Inside a fixed Bitcoin forecast: a worked example

The question this calculation answers

BTC Horizon’s public CMC edition describes the price at a declared future timestamp. It does not estimate whether Bitcoin touches a target first. This note reproduces the fixed 24-hour model rather than reporting a new performance study. All prices in the example are hypothetical.

The public methodology declares a log-return mean μ = 0.0005 and standard deviation σ = 0.026 for 24 hours. With starting price S, the model assumes log(P / S) follows a normal distribution with those parameters. Both parameters are fixed: a large market move does not automatically change tomorrow’s uncertainty estimate.

A reproducible example at a hypothetical $80,000

The median is S × exp(μ). At S = $80,000 this gives approximately $80,040. The mean price is a different quantity: S × exp(μ + σ² / 2), approximately $80,067. Neither number is a measured expected profit, and transaction costs are outside this calculation.

A central 80% interval uses normal quantiles ±1.28155157. Its endpoints are S × exp(μ − 1.28155157 × σ) and S × exp(μ + 1.28155157 × σ): approximately $77,417 to $82,752. The 80% label belongs to the assumed distribution; only later outcomes can show whether that coverage holds in practice.

The probability of finishing above the starting price is Φ(μ / σ), where Φ is the standard normal cumulative distribution function. Here μ / σ is approximately 0.01923, giving about 50.77%. The small positive tilt is built into the parameters. It is not evidence that the model has learned an advantage from current conditions.

What would change the conclusion?

If observed volatility rises but σ stays fixed, the advertised interval may become too narrow. If comparable resolved forecasts repeatedly underperform a constant 50% direction forecast, the model’s positive tilt has not earned its complexity. Inspect sample size, Brier score and interval coverage together rather than choosing whichever metric looks best.

The 7-day and 30-day parameters are separately declared in the methodology. They should not be inferred by multiplying this 24-hour probability. A new model or a change of input source requires its own identifiable edition and evidence.

How to audit a real edition

Start with the public forecast record and note the model edition, CMC reference price, publication timestamp, target timestamp and outcome status. Read the methodology for input freshness and resolution tolerance. A provider display average on the dashboard is not the CMC reference used for the public model.

This worked example checks arithmetic and interpretation only. It does not establish calibration, predictive skill or suitability for a trading decision.