The Sharpe ratio uses a standard definition with the risk-free rate fixed at 0, applied to the close-to-close return series of portfolio equity sampled on the backtest’s native timeframe.

• Source series: initial capital, then portfolio equity at each close of the main timeframe
• Elementary return: $r_i=\frac{E_i}{E_{i-1}}-1$
• Risk-free rate: 0
• Mean return: $\mu =\frac{\sum r_i}{N}$
• Standard deviation: $\sigma =\sqrt{\frac{\sum {(r_i-\mu )}^2}{N-1}}$
• Annualization: $A=\sqrt{\frac{\text{Year\_ms}}{\Delta }}$, using a 24/7 crypto year of 365 days

The Sortino ratio uses a standard definition with a downside target fixed at 0, applied to the same close-to-close return series of portfolio equity, again on the backtest’s native timeframe.

• Source series: initial capital, then portfolio equity at each close of the main timeframe
• Elementary return: $r_i=\frac{E_i}{E_{i-1}}-1$
• Downside target: 0
• Downside component: $d_i=\text{min}(0,r_i)$
• Downside deviation: ${\sigma }_{\text{down}}=\sqrt{\frac{\sum d_i^2}{N}}$
• Annualization: $A=\sqrt{\frac{\text{Year\_ms}}{\Delta }}$, using a 24/7 crypto year of 365 days

For a 4W timeframe, the nominal duration used is 28 fixed days, not a calendar month.

When the calculation is undefined, the returned value is NaN, notably when there are fewer than two valid returns, when previous equity is less than or equal to 0, when an observation is not finite, or when the relevant volatility is zero.

• Formula: $\text{Calmar}=\frac{\text{CAGR}}{\text{MDD}}$
• CAGR: $\text{CAGR}={\left(\frac{\text{Final capital}}{\text{Initial capital}}\right)}^{\frac{\text{Year\_ms}}{\Delta }}-1$, using a 24/7 crypto year of 365 days and the effective backtest duration

This design keeps Calmar aligned with the finalized backtest window used by the engine and avoids rebuilding a second drawdown series from stored equity samples.

When the calculation is undefined, the returned value is NaN. This happens notably when initial capital is less than or equal to 0, final capital is less than or equal to 0, elapsed duration is less than or equal to 0, maximum drawdown percent is less than or equal to 0, or any intermediate value is not finite.