The following data have been developed for a listed company, Happy Cat.

$\backslash$table$[[$Year$,$Market's Return,Happy Cat's Return$],[2018,0\mathrm{.}1,0\mathrm{.}06],[2019,0,-0\mathrm{.}04],[2020,0\mathrm{.}16,0\mathrm{.}12],[2021,-0\mathrm{.}06,0\mathrm{.}01],[2022,0\mathrm{.}15,0\mathrm{.}25]]$

The YTM on risk$-$free Treasury Bills is $4\%$ and is expected to remain at this point for the foreseeable future.

a$.$ Calculate the sample variance of the market return. Show your calculations. Correct your answers to $4$ decimal places.

$[4$ marks$]$

b$.$ Find the sample covariance between the return for Happy Cat and the market. Show your calculations. Correct your answers to $6$ decimal places. $[4$ marks$]$

c$.$ Calculate the beta of Happy Cat. Show your calculations.

$[2$ marks$]$

d$.$ Use the CAPM to find the required rate of return of Happy Cat.

$[3$ marks$]$

e$.$ If Happy Cat distributes $$2$ annual dividend in one year and the annual dividend is assumed to grow at $4\%$ per year indefinitely, find the fair stock price of Happy Cat now. Show your workings.

$[3$ marks$]$

f$.$ Suppose Steven buys $5,000$ shares of Happy Cat at the fair stock price now. If the market drops by $1\mathrm{.}5\%$ in one month, estimate the dollar amount of capital gain or loss for his investment in one month. Explain your answer. $[4$ marks$]$