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3.4. FUNDAMENTALS AND EXCHANGE RATE VOLATILITY 89Table 3.1: Descriptive statistics for exchange-rate and equity returns,and their fundamentals.AutocorrelationsMean Std.Dev. Min. Max. ρ 1 ρ 4 ρ 8 ρ 16ReturnsS&P 2.75 5.92 -13.34 18.31 0.24 -0.10 0.15 0.09UKP 0.41 5.50 -13.83 16.47 0.12 0.03 0.01 -0.29DEM 0.46 6.35 -13.91 15.74 0.09 0.23 0.04 -0.07YEN 0.73 6.08 -15.00 16.97 0.13 0.18 0.06 -0.29Deviation from fundamentalsDiv. 1.31 0.30 0.49 1.82 1.01 1.03 1.05 0.94UKP 0 0.18 -0.46 0.47 0.89 0.61 0.25 -0.12DEM 0 0.31 -0.61 0.59 0.98 0.91 0.77 0.55YEN 0 0.38 -0.85 0.50 0.98 0.88 0.76 0.68Notes: Quarterly observations from 1973.1 to 1997.4. Percentage returns on theStandard and Poors composite index (S&P) and its log dividend yield (Div.) arefrom Datastream. Percentage exchange rate returns and deviation of exchange ratefrom fundamentals (s t −f t )withf t =(m t −m ∗ t )−(y t−yt ∗)arefromtheInternationalFinancial Statistics CD-ROM. (s t − f t ) are normalized to have zero mean. The USdollar is the numeraire currency. UKP is the UK pound, DEM is the deutschemark,and YEN is the Japanese yen.Stylized Facts on Volatility and Dynamics.Some descriptive statistics for dollar quarterly returns on the pound,deutsche-mark, yen are shown in the Þrst panel of Table 3.1. To underscorethe similarity between the exchange rate and equity prices,the table also includes statistics for the Standard and Poors compositestock price index. The second panel displays descriptive statistics forthe deviation of the respective asset prices from their fundamentals.For equities, this is the S&P log dividend yield. For currency values, itis the deviation of the exchange rate from the monetary fundamentals, ⇐(62)f t − s t have been normalized to have mean 0. The volatility of a timeseries is measured by its sample standard deviation.