The National Australia Bank in Australia has a bid price of A$$0\mathrm{.}2409$ and an ask price of A$$0\mathrm{.}2664$ for Hong Kong dollars. The HSBC Bank in Hong Kong has a bid price of A$$0\mathrm{.}2044$ and an ask price of A$$0\mathrm{.}2271$ for Hong Kong dollars.

$($a$)$ Can you make a locational arbitrage profit?

$($b$)$ If the answer to $($a$)$ is yes, what is the arbitrage profit if you have A$$1$ million?