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Denote by $L_n$ the length of the perimeter of the convex hull of $n$ stepsof a planar random walk whose increments have finite second moment and non-zeromean. Snyder and Steele showed that $n^{-1} L_n$ converges almost surely to adeterministic limit, and proved an upper bound on the variance $Var [ L_n] =O(n)$. We show that $n^{-1} Var [L_n]$ converges and give a simple expressionfor the limit, which is non-zero for walks outside a certain degenerate class.This answers a question of Snyder and Steele. Furthermore, we prove a centrallimit theorem for $L_n$ in the non-degenerate case.

Convex hulls of planar random walks with drift