Run the following R code. The set.seed$()$ command insures that everyone using this code will have the same random numbers and will obtain the same price series. There are $253$ trading days per year, so you are simulating $1$ year of daily returns nine times. The price starts at $120.$

The code par$($mfrow$=$c$(3,3))$ on line $3$ opens a graphics window with three rows and three columns and rnorm$()$ on line $6$ generates normally dis$-$ tributed random numbers.

$1$ set.seed$(2012)$

$2$ n$=253$

$3$ par$($mfrow$=$c$(3,3))$

$4$ for $($i in $(1$:$9))$

$5\{$

$6$ logr $=$ rnorm$($n$,0\mathrm{.}05/253,0\mathrm{.}2/$ sqrt$(253))$

$7$ price $=$ c$(120,120*$ exp$($cumsum$($logr$)))$

$8$ plot$($price$,$ type $="$b$")$

$9\}$

Problem $9$ In this simulation, what are the mean and standard deviation of the log$-$returns for $1$ year?