Times Three: The Multiplier Nobody Derived

The capital standing behind the world's trading books is set by the Basel Committee's January 1996 market-risk formula: the higher of the previous day's value-at-risk and a multiplication factor times the sixty-business-day average value-at-risk. The formula carries two numbers nobody derived. The multiplication factor is floored at 3 ('subject to an absolute minimum of 3'), presented in the Committee's documents as supervisory judgment with no derivation anywhere in the record, plus a backtesting plus-factor (green 0-4 exceptions +0.00; 5 +0.40; 6 +0.50; 7 +0.65; 8 +0.75; 9 +0.85; red 10 or more +1.00). The ten-day holding period is reached from one-day value-at-risk by the square root of time, exact only for independent Gaussian returns, a premise volatility clustering falsifies (Diebold and co-authors: the conversion is inappropriate except under very special circumstances routinely violated in practice; Danielsson and Zigrand: systematically underestimates risk under jumps). The production notebook recomputes every cumulative probability in the Committee's backtesting table from Binomial(250, 0.01) and matches all eleven values (0 exceptions 8.11 percent through 9 exceptions 99.97 percent); a correct model still lands outside the green zone with probability about 10.8 percent in any 250-day window. Basel II paragraph 718 carried the floor of 3 forward verbatim; the Fundamental Review of the Trading Book later replaced the machinery (expected shortfall, desk-level approval, asset-class liquidity horizons) rather than deriving either number. Grade: TWO IMPORTED NUMBERS SET THE WORLD'S TRADING CAPITAL — ONE A JUDGMENT SPENT AS A CONSTANT, ONE A SQUARE ROOT SPENT AS A LAW. This paper belongs to the breadth program of the author's corpus; it touches no claim of the physics core.