Expected Long-Term Rates of Return When Short-Term Returns Are Serially Correlated

When short-term returns are serially uncorrelated, expected long-term and short-term returns are equal. However, we show that negative serial correlation among the short-term returns make the expected long-term returns lower than the short-term ones. Such serial correlation is likely to arise, for example, for an investor whose portfolio is invested abroad in assets denominated in foreign currencies, but who wants to make withdrawals in proportion to the fund’s value in the domestic currency, and the exchange rate obeys long-term purchasing-power parity. Small-country sovereign wealth funds are leading examples of such investors. Such funds should thus calibrate withdrawals to the expected long-term returns rather than the short-term ones. Negative contemporaneous correlation between the exchange rate and global asset returns may weaken this result but is unlikely to reverse it