During the past $7$ years, Hazelwood owned two stocks that had the following annual rates of return:

Year

Stock Z

Stock M

$2021$

$-0\mathrm{.}19$

$-0\mathrm{.}14$

$2020$

$0\mathrm{.}08$

$-0\mathrm{.}05$

$2019$

$-0\mathrm{.}09$

$0\mathrm{.}11$

$2018$

$-0\mathrm{.}03$

$0\mathrm{.}07$

$2017$

$0\mathrm{.}12$

$-0\mathrm{.}03$

$2016$

$0\mathrm{.}11$

$-0\mathrm{.}1$

$2015$

$0\mathrm{.}03$

$0\mathrm{.}05$

a$)$ Compute the arithmetic mean annual return for each stock. Which stock is most desirable by this measure?

b$)$ Compute the standard deviation of the annual return for each stock. By this measure, which is the preferable stock?

c$)$ Compute the coefficient of variation for each stock. By this relative measure of risk, which stock is preferable?

d$)$ Compute the geometric mean return for each stock. Discuss the difference between the arithmetic and the geometric mean return for each stock. Discuss the difference in the mean returns relative to the standard deviation of the return for each stock.

e$)$

You decide to go an extra step by calculating the coefficient of correlation using the data provided above and explain how to interpret the results. Would the combination of the common stocks of Z and M be good for diversification?