$2$ Event Study $(50$ points$)$

Consider a stock that responded to a certain event by gaining $0\mathrm{.}5\%$ on the day before the

announcement, $1\mathrm{.}25\%$ at the announcement date, and $0\mathrm{.}75\%$ on the following day. On the

same dates, the market return was $0\mathrm{.}2\%,0\mathrm{.}4\%,$ and $-0\mathrm{.}1\%,$ respectively. The risk$-$free rate

was constant at $0\mathrm{.}05\%.$ Assume that the event window includes all three days and the

standard deviation of the stock return in the pre$-$event window is $5\mathrm{.}2\%$ per month.

The market model estimated for the stock in the pre$-$event window yields

Rett $$ RFt $=0\mathrm{.}12$

$(0\mathrm{.}09)+1\mathrm{.}20$

$(0\mathrm{.}36)($M KTt $$ RFt$)+$ t$,$ R$2=0\mathrm{.}23$

i$.$ Use the market model to calculate the cumulative abnormal return to the stock in

the event window. $(5$ points$)$

ii$.$ Use the R$-$square of the market model to compute the daily standard deviation of

abnormal return $($aka regression residual$).$ Assume $22$ trading days per month.$(10$

points$)$

iii. Did the event have a statistically significant impact on the stock price? $(10$ points$)$

iv$.$ Use the market model to compute the daily standard deviation of the market port$-$

folio. $(10$ points$)$

v$.$ Was the event$-$window run$-$up for the market portfolio statistically significant?

$(10$ points$)$

vi$.$ Assume that returns above are the average for a portfolio of $100$ stocks that had

similar events and the $100$ event windows do not overlap. Assume also that the

standard deviation of returns and the parameters of the market model are the same

for all $100$ stocks. How does it change your answer to $($iii$)?(5$ points$)$

vii. Bonus question: Suppose someone tells you that volatility should be measured in

calendar time, not in trading time, because Saturdays and Sundays have the same

amount of news as business days, even though trading on the weekend news is delayed

until Monday. If you know that the event happened on Monday, how does it change

your answer to $($iii$)?$ Assume $30$ calendar days in a month. $(10$ points$)$

$2$