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. For the Norwegian GPFG, the expected annualized long-term rate of return in Norwegian kroner may be 0.7 to 1.8 percentage points lower than the expected short-term return. Negative contemporaneous correlation between global returns and changes in the real exchange rate may dampen and even reverse this result. Empirical evidence suggests that this may be the case for investors in USD-denominated assets domiciled in the United Kingdom, but not for investors domiciled in Norway or Germany. Empirically, we furthermore find that long-term annualized returns may fall short of short-term returns even when evaluated in real USD. Although negative serial correlation also shrinks the long-term variance, funds such as the GPFG should calibrate withdrawals to the expected long-term returns rather than the short-term ones.