by a recomputation in US Dollars, despite the Asian crises. The separate indices are more risky than the MSCI World Index, as can be seen by the standard deviations and the largest cumulative loss numbers. Thus it is clear that country specific risks are reduced by the broad diversified world index. The return distribution is strongly leptokurtic for all indices and is negatively skewed for a majority of the indices. Thus large negative shocks occur more frequently than large positive shocks. The local interest rates are used for computing the Sharpe ratio (i.e. the extra return over the risk-free interest rate per extra point of risk as measured by the standard deviation) in local currency, while the rates on 1-month US certificates of deposits are used for computing the Sharpe ratio in US Dollars. The Sharpe ratio is negative for 23 indices, if expressed in local currency or in US Dollars, indicating that these indices were not able to beat a continuous risk free investment. Only the European and US stock market indices as well as the Egyptian and Israeli stock market indices were able in generating a positive excess return over the risk-free interest rate. For more than half of the indices the largest cumulative loss is larger than 50% if expressed in local currency or US Dollars. For example, during the Argentine economic crises the Merval lost 77% of its value in local currency and 91% of its value in US Dollars. The Russian Moscow Times lost 94% of its value in US Dollars in a short period of approximately one year between August 1997 and October 1998. The largest decline of the MSCI World Index is equal to 39% and occurred in the period March 27, 2000 through September 21, 2001. Of the 14 indices for which we have data preceding the year 1987, only for 4 indices, namely the DJIA, the NYSE Composite, the Australian ASX and the Dutch AEX, the largest cumulative loss, when measured in local currency, occurred preceding and during the crash of 1987. If measured in US Dollars, only the largest decline for the Dutch AEX changes and took place in the period January 4, 2000 through September 21, 2001. Remarkably for most indices the largest decline started well before the terrorist attack against the US on September 11, 2001, but stopped only 10 days after it2. With hindsight, the overall picture is that the European and US stock markets performed the best, but also the Egyptian and Israeli stock markets show remarkably good results.
We computed autocorrelation functions (ACFs) of the returns and significance is tested with Bartlett (1946) standard errors and Diebold's (1986) heteroskedasticity-consistent standard errors3. Typically autocorrelations of the returns are small with only few lags