$\backslash$table$[[$A$,$B$,$C$,$D$,$E$,$F$,$G$,$H$,,$J$,$K$,$L$],[$Date$,$MSFT$,$S$\backslash$table$[[$A$,$B$,$C$,$D$,$E$,$F$,$G$,$H$,,$J$,$K$,$L$],[$Date$,$MSFT$,$S

a$.$ Using all $45$ monthly returns for Microsoft and the two stock market indexes, compute Microsoft's beta using the S&P $500$ Index as the market proxy. Then compute the beta using the NASDAQ index as the market portfolio proxy. Compare the two beta estimates.

$\backslash$table$[[4,$A$,$B$,$C$,$D$,$E$,$F$,$G$,$H$,$I,$J,$K$,$L$],[1,$Date,MSFT$,$S$8$P$500,$Nasdaq,Date,MSFT$,$SRP$500,$Nasdag,Date,MSFT$,$S$8$P$500,$Nasdag$],[2,$Dec $20,4\mathrm{.}17\%,3\mathrm{.}71\%,5\mathrm{.}65\%,$Sep $2019,1\mathrm{.}18\%,1\mathrm{.}72\%,0\mathrm{.}46\%,$Jun $2018,0\mathrm{.}20\%,0\mathrm{.}48\%,0\mathrm{.}92\%],[3,$Nov $20,5\mathrm{.}73\%,10\mathrm{.}75\%,11\mathrm{.}80\%,$Aug $2019,1\mathrm{.}17\%,-1\mathrm{.}81\%,-260\%,$May $2018,5\mathrm{.}69\%,2\mathrm{.}16\%,5\mathrm{.}32\%],[4,$Oct $20,-3\mathrm{.}74\%,-2\mathrm{.}77\%,-229\%,$Jul $2019,1\mathrm{.}72\%,1\mathrm{.}31\%,2\mathrm{.}11\%,$Apr $2018,2\mathrm{.}47\%,0\mathrm{.}27\%,0\mathrm{.}04\%],[5,$Sep $20,-6\mathrm{.}51\%,-3\mathrm{.}92\%,-5\mathrm{.}16\%,$Jun $2019,8\mathrm{.}71\%,6\mathrm{.}89\%,7\mathrm{.}42\%,$Mar $2018,-221\%,-2\mathrm{.}69\%,-2\mathrm{.}88\%],[6,$Aug $20,10\mathrm{.}01\%,7\mathrm{.}01\%,9\mathrm{.}59\%,$May $2019,-5\mathrm{.}30\%,-6\mathrm{.}58\%,-7\mathrm{.}93\%,$Feb $2018,-1\mathrm{.}31\%,-3\mathrm{.}89\%,-1\mathrm{.}87\%],[7,$Jul $20,0\mathrm{.}74\%,5\mathrm{.}51\%,6\mathrm{.}82\%,$Apr $2019,10\mathrm{.}73\%,3\mathrm{.}93\%,4\mathrm{.}74\%,$Jan $2018,11\mathrm{.}07\%,5\mathrm{.}62\%,7\mathrm{.}36\%],[8,$Jun $20,11\mathrm{.}37\%,1\mathrm{.}84\%,5\mathrm{.}99\%,$Mar $2019,5\mathrm{.}72\%,1\mathrm{.}79\%,261\%,$Dec $2017,2\mathrm{.}14\%,3\mathrm{.}43\%,0\mathrm{.}43\%],[9,$May $20,2\mathrm{.}25\%,4\mathrm{.}53\%,6\mathrm{.}75\%,$Feb $2019,7\mathrm{.}28\%,2\mathrm{.}97\%,3\mathrm{.}44\%,$Nov $2017,1\mathrm{.}19\%,0\mathrm{.}37\%,2\mathrm{.}17\%],[10,$Apr $20,13\mathrm{.}63\%,12\mathrm{.}68\%,15\mathrm{.}45\%,$Jan $2019,282\%,7\mathrm{.}87\%,9\mathrm{.}74\%,$Oct $2017,11\mathrm{.}67\%,222\%,3\mathrm{.}57\%],[11,$Mar $20,-2\mathrm{.}39\%,-12\mathrm{.}51\%,-10\mathrm{.}12\%,$Dec $2018,-8\mathrm{.}01\%,-9\mathrm{.}18\%,-9\mathrm{.}48\%,$Sep $2017,0\mathrm{.}16\%,1\mathrm{.}93\%,1\mathrm{.}05\%],[12,$Feb $20,4\mathrm{.}83\%,-8\mathrm{.}41\%,-6\mathrm{.}38\%,$Nov $2018,3\mathrm{.}82\%,1\mathrm{.}79\%,0\mathrm{.}34\%,$Aug $2017,2\mathrm{.}85\%,0\mathrm{.}05\%,1\mathrm{.}27\%],[13,$Jan $20,7\mathrm{.}95\%,-0\mathrm{.}16\%,1\mathrm{.}99\%,$Oct $2018,-6\mathrm{.}61\%,-6\mathrm{.}94\%,-9\mathrm{.}20\%,$Jul $2017,5\mathrm{.}47\%,1\mathrm{.}93\%,3\mathrm{.}38\%],[14,$Dec $19,4\mathrm{.}53\%,286\%,3\mathrm{.}54\%,$Sep $2018,2\mathrm{.}21\%,0\mathrm{.}43\%,-0\mathrm{.}78\%,$Jun $2017,-0\mathrm{.}74\%,0\mathrm{.}48\%,-0\mathrm{.}94\%],[15,$Nov $19,5\mathrm{.}59\%,3\mathrm{.}40\%,4\mathrm{.}50\%,$Aug $2018,5\mathrm{.}89\%,3\mathrm{.}03\%,5\mathrm{.}71\%,$May $2017,202\%,1\mathrm{.}16\%,2\mathrm{.}50\%],[16,$Oct $19,3\mathrm{.}12\%,204\%,3\mathrm{.}65\%,$Jul $2018,7\mathrm{.}58\%,3\mathrm{.}60\%,2\mathrm{.}15\%,$Apr $2017,395\%,0\mathrm{.}91\%,230\%]]$

