A trade is priced at 18 basis points on a notional of $2.4bn. How many dollars is that? Show the scaling you used rather than a long multiplication.

A trade is priced at 18 basis points on a notional of $2.4bn. How many dollars is that? Show the scaling you used rather than a long multiplication.

Approach: Fix the value of one basis point on a round notional first, then multiply by the quoted number of points, keeping mantissa and exponent separate.

4320000. One basis point is 0.0001, so one basis point on $1bn is $100000. On a notional of $2.4bn a basis point is $240000, and 18 basis points is 18 * 240000, which is 4320000 dollars. Doing it by scaling powers of ten separately removes the decimal errors: 2.4 * 10^9 * 18 * 10^{-4} = 2.4 * 18 * 10^5 = 43.2 * 10^5. The anchor worth memorising is that a basis point on a billion is a hundred thousand dollars, so any notional quoted in billions converts by inspection. The same anchor prices a bid-offer of half a basis point on $500m at $25000 a round turn.

Follow-up: The same trade is 18 bp on $2.4bn but settles in a currency at 1.28 to the dollar. What is the cost in that currency?

Key concepts: basis point, notional, scaling powers of ten.