The dot-com crash began on 10 March 2000.
(a) Plot the price of Microsoft shares and the associated log returns. Verify that the biggest falls in the share price occurs in April 2000 where there is a negative return of \(42.07 \%\) for the month and that the large negative return of \(27.94 \%\) in December 2000 is followed by a correction of \(34.16 \%\) in January 2001.
(b) Estimate the CAPM model for Micosoft

\[
r_{i t}-r_{f t}=\beta_{0}+\beta_{1}\left(r_{m t}-r_{f t}\right)+u_{t}
\]

in which \(r_{f t}\) and \(r_{m t}\) are the risk free and market returns, respectively. Draw a line time series plot the residuals and see if these large returns are evident.
(c) Draw a histogram of the residuals with a normal distribution overlaid. Test the residuals for normality using a Jarque-Bera test. Comment on your results.
(d) Construct the dummy variables

\[
\begin{aligned}
& D_{1 t}= \begin{cases}1: & \text { Apr. } 2000 \\
0: & \text { Otherwise }\end{cases} \\
& D_{2 t}= \begin{cases}1: & \text { Dec. 2000 } \\
0: & \text { Otherwise }\end{cases} \\
& D_{3 t}= \begin{cases}1: & \text { Jan. } 2001 \\
0: & \text { Otherwise }\end{cases}
\end{aligned}
\]

Estimate the regression

\[
r_{i t}-r_{f t}=\beta_{0}+\beta_{1}\left(r_{m t}-r_{f t}\right)+\gamma_{1} D_{1 t}+\gamma_{2} D_{2 t}+\gamma_{3} D_{3 t}+u_{t}
\]

Comment on the results.
(e) Test the null hypothesis that all the \(\gamma_{i}\) coefficients are zero.
(f) Draw a histogram of the residuals with a normal distribution overlaid. Test the residuals for normality using a Jarque-Bera test. Compare these results with those in part (c).