A market maker quotes 4000 symbols, averages 900 trades per symbol per day, and the average trade is $8000 of notional. What is the daily traded notional in billions of dollars?

A market maker quotes 4000 symbols, averages 900 trades per symbol per day, and the average trade is $8000 of notional. What is the daily traded notional in billions of dollars?

Approach: Separate every factor into a leading digit and a power of ten, multiply the leading digits together and add the exponents, keeping the two apart until the last step.

28.8. Chain the factors as an order of magnitude calculation rather than multiplying digit by digit. The trade count is 4 * 10^3 * 9 * 10^2 = 36 * 10^5 = 3.6 * 10^6 trades a day, and each trade is 8 * 10^3 dollars, so the daily notional carries the mantissa 3.6 * 8 = 28.8 against an exponent of 10^9, which is $28.8bn a day. The annual figure follows as 28.8 * 252, split as 28.8 * 250 = 7200 plus 28.8 * 2 = 57.6. That totals $7.26 trillion. Keeping the mantissa and exponent apart is what makes a four factor chained estimate safe under a clock, since every error of a factor of ten comes from miscounting the exponent and never from the leading digits.

Follow-up: The firm captures 0.4 basis points of the notional it trades and pays $0.03 of fees per trade. What is the daily net revenue?

Key concepts: order of magnitude, mantissa and exponent, chained estimate.