The assumption that banks interest rate are only decided by RBA is not accurate, specially when a good chunk of banks funding is via external source. Banks require external funding because we don't have enough domestic savings.
Higher AUD helps in reducing inflation pressure to a great extent, But its kills our domestic business which are not prepared to handle dollar pority let alone higher aud.
The other side of the coin, ie RBA drops interest rate, is lower AUD, much higher inflation and not necessarily lower mortguage interest rates due to reliance on external funding.
