Drawdown (economics, $D_t={\max }_{s\le t}{y}_s-y_t$)

The absolute decline from a previous running peak of a cumulative-value process. For positive peak values a relative decline can also be defined, but that is a different unit convention. Flat intervals do not end a drawdown, and a brief recovery that stays below the previous peak does not necessarily end it either. A maximum consecutive strictly negative run is therefore not generally a maximum drawdown.

For increments $X_t=a_{t-2}{a}_{t-1}+a_t$ with freely admissible starting sign history, the worst absolute financial drawdown over $N$ steps is the displayed value. A four-state recursion $d_{n+1}(b,c)={\min }_{a=\pm 1}[d_n(a,b)+ab+c]$ computes the minimum cumulative increment, with zero initial costs. The minimum is attained by nonpositive increments: $(-2,0{)}^k,-2$ for odd $N=2k+1$, and $(-2,0{)}^{k-1},-2,-2$ for even $N=2k$. The horizon-free bound is infinite. At most two strictly negative increments can be consecutive, but confusing that losing-run bound with drawdown would be incorrect.