The Wikipedia article on the Hansen-Jagannathan bound is short, giving only the following:
Hansen–Jagannathan bound is a theorem in financial economics that says that the ratio of the standard deviation of a stochastic discount factor to its mean exceeds the Sharpe Ratio attained by any portfolio. This result is an application of the Cauchy–Schwarz inequality.
An important detail that is missing is a discussion of the theorem's significance. The Hansen-Jagannathan (H-J) bound gives us a type of mean-variance frontier. But what is importance/significance (in theoretical and empirical work) of the H-J bound over the classic mean-variance efficient frontier? (The two are different but related. What's the main insight from the H-J bound?)