The following table contains the closing

year$-$end prices of the Japanese stock$-$market index, the Nikkei$-225.$ Assume that each historical

rate of return was exactly one representative scenario $($independent sample draw$)$ that you can use

to estimate the future. If a Japanese investor had

purchased a mutual fund that imitated the Nikkei$225,$ what would her annual rates of return, compounded rate of return $($from the end of $1984$ to

the end of $2010),$ average rate of return, and risk

have been? $($Do you think history would have been

representative?$)$