What on earth can Kirk Caldwell possibly be doing for Territorial Savings Bank?

Caldwell’s compensation for his primary gig — Honolulu mayor — comes in at $164,928. He spends typically two of the vacation hours he accrues each month fulfilling his duties as a member of the Territorial board of directors.

For which he makes somewhere between $200,000 and $299,999 a year. We don’t know the exact dollar figure because the disclosure forms on file with the Honolulu Ethics Commission simply require that he specify a salary range.

But that would translate into somewhere between $8,333 and $12,500 an hour based on 24 vacation hours a year — not bad work, if you can get it.

We don’t mean to suggest that Caldwell is doing anything untoward or otherwise compromising his position in City Hall although, frankly, we don’t really know. Caldwell has pointed out that his work with Territorial has been reviewed twice before by the city Ethics Commission — once when he was the city’s managing director — and judged to pose no conflict of interest. The city has no financial holdings with Territorial, and the bank doesn’t do business with the city.

But his Territorial role has become a point of controversy in his re-election campaign, with his two top opponents calling his board membership into question. No matter what Caldwell’s justification for the work might be, it looks questionable. How can he earn a bigger paycheck from an organization to which he devotes a few hours a month than from the City and County of Honolulu where leadership is more than a full-time job?

When the issue came up during an Aug. 2 debate, Caldwell explained he was asked to join the Territorial board years ago because he “understand(s) their business very well” and that the bank is “getting the same thing from me as when I served on the board prior to me becoming mayor.”

Which is what, exactly?

For the city’s top elected official in a position of public trust, avoiding the appearance of impropriety is as important as avoiding actual impropriety.

Despite the ethics opinion and the fact that he’s held this position for some time, the public scrutiny Caldwell is facing is new. In a race in which the mayor’s oversight for the city Ethics Commission is already a major issue, he should neither be surprised that the matter has come up nor that the size of compensation has raised more than a few eyebrows.

And it’s not just the size, but the fact that his Territorial compensation is going up. Only six years ago, Caldwell reported the range of that compensation as $25,000 to $49,999. Now, the reports show, it’s at least $200,000 and maybe closer to $300,000.

Those are big numbers, and the explanation for them may be entirely reasonable. But for the city’s top elected official in a position of public trust, avoiding the appearance of impropriety is as important as avoiding actual impropriety.

Caldwell would do well to provide a more thorough accounting of his board position. A couple of opinions from the ethics office and the very general explanation he’s offered thus far may not pass the smell test, leaving voters with unanswered questions at a time when those answers may really matter.