Overlapping financial returns are sometimes used to increase the efficiency and power of statistical tests and for Value-at-Risk analysis. This is particularly useful when there are not many observations, such as daily returns for emerging markets. Sometimes, returns show autocorrelation. In this paper, unbiased variance estimators are derived for overlapping returns when the returns are generated by AR(1) or MA(1) processes. A limited Monte Carlo experiment reveals that alternative estimators can suffer from substantial bias. The relevance of using proper estimators is emphasized by considering daily returns for six emerging markets.