My stock is Tesla. I will provide the sixty monthly returns at the end of the questions$($s$).3.$ Run three regressions of the sixty monthly returns on each stock minus the monthly return on the risk$-$free rate against the market risk premiums $($monthly returns on the S&P $500$ Index $$ the monthly risk$-$free rate$).$ Show all the results.

$4.$ The three Regressions are conducted as follows: $($The monthly return on stock i$,$ in period t$)($The monthly risk$-$free rate in month t$)=$ Alpha $+$ Beta$[($Monthly returns in period t$)$ on the S&P $500$ Index $$ The corresponding risk$-$free rate in month t$]+$ an error term epsilon $($in month t$)$

$5.$ Estimate the Alpha and Beta for each of the four stocks and interpret your results. Which stock outperforms the market for this period? Also estimate the standard deviations of the error terms, epsilon.

$6.$ Estimate the Coefficient of Determination for each stock and interpret your results.

$7.$ Create a three$-$by$-$three Correlation matrix of the correlations among the four stocks selected and interpret your results.

Monthly returns from August $31,2018$ August $31,2023$

September $2018$: $-21\mathrm{.}27\%$

October $2018$: $8\mathrm{.}59\%$

November $2018$: $-6\mathrm{.}11\%$

December $2018$: $-10\mathrm{.}57\%$

January $2019$: $3\mathrm{.}52\%$

February $2019$: $21\mathrm{.}47\%$

March $2019$: $-14\mathrm{.}69\%$

April $2019$: $1\mathrm{.}74\%$

May $2019$: $-14\mathrm{.}80\%$

June $2019$: $-3\mathrm{.}87\%$

July $2019$: $7\mathrm{.}30\%$

August $2019$: $3\mathrm{.}61\%$

September $2019$: $-8\mathrm{.}73\%$

October $2019$: $4\mathrm{.}22\%$

November $2019$: $10\mathrm{.}20\%$

December $2019$: $56\mathrm{.}68\%$

January $2020$: $145\mathrm{.}33\%$

February $2020$: $-11\mathrm{.}87\%$

March $2020$: $-43\mathrm{.}33\%$

April $2020$: $-21\mathrm{.}92\%$

May $2020$: $-16\mathrm{.}21\%$

June $2020$: $-13\mathrm{.}87\%$

July $2020$: $-24\mathrm{.}67\%$

August $2020$: $75\mathrm{.}14\%$

September $2020($adjusted for the stock split$)$: $-66\mathrm{.}59\%$

October $2020$: $-24\mathrm{.}97\%$

November $2020$: $47\mathrm{.}74\%$

December $2020$: $47\mathrm{.}44\%$

January $2021$: $20\mathrm{.}06\%$

February $2021$: $-12\mathrm{.}13\%$

March $2021$: $-6\mathrm{.}24\%$

April $2021$: $15\mathrm{.}12\%$

May $2021$: $-12\mathrm{.}29\%$

June $2021$: $-2\mathrm{.}06\%$

July $2021$: $2\mathrm{.}59\%$

August $2021$: $7\mathrm{.}07\%$

September $2021$: $5\mathrm{.}40\%$

October $2021$: $43\mathrm{.}64\%$

November $2021$: $2\mathrm{.}77\%$

December $2021$: $-7\mathrm{.}68\%$

January $2022$: $-11\mathrm{.}35\%$

February $2022$: $-7\mathrm{.}08\%$

March $2022$: $23\mathrm{.}79\%$

April $2022$: $-19\mathrm{.}21\%$

May $2022$: $-12\mathrm{.}92\%$

June $2022$: $-11\mathrm{.}20\%$

July $2022$: $32\mathrm{.}39\%$

August $2022$: $-7\mathrm{.}24\%$

September $2022$: $-3\mathrm{.}74\%$

October $2022$: $-14\mathrm{.}20\%$

November $2022$: $-14\mathrm{.}42\%$

December $2022$: $-36\mathrm{.}69\%$

January $2023$: $40\mathrm{.}61\%$

February $2023$: $18\mathrm{.}74\%$

March $2023$: $0\mathrm{.}85\%$

April $2023$: $-20\mathrm{.}80\%$

May $2023$: $24\mathrm{.}12\%$

June $2023$: $28\mathrm{.}47\%$

July $2023$: $2\mathrm{.}16\%$

August $2023$: $-3\mathrm{.}50\%$

Monthly risk$-$free rates on $30-$year T$-$ Bonds

$9/1/2018$: $3\mathrm{.}197\%$

$10/1/2018$: $3\mathrm{.}402\%$

$11/1/2018$: $3\mathrm{.}311\%$

$12/1/2018$: $3\mathrm{.}02\%$

$1/1/2019$: $3\mathrm{.}005\%$

$2/1/2019$: $3\mathrm{.}083\%$

$3/1/2019$: $2\mathrm{.}822\%$

$4/1/2019$: $2\mathrm{.}94\%$

$5/1/2019$: $2\mathrm{.}583\%$

$6/1/2019$: $2\mathrm{.}528\%$

$7/1/2019$: $2\mathrm{.}527\%$

$8/1/2019$: $1\mathrm{.}97\%$

$9/1/2019$: $2\mathrm{.}121\%$

$10/1/2019$: $2\mathrm{.}176\%$

$11/1/2019$: $2\mathrm{.}202\%$

$12/1/2019$: $2\mathrm{.}389\%$

$1/1/2020$: $2\mathrm{.}015\%$

$2/1/2020$: $1\mathrm{.}671\%$

$3/1/2020$: $1\mathrm{.}351\%$

$4/1/2020$: $1\mathrm{.}266\%$

$5/1/2020$: $1\mathrm{.}407\%$

$6/1/2020$: $1\mathrm{.}409\%$

$7/1/2020$: $1\mathrm{.}198\%$

$8/1/2020$: $1\mathrm{.}452\%$

$9/1/2020$: $1\mathrm{.}451\%$

$10/1/2020$: $1\mathrm{.}64\%$

$11/1/2020$: $1\mathrm{.}573\%$

$12/1/2020$: $1\mathrm{.}646\%$

$1/1/2021$: $1\mathrm{.}858\%$

$2/1/2021$: $2\mathrm{.}182\%$

$3/1/2021$: $2\mathrm{.}425\%$

$4/1/2021$: $2\mathrm{.}301\%$

$5/1/2021$: $2\mathrm{.}263\%$

$6/1/2021$: $2\mathrm{.}065\%$

$7/1/2021$: $1\mathrm{.}897\%$

$8/1/2021$: $1\mathrm{.}927\%$

$9/1/2021$: $2\mathrm{.}092\%$

$10/1/2021$: $1\mathrm{.}942\%$

$11/1/2021$: $1\mathrm{.}787\%$

$12/1/2021$: $1\mathrm{.}905\%$

$1/1/2022$: $2\mathrm{.}098\%$

$2/1/2022$: $2\mathrm{.}182\%$

$3/1/2022$: $2\mathrm{.}448\%$

$4/1/2022$: $2\mathrm{.}947\%$

$5/1/2022$: $3\mathrm{.}057\%$