High$-$Variance Margin Buying and Short Selling $(45$ points$)$ You are given the following information for two assets, one stock that is only available for purchase on margin $($long$)$ and another only available to short sell. Assume for each asset, a separate coin is flipped exactly one year from today and either the happy or sad state of the world is realized. Additional Information: The initial margin requirement $($IMR$)$ for both stocks is $\backslash (50\backslash \%\backslash ).$ The maintenance margin requirement $($MMR$)$ for the Long Stock is $\backslash (40\backslash \%\backslash )$ and the Short Stock is $\backslash (30\backslash \%\backslash ).$ In both cases you will always begin by borrowing the maximum allowed and we will assume any transaction, long or short, is for exactly $100$ shares. Question $1\mathrm{.}2$: $(15$ points$)$ For each stock, show whether the happy state and$/$or the sad state of the world will result in a margin call. Justify your answer by calculating the relevant thresholds. $($Hint: there are four possible stock$/$state combinations, but you may not have to calculate four thresholds$).$ High$-$Variance Margin Buying and Short Selling $(45$ points$)$

You are given the following information for two assets, one stock that is only available for purchase on margin $($long$)$ and another only available to short sell. Assume for each asset, a separate coin is flipped exactly one year from today and either the happy or sad state of the world is realized.

Additional Information: The initial margin requirement $($IMR$)$ for both stocks is $\backslash (50\backslash \%\backslash ).$ The maintenance margin requirement $($MMR$)$ for the Long Stock is $\backslash (40\backslash \%\backslash )$ and the Short Stock is $\backslash (30\backslash \%\backslash ).$ In both cases you will always begin by borrowing the maximum allowed and we will assume any transaction, long or short, is for exactly $100$ shares.

Question $1\mathrm{.}2$: $(15$ points$)$

For each stock, show whether the happy state and$/$or the sad state of the world will result in a margin call. Justify your answer by calculating the relevant thresholds. $($Hint: there are four possible stock$/$state combinations, but you may not have to calculate four thresholds$).$