a$.$ Using all $45$ monthly returns for Microsoft and the two stock market indexes, compute Microsoft's beta using the S&P $500$ Index as the market proxy. Then compute the beta using the NASDAQ index as the market portfolio proxy. Compare the two beta estimates.

$\backslash$table$[[4,$A$,$B$,$C$,$D$,$E$,$F$,$G$,$H$,$I,$J,$K$,$L$],[1,$Date,MSFT$,$S$8$P$500,$Nasdaq,Date,MSFT$,$SRP$500,$Nasdag,Date,MSFT$,$S$8$P$500,$Nasdag$],[2,$Dec $20,4\mathrm{.}17\%,3\mathrm{.}71\%,5\mathrm{.}65\%,$Sep $2019,1\mathrm{.}18\%,1\mathrm{.}72\%,0\mathrm{.}46\%,$Jun $2018,0\mathrm{.}20\%,0\mathrm{.}48\%,0\mathrm{.}92\%],[3,$Nov $20,5\mathrm{.}73\%,10\mathrm{.}75\%,11\mathrm{.}80\%,$Aug $2019,1\mathrm{.}17\%,-1\mathrm{.}81\%,-260\%,$May $2018,5\mathrm{.}69\%,2\mathrm{.}16\%,5\mathrm{.}32\%],[4,$Oct $20,-3\mathrm{.}74\%,-2\mathrm{.}77\%,-229\%,$Jul $2019,1\mathrm{.}72\%,1\mathrm{.}31\%,2\mathrm{.}11\%,$Apr $2018,2\mathrm{.}47\%,0\mathrm{.}27\%,0\mathrm{.}04\%],[5,$Sep $20,-6\mathrm{.}51\%,-3\mathrm{.}92\%,-5\mathrm{.}16\%,$Jun $2019,8\mathrm{.}71\%,6\mathrm{.}89\%,7\mathrm{.}42\%,$Mar $2018,-221\%,-2\mathrm{.}69\%,-2\mathrm{.}88\%],[6,$Aug $20,10\mathrm{.}01\%,7\mathrm{.}01\%,9\mathrm{.}59\%,$May $2019,-5\mathrm{.}30\%,-6\mathrm{.}58\%,-7\mathrm{.}93\%,$Feb