Now you're obligated to show them your bank accounts
Probably best if we clarified this hypothetical scenario a bit, and defined said "obligation".
Since you used past tense, we'll assume this request is made upon leaving a country. While I'm not a lawyer, if such a request was made, I presume a failure to fulfill such a request would at
worst potentially bar one from re-entering the country in the future. I'm
highly doubtful if 'failure to furnish financial information to an immigration officer' is considered a criminal offense
anywhere in the world... (happy to be proved otherwise of course)
From my experience, the only time one would be questioned on such matters is on the way
into a country, not the way out (I can't remember the last time an outbound immigration officer anywhere ever spoke a single word to me.. which explains why they're being slowly replaced by e-gates).
Generally speaking, on the way in, you need convincing proof of the tourist nature of your trip, and in some cases that can readily include bank statements (simply to show your ability to sustain yourself during the proposed stay; not your entire financial/trading history..). Now if you're hitting anywhere near 160 days in any one country, well you better have a
very convincing explanation... Worst case scenario, they don't believe you, you don't get admitted, and you fly somewhere else. While I'm sure this happens often, the only example I've personally heard of this happening to was a married couple trying to get into the US. The husband was American/wife was British. US customs felt they over-packed, thus weren't convinced the wife intended to return to Britain (not that I'd ever want to go back to Britain either!). So as a general tip - don't over-pack!
Lastly, funny you mention Australia & 160 days. I know a couple that goes there every year for roughly half the year (they own an investment property). While technically on tourist visas, they might as well be quasi-residents. Year after year, never an issue at the border.. As long as you're not overstaying your visa, not taking a job from a local, not causing a ruckus, do you honestly think any country really gives a damn beyond that?
I think countries will eventually expand tourist visas to include some type of 'personal online work' exception (rather than keeping it in this disapproved-but-semi-acknowledged grey area as it is now). Especially given the large and growing digital nomad trend. They tend to be very social-heavy types, thus a crackdown on online working tourists would likely backfire quite heavily.
), then perhaps you should consider never leaving the house and only owning bitcoins.. you'll certainly sleep easier that way.. 
