## Term Glossary

### Down Number Ratio

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

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

###### Function Reference
portfolio_downNumberRatio, position_downNumberRatio