We study a new class of unconditional and conditional mean‐variance spanning tests that exploits the duality between Hansen‐Jagannathan bounds (1991) and mean‐standard deviation frontiers. The tests are shown to be equivalent to standard spanning tests in population, but we document substantial differences in the small sample performance of alternative tests. Our empirical application examines the diversification benefits from emerging equity markets using an extensive new data set on U.S. and U.K.‐traded closed‐end funds. We find significant diversification benefits for the U.K. country funds, but not for the U.S. funds. The difference appears to relate to differences in portfolio holdings rather than to the behavior of premiums in the United States versus the United Kingdom.