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Sales & Trading · Topic lesson

Mental Math

The two drills a trading floor runs in its head: percentages and fractions by recognition rather than calculation, and compounding by counting doublings with the rule of 72, with live numbers to practice on.

2 chapters About 20 minutes0 of 2 complete
Start chapter 1

Mental math on a trading floor is not about being a calculator. It is about recognizing shapes so that the arithmetic takes no attention: 12.5% is an eighth, a 25% rise needs a 20% fall to undo, one basis point on a million is a hundred dollars, and 8% for 27 years is three doublings. Interviewers ask these to see whether you reach for a shape or start multiplying, and they ask them fast.

The method from the old lesson survives as the habit. Say the units first, choose an anchor, calculate, sanity-check the order of magnitude, and say how exact you are being. Rounding is fine when it is stated; false precision and missing units are not. A yield, a price, a notional and a P&L each have their own unit, and translating between them consistently is most of the job.

  • Percentages and fractions. A percentage of a number by decomposition, a change from the start, the original before a rise, a rise then a fall, fractions as percentages, basis points on a notional, the fall that undoes a rise, which of four is largest.
  • The rule of 72. Doubling time and the exact answer, the rate to double in a given time, k-fold growth in doublings, a future value by counting, one rate against another, inflation's halving time, where the rule errs.
The rule that runs through both

Turn the question into something you already know. A percentage into tenths and eighths; a change into a factor; a compounding problem into a count of doublings. The calculation is then recall, and the sanity check is the only thinking left.

How to answer a floor arithmetic question

Each step points to the chapter that practices it.

  1. 1
    Say the units

    Percent, basis points, dollars, years.

    Chapter 1Chapter 2
  2. 2
    Find the shape

    An eighth; a factor; a doubling.

    Chapter 1Chapter 2
  3. 3
    Calculate from the anchor

    10% and 5%; 1 bp on $1M; 72 ÷ rate.

    Chapter 1Chapter 2
  4. 4
    Sanity-check the magnitude

    A 25% rise cannot be undone by 25%; three doublings is eight times.

    Chapter 1Chapter 2
  5. 5
    State the exactness

    "About nine years; exactly 9.01."

    Chapter 2

Chapters

1

Percentages and fractions: recognize, do not compute

10 min

On a floor, percentages are done in your head and fast, and the trick is never to calculate what you can recognize. An eighth, ten plus five plus two and a half, a rise that a smaller fall undoes: hold a few shapes and most questions are recall.

  • Take a percentage of a number by decomposing it into pieces you know
  • Compute a percentage change from the starting value, and undo one from the ending value
  • Chain a rise and a fall by multiplying factors, not adding percentages
  • Convert fractions and basis points instantly
2

The rule of 72: compounding in doublings

10 min

Compounding is hard in your head and easy in doublings. Money at r percent doubles in about 72 ÷ r years; once you count doublings, 8% for 27 years is three of them, so eight times. Know where the rule is off before you quote it.

  • Estimate a doubling time from a rate, and a rate from a doubling time, and know the exact versions
  • Estimate a future value by counting doublings
  • Apply the rule to inflation: the halving time of purchasing power
  • Say which way the rule errs at low and high rates