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Problem $7-09$

Suppose that you have estimated the Fama$$French three$-$factor and four$-$factor models for three different stocks: BCD$,$ FGH$,$ and JKL$.$ Specifically, using return data from $2005$ to $2009,$ the following equations were estimated:

Three$-$Factor Model:

BCD: $[$E$($R$)-$ RFR$]=(0\mathrm{.}976)(\backslash$lambda M$)+(-0\mathrm{.}022)(\backslash$lambda SMB$)+(-0\mathrm{.}416)(\backslash$lambda HML$)$

FGH: $[$E$($R$)-$ RFR$]=(1\mathrm{.}019)(\backslash$lambda M$)+(-0\mathrm{.}039)(\backslash$lambda SMB$)+(0\mathrm{.}394)(\backslash$lambda HML$)$

JKL: $[$E$($R$)-$ RFR$]=(1\mathrm{.}193)(\backslash$lambda M$)+(0\mathrm{.}547)(\backslash$lambda SMB$)+(0\mathrm{.}502)(\backslash$lambda HML$)$

Four$-$Factor Model:

BCD: $[$E$($R$)-$ RFR$]=(1\mathrm{.}001)(\backslash$lambda M$)+(-0\mathrm{.}002)(\backslash$lambda SMB$)+(-0\mathrm{.}342)(\backslash$lambda HML$)+(0\mathrm{.}063)(\backslash$lambda MOM$)$

FGH: $[$E$($R$)-$ RFR$]=(1\mathrm{.}114)(\backslash$lambda M$)+(-0\mathrm{.}019)(\backslash$lambda SMB$)+(0\mathrm{.}493)(\backslash$lambda HML$)+(0\mathrm{.}185)(\backslash$lambda MOM$)$

JKL: $[$E$($R$)-$ RFR$]=(1\mathrm{.}021)(\backslash$lambda M$)+(0\mathrm{.}477)(\backslash$lambda SMB$)+(0\mathrm{.}355)(\backslash$lambda HML$)+(-0\mathrm{.}269)(\backslash$lambda MOM$)$

You have also estimated factor risk premia over a recent $15-$year period as: $\backslash$lambda M $=7\mathrm{.}22$ percent, $\backslash$lambda SMB $=2\mathrm{.}09$ percent, $\backslash$lambda HML $=4\mathrm{.}36$ percent, and $\backslash$lambda MOM $=5\mathrm{.}00$ percent. Use these estimated risk premia along with two factor models estimated to calculate the expected excess returns for the three stocks. Round your answers to two decimal places.

Three$-$factor model Four$-$factor model

BCD:

$\%$

$\%$

FGH:

$\%$

$\%$

JKL:

$\%$

$\%$

Suppose that you have also estimated historical factor risk prices for two different time frames: $(1)30-$year period: $(\backslash$lambda M $=7\mathrm{.}19$ percent, $\backslash$lambda SMB $=1\mathrm{.}43$ percent, and $\backslash$lambda HML $=5\mathrm{.}24$ percent$),$ and $(2)80-$year period: $(\backslash$lambda M $=8\mathrm{.}01$ percent, $\backslash$lambda SMB $=3\mathrm{.}62$ percent, and $\backslash$lambda HML $=5\mathrm{.}11$ percent$).$ Calculate the expected excess returns for BCD$,$ FGH$,$ and JKL using both of these alternative sets of factor risk premia in conjunction with the three$-$factor risk model. Round your answers to two decimal places.

$30-$year period $80-$year period

BCD:

$\%$

$\%$

FGH:

$\%$

$\%$

JKL:

$\%$

$\%$

You now also consider historical estimates for the MOM risk factor over the two additional time frames: $(1)\backslash$lambda MOM $=7\mathrm{.}89$ percent $(30-$year period$),$ and $(2)\backslash$lambda MOM $=9\mathrm{.}69$ percent $(80-$year period$).$ Using this additional information, calculate the expected excess returns for BCD$,$ FGH$,$ and JKL in conjunction with the four$-$factor risk model. Round your answers to two decimal places.

$30-$year period $80-$year period

BCD:

$\%$

$\%$

FGH:

$\%$

$\%$

JKL:

$\%$

$\%$

Do all of the expected excess returns you calculated in part $($a$)$ and part $($b$)$ make sense? If not, identify which ones seem inconsistent with asset pricing theory and discuss why.

The excess returns for

$-$Select$-($which stocks?$)$

for all periods seem moderately large. This is partly due to the fact that the regressions unlike factor risk premia were estimated using data from much

$-$Select$-($shorter$/$ longer$)$

periods.