$\begin{array}{|l|l|l|l|}
\hline \text { Factor } & {\left[\mathrm{E}\left(\mathrm{R}_{\mathrm{M}}\right)-\mathrm{R}_{\mathrm{F}}\right)} & \mathrm{SMB} & \mathrm{HML} \
\hline \text { Sensitivity } & \mathrm{b}_{\mathrm{i}}=0.60 & \mathrm{~s}_{\mathrm{i}}=-0.44 & \mathrm{~h}_{\mathrm{i}}=0.28 \
\hline \text { Risk premium } & 12.7 \% & -2.17 \% & 3.25 \% \
\hline
\end{array}$
-An asset has the above sensitivity to the market portfolio and the risk-free rate is 6%.If an investor uses the CAPM model,but the Fama-French model is the correct model,by how much is the asset's expected return differ?

A) $ 1.2 \% $
B) $ 0.9 \% $
C) $ 3.1 \% $
D) $ 4.5 \% $

Question

$\begin{array}{|l|l|l|l|}
\hline \text { Factor } & {\left[\mathrm{E}\left(\mathrm{R}_{\mathrm{M}}\right)-\mathrm{R}_{\mathrm{F}}\right)} & \mathrm{SMB} & \mathrm{HML} \
\hline \text { Sensitivity } & \mathrm{b}_{\mathrm{i}}=0.60 & \mathrm{~s}_{\mathrm{i}}=-0.44 & \mathrm{~h}_{\mathrm{i}}=0.28 \
\hline \text { Risk premium } & 12.7 \% & -2.17 \% & 3.25 \% \
\hline
\end{array}$
-An asset has the above sensitivity to the market portfolio and the risk-free rate is 6%.If an investor uses the CAPM model,but the Fama-French model is the correct model,by how much is the asset's expected return differ?

A) $ 1.2 \% $
B) $ 0.9 \% $
C) $ 3.1 \% $
D) $ 4.5 \% $

Quizplus · Accepted Answer

Using equation 9.8,which can be expressed as E(R_i)= R_f + F1F1F1S1F1F1F10_i[(R_m)- R_f] + s_iE(SMB)+ h_iE(HML),the expected return can be calculated as E(R)= 0.06 + 0.60(0.127)- 0.44(-0.0217)+ 0.28(0.0325)= 0.1448 or 14.5%.Hence,the Fama-French expected return is 14.5%.Using the CAPM (see the case study on page 283),which can be expressed as E(R_i)= R_f + F1F1F1S1F1F1F10_i[(R_m)- R_f],the expected return can be calculated as E(R)= 0.06 +0.60(0.127)= 0.136 or 13.6%.Therefore,the CAPM understates the true expected return by 0.145 - 0.136 = 0.009 or 0.9%.

-An Asset Has the Above Sensitivity to the Market Portfolio