Term Glossary

Down Percentage Ratio

Down Percentage Ratio measures the number of periods in which the asset's compound return was higher then benchmark (e.g. market index) return when benchmark was down, divided by the number of periods in which the benchmark was down. The higher is this ratio, the better is relative performance of an asset. $$DPR = \frac{\sum_{i=1}^{T}\mathbf{1}_{r_i>r_{M,i},r_{M,i}<0}}{\sum_{i=1}^{T}\mathbf{1}_{r_{M,i}<0}}$$ $$\mathbf{1}_A = \begin{cases} 1 &\text{if } x \in A, \\0 &\text{if } x \notin A.\end{cases}$$

$r_i$
asset return for period i
$r_{M,i}$
market index (benchmark) return for period i

Function Reference
portfolio_downPercentageRatio, position_downPercentageRatio