Distibuted Computing in Julia Slower than Serial

I have a julia function that seems very amenable to optimization. Each iteration only manipulates the stuff in its particular index. Yet this function, when implemented with distributed as below, is slower than its serial equivalent. I have tried an equivalent implementation with Distributed instead of Shared arrays, and it is even slower. There must be something simple I am missing here, but I cannot figure it out.

function f(A1, A2, I1, I2, n1, n2, n3)
    B1 = convert(SharedArray, zeros(n1, n2))
    B2 = convert(SharedArray, zeros(n2, n3))
    @sync @distributed for d in 1:n2
        for i in 1:n3
            B1[d, i] = A1[I1[d], I2[d][i]] / (A1[I1[d], I2[d][i]] + A2[I1[d], I2[d][i]]))
            B2[:, d] .+= log.(A2[:, I2[d]);
        end
        B2[:, d] .-= logsumexp(B2[:, d])
    end
    B1 = convert(Array, B1)
    B2 = convert(Array, B2)
    
    B2 = exp.(B2)
    return B1, B2
end