  Let $(\mathcal{F}_n)_{n\ge 0}$ be the standard dyadic filtration on $[0,1]$.
Let $\mathbb{E}_{\mathcal{F}_n}$ be the conditional expectation from $
L_1=L_1[0,1]$ onto $\mathcal{F} _n$, $n\ge 0$, and let $\mathbb{E}_{\mathcal{F}
_{-1}} =0$. We present the sharp estimate for the distribution function of the
martingale transform $T$ defined by \begin{align*} Tf=\sum_{m=0}^\infty \left(
\mathbb{E}_{\mathcal{F}_{2m}} f-\mathbb{E}_{\mathcal{F}_{2m-1}}f \right), ~f\in
L_1, \end{align*} in terms of the classical Calder\'{o}n operator. As an
application, for a given symmetric function space $E$ on $[0,1]$, we identify
the symmetric space $\mathcal{S}_E$, the optimal Banach symmetric range of
martingale transforms/Haar basis projections acting on $E$.
