We compute four-point functions of the stress tensor and conserved currents in ${\mathrm{AdS}}_4/{\mathrm{CFT}}_3$ using bulk perturbation theory. We work at tree-level in the bulk theory, which we take to be either pure gravity or Yang-Mills theory in AdS. We bypass the tedious evaluation of Witten diagrams using recently developed recursion relations for these correlators. In this approach, the four-point function is obtained as the sum of residues of a rational function at easily identifiable poles. We write down an explicit formula for the four-point correlator with arbitrary external helicities and momenta. We verify that, precisely as conjectured in a companion paper, the Maximally Helicity Violating (MHV) amplitude of gravitons or gluons appears as the coefficient of a specified singularity in the MHV stress-tensor or current correlator. We comment on the remarkably simple analytic structure of our answers in momentum space.

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