Assume that the market is in equilibrium and that stock betas can be estimated with historical data.The returns on the market,the returns on United Fund (UF) ,the risk-free rate,and the required return on the United Fund are shown below.Based on this information,what is the required return on the market,r_M? $\begin{array} { l c r } \text { Year } & \text { Market }& { U F } \\ 2008& -9 \% & - 14 \% \\ 2009 & 11 \% & 16\% \\ 2010 & 15 \% & 22\% \\ 2011 & 5 \% & 7 \% \\ 2012 & - 1 \% & -2 \% \end{array}$
$\mathrm { r } _ { \mathrm { RF } : } \mathrm { 7.00 \%}$ $\quad$ $\quad$ $\quad$ $r _ { \text {United } } : 15.00 \%$

Question

Assume that the market is in equilibrium and that stock betas can be estimated with historical data.The returns on the market,the returns on United Fund (UF) ,the risk-free rate,and the required return on the United Fund are shown below.Based on this information,what is the required return on the market,r_M?

\begin{array} { l c r } \text { Year } & \text { Market }& { U F } \\ 2008& -9 \% & - 14 \% \\ 2009 & 11 \% & 16\% \\ 2010 & 15 \% & 22\% \\ 2011 & 5 \% & 7 \% \\ 2012 & - 1 \% & -2 \% \end{array}

\mathrm { r } _ { \mathrm { RF } : } \mathrm { 7.00 \%}

\quad

\quad

\quad

r _ { \text {United } } : 15.00 \%

Quizplus · Accepted Answer

The following graph shows that United's returns are perfectly correlated with the market. 11ea42d0_c0ac_c42d_9abf_c7b725a09b6b_TB2090_00 
 $$\begin{array} { l l } 
\mathrm { r } _ { \mathrm { RF } } : & 7.010 \% \
\mathrm { r } _ { \mathrm { United } } : & 1500 \%
\end{array}$$ 1. Find beta: We faund beta using Eacel but it caula be faund nith a calculatar ar using the rise-cver-run method as shown below:
$\frac { \text { Rise } } { \text { Run } } = \frac { 22 - 16 } { 15 - 11 } = \frac { 6 } { 4 } = \mathrm { b } = 1.5$
2. NaW Eind RPM
$\begin{array} { l } 
r _ { 5 } = 15 \% = 7 \% + 1.5 \left( R P _ { M } \right) \
R P _ { M } = ( 15 - 7 ) 11.5 = 5.33 \%
\end{array}$
3. Find $r _ { M : } r _ { M } = r _ { R F } + R P _ { M } = 12.33 \%$

Assume That the Market Is in Equilibrium and That Stock