Christoph of Blade Capital now believes the Swiss franc will appreciate versus the US dollar in the coming three$-$month period. He has $$100,000$ to invest. The current spot rate is $$0\mathrm{.}5820/$SF$,$ the three$-$month forward rate is $$0\mathrm{.}5640/$SF$,$ and he expects the spot rates to reach $$0\mathrm{.}6250/$SF in three months.

a$.$ Calculate Christoph's expected profit assuming a pure spot market speculation strategy.

b$.$ Calculate Christoph's expected profit assuming he buys or sells SF three months forward. Which option $($a or b$)$ will Christoph choose? Why?