Owners of a salt mine can’t deduct hundreds of thousands of dollars in annual net losses from farming and training horses because those activities are a hobby, not a for-profit venture, the Second Circuit affirmed Thursday.

Joseph and Elaine Bucci, who own the Retsof Salt Mine in western New York, appealed the US Tax Court’s decision to deny their deduction claims, arguing the judge had applied the wrong legal standard when reviewing the profit motives of their equestrian activities. But that wasn’t so, the US Court of Appeals for the Second Circuit ruled.

“Although a reasonable expectation of profit is …