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One of the main applications of balance indices is in tests of null models ofevolutionary processes. The knowledge of an exact formula for a statistic of abalance index, holding for any number n of leaves, is necessary in order to usethis statistic in tests of this kind involving trees of any size. In this paperwe obtain exact formulas for the variance under the Yule model of the Sackinindex, the Colless index and the total cophenetic index of binary rootedphylogenetic trees with n leaves. We also obtain the covariance of the Sackinand the total cophenetic index.

Exact formulas for the variance of several balance indices under the Yule model