  In this note we show a close relation between the following objects:
Classical Yang -- Baxter equation (CYBE), conformal algebras (also known as
vertex Lie algebras), and averaging operators on Lie algebras. It turns out
that the singular part of a solution of CYBE (in the operator form) on a Lie
algebra $\mathfrak g$ determines an averaging operator on the corresponding
current conformal algebra $\mathrm{Cur} \mathfrak g$. For a finite-dimensional
semisimple Lie algebra $\mathfrak g$, we describe all homogeneous averaging
operators on $\mathrm{Cur}\mathfrak g$. It turns out that all these operators
actually define solutions of CYBE with a pole at the origin.
