwise hold.

Bitcoin’s volatility itself is changing structurally. A pattern emerged in 2025 that didn’t appear in earlier cycles: bitcoin posted a fresh all-time high (~$126K in October) while realized volatility printed decade-lows in the same window — new ATH and new ATL volatility, simultaneously. The MVRV ratio (market value to realized cost basis) has held steady around 2.0× through the recent top, against 4–6× peaks at the 2017 and 2021 highs. The institutional infrastructure has thickened: roughly 6.4% of supply now sits in spot bitcoin ETPs; 23 nation-states are net accumulators; 49+ public companies hold corporate treasury positions of more than 1,000 BTC each. None of this guarantees the trend continues; all of it makes a sudden mean-reversion to earlier-cycle volatility behavior less likely. The asset that the ten-year backtests on this page are measuring is empirically migrating — slowly but visibly — from speculative-crypto behavior toward something closer to a high-vol equity allocation with a structural tailwind.

As with the rest of this site, the right reading isn’t “this is the answer.” The right reading is: here’s the historical record and the trend the model expects from here, presented honestly — including the cases where the picture is less favorable. The decision about whether to take a position, how large, and over what horizon is yours. The page has done its job by giving you enough structural detail to make that decision with eyes open.

Math & methodology — click to expand the data sources and formulas behind the calculators

Bitcoin price data. Daily-close BTC/USD prices since the bitcoin genesis block (January 3, 2009), as embedded in the site-wide PL_DATA array. For the retrospective calculators on this page, the BTC price on each preset top date is interpolated from the daily data.

S&P 500 total return. Monthly closes built from documented annual total-return figures (price return plus dividends reinvested) sourced from S&P Dow Jones Indices, Damodaran (NYU Stern), and Slickcharts. The annual returns are documented to within ~10 basis points across sources. Monthly closes between year-ends are linearly interpolated. This is an approximation for prototype purposes — specifically, it smooths over intra-year volatility. A NotebookLM-verified daily series will refine the calculations in a later iteration.

NASDAQ-100 total return (^XNDX). Same methodology as the S&P 500, using documented annual total-return figures for the NASDAQ-100 Index. The NASDAQ-100 excludes financials and concentrates roughly 52–55% in information technology; long-run nominal CAGR is approximately 16.3% over the 18-year window 2007–2026 (with a recent 10-year CAGR closer to 18.8%). The page uses NASDAQ-100 rather than the broader Composite because the institutional-investor literature treats ^XNDX as the canonical tech-tilted comparator; the Composite’s long-run CAGR sits a few percentage points lower.

Gold. Not included as a comparator on this page in its current form. Gold operates on materially different drivers (central-bank demand, currency debasement, store-of-value rotation, ETF cost structure differences between GLDM and GLD, the 28% collectibles capital-gains tax rate on physical-gold ETPs in U.S. taxable accounts) and warrants a dedicated comparison rather than a sidebar treatment. See the forthcoming Bitcoin vs. Gold page for the dedicated treatment.

Power Law trend. The site-wide canonical Power Law trend used by every calculator on this site, P(d) = 1.6 × 10−17 × d5.77, where d is days since the bitcoin genesis block (January 3, 2009). The model is canonically associated with Matthew Mežinskis (Porkopolis Economics, 2018) and Giovanni Santostasi (2018); R2 exceeds 0.95 across the full 2010–2026 fit window. The same coefficients power the projections on the Power Law page, the Bitcoin Retirement page, and the Bitcoin-Backed Mortgages page. Critics including Adrian Morris (overfitting) and Tim Stolte/Amdax (log-time-scaling cointegration concerns) have published methodological critiques; defenders (Burger & Santostasi; Fulgur Ventures) have published rebuttals showing the residuals are stationary and the out-of-sample fit has improved over six years of post-publication validation. Santostasi himself states the theory is falsifiable: sustained deviation from the trend for an extended period would invalidate it.

Comparator forward trends. For the projection chart, the comparator trends compound at their approximate historical nominal CAGRs: S&P 500 at 10.9% (1992–2026 total return per Damodaran/SP DJI) and NASDAQ-100 at 16.3% (2007–2026 long-run; recent-10y closer to 18.8%). These are central-tendency expectations; the trend the bitcoin Power Law projects exceeds both comparators’ expected CAGR for several decades before slope-matching occurs. Approximate trend-line convergence dates — the year by which the comparator’s constant-CAGR trajectory catches the Power Law trend, starting from today — are around 2066–2080 for NASDAQ-100 and 2139 for the S&P 500. The practical implication isn’t the year — it’s that the bitcoin advantage persists for the entire 10-to-30-year horizon any current investor would meaningfully care about.

What the calculators don’t model. Tax treatment (pre-tax comparison only). Transaction costs and platform fees. Currency: USD throughout. Capital-gains realization on rebalancing. Survivorship bias — bitcoin has survived to be measured; many crypto peers (BCH, BSV, XRP, ETC and a long tail of altcoins) have not. Empirical research suggests omitting failed-asset returns inflates measured CAGRs by approximately 0.9–2.1% per year; the bitcoin numbers on this page benefit from that bias by virtue of being bitcoin-specific, but readers comparing crypto-asset-class performance to equities should adjust the headline returns downward by that range. The lump-sum and DCA calculations assume the position was held without sale or rebalancing through to today.

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