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The Power Law channel is the structural model that anchors most of the quantitative arguments on this site. The solid line is bitcoin’s trend price under proportional (not exponential) growth; the dashed lines bound a floor at 0.42× trend and an upper band at 3× trend — a range price has rarely strayed beyond across fifteen years and nine orders of magnitude.

The ±2y view zooms to decision-relevant time. Where the price is right now relative to the channel is the question most people are actually asking when they look at this chart — the all-time log-log view is what proves the model; this is what makes it actionable.

The Power Law implies a specific annualized return from each starting year. Each bar is the model's projected CAGR through 2035 for a bitcoin purchase made in that year; the dashed line is the S&P 500's historical ~10% annual average. Even at the conservative end — buying in 2030 — the model's implied CAGR through 2035 is roughly three times the equity benchmark.

On convergence: Bitcoin's implied CAGR declines as the model decelerates, but at every starting year on this chart it remains more than 2× the S&P 500's 10% benchmark. Even projecting out to the year 2150, bitcoin's implied annualized return — though steadily decreasing — still sits above 10%. The chart's window shows the strongest period of relative outperformance; the gap, while shrinking, persists for over a century beyond it.

In 2013, you needed 367 bitcoin to buy the median US house. By 2025, you needed roughly 5. That's a 98.6% decline in the bitcoin-denominated cost of housing across twelve years. Yes, the line is volatile — bitcoin is volatile — but look at the direction. No amount of fiat appreciation in home values can disguise what is happening on this chart.

The house is demonetizing — shedding its store-of-value premium — as bitcoin absorbs the monetary energy that was artificially trapped in real estate. The dashed line is where the historical trend points to next, not a price prediction.

Cherry-picking 2013 as a starting year for bitcoin's outperformance is the standard skeptic's objection. So pick any other year. From every starting year since 2014 — through every bear market, every drawdown, every 'cycle is over' moment — $1 invested in bitcoin outperformed $1 invested in housing by orders of magnitude. The toggle lets you choose your own starting point and see for yourself.

Demographia tracks median home price as a multiple of median household income, every year, across major English-speaking markets. The dashed green line is the 3.0× threshold they label ‘affordable.’ Hong Kong has sat above 11× for fifteen years. Vancouver, Sydney, and Greater London cluster near or above 10×. The United States is closest to the threshold — and even it is comfortably above, with a clearly upward trajectory through 2021.

What's remarkable about the chart isn't any one city's number — it's that every market shown has been judged unaffordable for the entire data window. The denominator is income, and incomes have not kept pace with housing globally for two decades.

At today's Power Law trend price, you'd need roughly 20 BTC to fund a $100K/year retirement under the 4% rule (a $2.5M nest egg). Push the retirement year out ten years, and the requirement falls to ~1.4 BTC. Twenty years, ~0.23 BTC. Thirty years, ~0.06 BTC.

Each anchor is its own scenario — this isn't a single stack drawing down. The chart shows that as bitcoin's trend price compounds, the BTC count required to support the same lifestyle falls sharply. The math privileges patience.

Returns from 2013 are spectacular and unrepeatable. To dodge that cherry-pick entirely, here's the harder comparison: the annualized return over every rolling four-year window since 2017. Each point answers the same question — what would a 4-year holder's annualized return have been ending each year — for bitcoin, the S&P 500 (total return), and the NASDAQ-100 (total return).

Two things to notice. First, bitcoin's 4-year returns have declined — from a peak of 128% annualized in the 2015–2019 window down to 17–54% in the most recent windows. That deceleration is exactly what the Power Law model in Chart 2 projects. Second, even after that deceleration, bitcoin's 4-year CAGR exceeded both equity comparators in every window shown — by margins ranging from 1.5× to 13×. The narrowest test is the 2021–2025 window (cycle-top to cycle-low): even there, bitcoin's 16.7% annualized beat the S&P 500's 11.1% and the NASDAQ-100's 13.3%.

Every cell is a single bitcoin investment: enter on the column's month, hold for the row's horizon (1, 2, 3, 5, 7, or 10 years), compare the outcome against the same dollars invested in the S&P 500. Amber means bitcoin outperformed; red means it underperformed; the brighter the cell, the wider the margin.

At short horizons there are visible red pockets — pre-bear-market entries that hadn't fully recovered yet within the cell's window. At long horizons, the pattern is almost entirely amber: there is no historical 5-year window in which a bitcoin holder failed to outperform the S&P 500. Toggle to Held to today to see how most of those red cells turn amber once the holder simply kept holding past the cell's nominal exit — the underperformance was timing-of-exit, not timing-of-entry.

The official CPI rate (~3.5%) understates the actual debasement of fiat. A more honest proxy is M2 monetary-base growth — how fast new dollars are created — which has averaged closer to 6.5% per year across recent decades. At that rate, $100 held in cash today is worth $50 in purchasing power in roughly eleven years, and a quarter of its value in twenty-two.

The chart is a clean exponential decay because the mechanism is. Cash is not a stable store of value; it is a slowly evaporating one. Every argument for holding bitcoin against equities applies more forcefully against cash — equities at least share in monetary expansion; cash is what's being expanded.

At a one-year holding horizon, bitcoin's worst rolling return was deeply negative — the 'too volatile' objection in one bar. But look what happens as the horizon lengthens. Each bar collapses inward: the worst-case return rises, the best-case return falls, and the distribution narrows around a positive median. By a three-year horizon, bitcoin's worst historical rolling CAGR is already positive. By ten years, the bitcoin range collapses into a tight band entirely above the S&P 500's.

Volatility is not risk. Volatility is the width of the short-term distribution. Risk is the probability of permanent loss of purchasing power. At horizons of five years or more, bitcoin's historical record shows the former but not the latter — the wide one-year bars compress into something the S&P 500's never does: a wide median, narrow range, no negative tail. That's the entire argument for time as bitcoin's strongest ally.

On the data: these stats are deliberately computed from January 2015 onwards, setting aside the parabolic 2013 run and the 2014 drawdown. Those years generated 1-year bitcoin returns above 4000% and below -75% that, while historically real, aren't representative of any plausible forward outcome. The 11 years that remain still cover three complete bitcoin cycles, and the same window is applied to the S&P 500 for an apples-to-apples comparison — which means the chart's SP500 numbers reflect the unusually strong 2015–2026 stretch, not the long-run ~10% historical mean.