$1.$ As a financial analyst, you evaluate financial data and extract relevant information to make investment recommendations. This time, you are tasked with analyzing NVIDIA based on its historical prices. $(15$ points$)$

Year

Price

Dividend

$2000$

$0\mathrm{.}77$

$0$

$2001$

$2\mathrm{.}15$

$0$

$2002$

$5\mathrm{.}48$

$0$

$2003$

$0\mathrm{.}86$

$0$

$2004$

$1\mathrm{.}85$

$0$

$2005$

$1\mathrm{.}91$

$0$

$2006$

$3\mathrm{.}75$

$0$

$2007$

$5\mathrm{.}11$

$0$

$2008$

$6\mathrm{.}15$

$0$

$2009$

$1\mathrm{.}99$

$0$

$2010$

$3\mathrm{.}85$

$0$

$2011$

$5\mathrm{.}98$

$0$

$2012$

$3\mathrm{.}69$

$0\mathrm{.}12$

$2013$

$3\mathrm{.}07$

$0\mathrm{.}12$

$2014$

$3\mathrm{.}93$

$0\mathrm{.}12$

$2015$

$4\mathrm{.}80$

$0\mathrm{.}12$

$2016$

$7\mathrm{.}32$

$0\mathrm{.}12$

$2017$

$27\mathrm{.}30$

$0\mathrm{.}16$

$2018$

$61\mathrm{.}45$

$0\mathrm{.}16$

$2019$

$35\mathrm{.}94$

$0\mathrm{.}16$

$2020$

$59\mathrm{.}11$

$0\mathrm{.}16$

$2021$

$129\mathrm{.}90$

$0\mathrm{.}16$

$2022$

$244\mathrm{.}86$

$0\mathrm{.}16$

$2023$

$195\mathrm{.}37$

$0\mathrm{.}16$

$2024$

$615\mathrm{.}27$

$0\mathrm{.}16$

a$)$ If a client invested $$10,000$ at the beginning of $2000,$ what is the total dollar return for that client, measured at the beginning of $2024?$

b$)$ What is the typical $($average$)$ return over the $24$ years?

c$)$ What is the average compound return per year over the $24-$year period? d$)$ Obtain the variance and standard deviation of returns.

e$)$ If the average risk$-$free rate during this period was $4\mathrm{.}5\%,$ what is Nvidia's risk premium? How can we interpret this number?