Which funds do you recommend for investment?

Data for $4$ mutual funds: GLCGX$,$ TRBCX$,$ DTMVX$,$ DVPEX

$>$ # GLCGX fund

$>$ r$\_$glcgx$=$da$GLCGX$-$tbills # excess return for GLCGX

$>$ #require$($graphics$)$

$>$ m$1=$lm$($r$\_$glcgx~rm$)$ # CAPM MODEL with one regressor

$>$ summary$($m$1)$

Call:

lm$($formula $=$ r$\_$glcgx ~ rm$)$

Residuals:

Min $1$Q Median $3$Q Max

$-0\mathrm{.}103809-0\mathrm{.}0087050\mathrm{.}0041350\mathrm{.}0097940\mathrm{.}043773$

Coefficients:

Estimate Std$.$ Error t value Pr$(>|$t$|)$

$($Intercept$)-0\mathrm{.}0070490\mathrm{.}002898-2\mathrm{.}4320\mathrm{.}0181*$

rm $1\mathrm{.}1672010\mathrm{.}05890619\mathrm{.}815<2$e$-16***$

$---$

Signif. codes: $0***0\mathrm{.}001**0\mathrm{.}01*0\mathrm{.}05.0\mathrm{.}11$

Residual standard error: $0\mathrm{.}02243$ on $58$ degrees of freedom

Multiple R$-$squared: $0\mathrm{.}8713,$ Adjusted R$-$squared: $0\mathrm{.}8691$

F$-$statistic: $392\mathrm{.}6$ on $1$ and $58$ DF$,$ p$-$value: $<2\mathrm{.}2$e$-16$

$>$ m$2=$lm$($r$\_$glcgx~rm$+$hml$+$smb$+$mom$)$ #Multifactor model

$>$ summary$($m$2)$

Call:

lm$($formula $=$ r$\_$glcgx ~ rm $+$ hml $+$ smb $+$ mom$)$

Residuals:

Min $1$Q Median $3$Q Max

$-0\mathrm{.}075820-0\mathrm{.}0066590\mathrm{.}0015660\mathrm{.}0096110\mathrm{.}033015$

Coefficients:

Estimate Std$.$ Error t value Pr$(>|$t$|)$

$($Intercept$)0\mathrm{.}00094670\mathrm{.}00245670\mathrm{.}3850\mathrm{.}701$

rm $1\mathrm{.}00758310\mathrm{.}049817020\mathrm{.}226<2$e$-16***$

hml $-0\mathrm{.}48322660\mathrm{.}0672459-7\mathrm{.}1861\mathrm{.}87$e$-09***$

smb $-0\mathrm{.}25847570\mathrm{.}0522464-4\mathrm{.}9477\mathrm{.}47$e$-06***$

mom $-0\mathrm{.}00185800\mathrm{.}0313426-0\mathrm{.}0590\mathrm{.}953$

$---$

Signif. codes: $0***0\mathrm{.}001**0\mathrm{.}01*0\mathrm{.}05.0\mathrm{.}11$

Residual standard error: $0\mathrm{.}01643$ on $55$ degrees of freedom

Multiple R$-$squared: $0\mathrm{.}9345,$ Adjusted R$-$squared: $0\mathrm{.}9297$

F$-$statistic: $196\mathrm{.}2$ on $4$ and $55$ DF$,$ p$-$value: $<2\mathrm{.}2$e$-16$

$>$ # TRCBX fund

$>$ r$\_$trbcx$=$da$TRBCX$-$tbills # excess return for TRBCX

$>$ m$3=$lm$($r$\_$trbcx~rm$)$ # CAPM MODEL with one regressor

$>$ summary$($m$3)$

Call:

lm$($formula $=$ r$\_$trbcx ~ rm$)$

Residuals:

Min $1$Q Median $3$Q Max

$-0\mathrm{.}040955-0\mathrm{.}005516-0\mathrm{.}0016230\mathrm{.}0055280\mathrm{.}034593$

Coefficients:

Estimate Std$.$ Error t value Pr$(>|$t$|)$

$($Intercept$)-0\mathrm{.}0014600\mathrm{.}001603-0\mathrm{.}9110\mathrm{.}366$

rm $1\mathrm{.}0075050\mathrm{.}03258430\mathrm{.}921<2$e$-16***$

$---$

Signif. codes: $0***0\mathrm{.}001**0\mathrm{.}01*0\mathrm{.}05.0\mathrm{.}11$

Residual standard error: $0\mathrm{.}01241$ on $58$ degrees of freedom

Multiple R$-$squared: $0\mathrm{.}9428,$ Adjusted R$-$squared: $0\mathrm{.}9418$

F$-$statistic: $956\mathrm{.}1$ on $1$ and $58$ DF$,$ p$-$value: $<2\mathrm{.}2$e$-16$

$>$ m$4=$lm$($r$\_$trbcx~rm$+$hml$+$smb$+$mom$)$ #Multifactor model

$>$ summary$($m$4)$

Call:

lm$($formula $=$ r$\_$trbcx ~ rm $+$ hml $+$ smb $+$ mom$)$

Residuals:

Min $1$Q Median $3$Q Max

$-0\mathrm{.}0277892-0\mathrm{.}00615670\mathrm{.}00009760\mathrm{.}00440260\mathrm{.}0227884$

Coefficients:

Estimate Std$.$ Error t value Pr$(>|$t$|)$

$($Intercept$)0\mathrm{.}0027860\mathrm{.}0013842\mathrm{.}0130\mathrm{.}049027*$

rm $0\mathrm{.}9458560\mathrm{.}02806633\mathrm{.}701<2$e$-16***$

hml $-0\mathrm{.}1473670\mathrm{.}037885-3\mathrm{.}8900\mathrm{.}000273***$

smb $-0\mathrm{.}1141670\mathrm{.}029434-3\mathrm{.}8790\mathrm{.}000283***$

mom $-0\mathrm{.}0834960\mathrm{.}017658-4\mathrm{.}7291\mathrm{.}61$e$-05***$

$---$

Signif. codes: $0***0\mathrm{.}001**0\mathrm{.}01*0\mathrm{.}05.0\mathrm{.}11$

Residual standard error: $0\mathrm{.}009256$ on $55$ degrees of freedom

Multiple R$-$squared: $0\mathrm{.}9698,$ Adjusted R$-$squared: $0\mathrm{.}9676$

F$-$statistic: $441\mathrm{.}7$ on $4$ and $55$ DF$,$ p$-$value: $<2\mathrm{.}2$e$-16$

$>$ # DTMVX fund

$>$ r$\_$dtmvx$=$da$DTMVX$-$tbills #alpha

$>$ m$5=$lm$($r$\_$dtmvx~rm$)$ #CAPM model with one regressor

$>$ summary$($m$5)$

Call:

lm$($formula $=$ r$\_$dtmvx ~ rm$)$

Residuals:

Min $1$Q Median $3$Q Max