The Risk Metric & Quantile Regression Fan

Burrito's flagship number is a 0–1 risk score: how expensive is price right now, relative to the asset's entire trend history? This page explains exactly how it's computed — no black box.

The idea

Bitcoin's long-run price is well described in log-log space: log price versus log time since inception. But a single best-fit line (least squares) gets dragged around by bubbles and tells you nothing about the distribution of price around trend. So instead of one line, we fit nine.

The fan

For quantiles τ ∈ {0.01, 0.05, 0.15, 0.30, 0.50, 0.70, 0.85, 0.95, 0.99} we fit a separate quadratic quantile regression:

ln(price) = a + b·z + c·z²      where z = standardized ln(days since inception)

Each fit minimizes pinball loss (the quantile-regression objective) via gradient descent (Adam, ~4000 steps), initialized from the ordinary least-squares fit shifted to the residual quantile. Because each quantile is fitted independently, the fan can be asymmetric — wider above the median than below, like Bitcoin's actual return distribution. Finally the curves are rearranged (sorted at every date) so quantiles can never cross.

• The τ = 0.50 curve is fair value — the median trend.
• The τ = 0.01 curve hugs the historical floor: every major bottom touched it.
• The τ = 0.99 curve bounds mania.

From fan to risk score

Risk = the interpolated quantile position of today's price inside the fan. If price sits on the median curve, risk = 0.50; on the 95th-percentile curve, 0.95; below the 1st percentile, 0.01. Linear interpolation in log space between adjacent quantile curves.

Calibration receipts

Fitted on full history and read back at known reference points:

No parameters were tuned to these points — they fall out of the fit.

Per-asset fans

Every tracked asset gets its own fan, fitted to its own history (time measured from its first trading day). Assets with under two years of history are flagged — a fan fitted to one partial cycle is a sketch, not a model. See the risk chart family and the Risk Dashboard.

Honest limitations

• Refit daily on full history — all readings shift slightly as data arrives; the model has hindsight the past didn't have. Extremes are meaningful; mid-range is noise.
• Trend extrapolation — the fan assumes the log-log growth regime persists. A true regime break (hyperbitcoinization or obsolescence) invalidates it in either direction.
• It's a valuation dial, not a timer — price can ride the 0.9 band for months.
• Related further reading: data-pipeline for where the price series comes from.