The Unit Trap Market

Question

“Make me a market on tomorrow's high temperature in this city, in Celsius.” You quote 18 / 22. “Fine, now make me the same market in Fahrenheit.” What must your new quote be, and what's the trap? (Still a live opener, it filters fast.)

Accepted Answer

Map both quote edges through the conversion F = frac95 C + 32: textbid: frac95(18) + 32 = 64.4, qquad textask: frac95(22) + 32 = 71.6. Your market must be 64.4 / 71.6. Anything else hands the interviewer a free round-trip: e.g., quoting a "round" 64/72 lets them buy your Celsius offer at 22 (= 71.6°F) and sell your Fahrenheit bid at... the consistency check is exactly what they run next. The traps, in the order candidates hit them: (1) converting the width by only multiplying by frac95 but re-centering wrong, the +32 moves both edges, it does NOT widen; (2) "rounding to clean numbers," which silently crosses your own book; (3) forgetting which leg is the bid after transformation (an increasing map preserves bid<ask; had the map been decreasing, say quoting in "degrees below boiling", the legs would swap). Why it persists in interviews: ten seconds of arithmetic exposes whether you treat your own quotes as one coherent book or as disconnected numbers. The grown-up version of the same reflex is quoting an asset and its future, or an FX pair and its inverse, consistency across representations is the first law of not getting arbitraged.

The Unit Trap Market

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