PLEASE ANSWER ALL QUESTIONS

Q$5.$

On OCT $10,2024$ a portfolio manager, PM$,$ observes that the DJIA $=42,454\mathrm{.}12.$ PM decides to hedge his portfolio using the Micro$-$Mini DJIA futures for the next $4$ months. On $10\mathrm{.}10\mathrm{.}2024$ the Micro$-$Mini DJIA value is $43,155\mathrm{.}75$ for delivery on MAR $2025.$ Moreover, PM$\text{'}$s portfolio's Beta with the Micro$-$Mini DJIA is $\backslash (\backslash$beta$=1\mathrm{.}5\backslash ).$

Given that the current PM$\text{'}$s portfolio market value is $\backslash (\backslash$$ $431,557\mathrm{.}50\backslash )$ and that the Dollar multiplier of the Micro$-$Mini DJIA is: $\backslash (\backslash$$ M$=\backslash$$ $\mathrm{.}50\backslash ),$ use a time table to describe the hedge that PM opens on $10/10/2024$ in order to hedge the portfolio value.

Q$6.$ On the same time table from Q$5.$ show the result of the hedge on February $152025$ when PM closes the hedge. On that day PM$\text{'}$s portfolio spot value is $\backslash (\backslash$$ $370,540\mathrm{.}00\backslash )$ and the Micro$-$Mini DJIA futures for MAR $2025$ is $38,804\mathrm{.}20.$ Calculate PM$\text{'}$s portfolio value with the P$/$L from the futures market.