September $2025.$

futures contract: futures price $=$ $$4\mathrm{.}66/$bu$,$ brokerage fee $=$ $$0\mathrm{.}01/$bu

put: strike $=$ $$4\mathrm{.}70/$bu$,$ premium $=$ $$0\mathrm{.}19/$bu$,$ brokerage fee $=$ $$0\mathrm{.}01/$bu

forward contract: price $=$ $$4\mathrm{.}00/$bu$,$ service fee $=$ $$0\mathrm{.}01/$bu

HTA contract: service fee $=$ $$0\mathrm{.}04/$bu

basis contract: basis $=-$$$0\mathrm{.}20/$bu$,$ service fee $=$ $$0\mathrm{.}03/$bu

minimum price contract: minimum price $=$ $$4\mathrm{.}30/$bu$,$ service fee $=$ $$0\mathrm{.}20/$bu

Based on these, calculate the prices that you expected to receive with each contract and then discuss the following points.

$($a$)$ If you believed the futures price was going to go up after September $2025($i$.$e$.$ increase beyond $$4\mathrm{.}66/$bu$),$ which contract$($s$)$ would have given you the best opportunities to obtain higher prices? And which contracts would have exposed you to more risk of ending up with lower prices?

$($b$)$ If you believed the futures price was going to go down after September $2025($i$.$e$.$ decrease below $$4\mathrm{.}66/$bu$),$ which contract$($s$)$ would have given you the best opportunities to protect against $($or avoid$)$ lower prices? And which contracts would have exposed you to more risk of ending up with lower prices?