  We derive an exact lower bound to a universal measure of frustration in
degenerate ground states of quantum many-body systems. The bound results in the
sum of two contributions: entanglement and classical correlations arising from
local measurements. We show that average frustration properties are completely
determined by the behavior of the maximally mixed ground state. We identify
sufficient conditions for a quantum spin system to saturate the bound, and for
models with twofold degeneracy we prove that average and local frustration
coincide.
