Role of Mental Math and Reaction Speed

Mental arithmetic is tested because it is used. Not as a proxy for intelligence, but because the calculations below happen continuously, in seconds, while other things demand your attention.

The calculations that actually occur

Spread and mid. Given 99.87 bid at 100.13, the mid is 100.00 and the spread is 26 cents. Instant, every time you look at a book.

Position value and P&L. Long 2,300 at 45.60, now 45.72: that is 12 cents on 2,300, so $276. No hesitation.

Fractions to decimals. Several markets quote in eighths, sixteenths or thirty-seconds. $\frac{5}{8} = 0.625$ and $\frac{11}{32} = 0.34375$ should be recall, not computation.

Expected value. A bet paying $70 with probability 0.4 and losing $30 otherwise: $0.4 \times 70 - 0.6 \times 30 = 28 - 18 = 10$. This is the core of every pricing question you will be asked.

Percentage moves. 3% of 847 is about 25. Interviewers ask for a fast approximation, not a precise answer, and saying "roughly 25" quickly beats saying "25.41" slowly.

Approximations worth knowing

so a 2% return compounded 5 times is roughly 10.4%, and the approximation gives 10%, close enough for a quote.

The rule of 72: doubling time at $r\%$ growth is about $\frac{72}{r}$ years.

Square roots to two significant figures, since $\sigma\sqrt{T}$ appears constantly. Knowing $\sqrt{252} \approx 15.9$ and $\sqrt{21} \approx 4.6$ saves real time when scaling volatility.

Percentage of a percentage: 15% of 80 is the same as 80% of 15, which is 12. Swapping the terms often makes it trivial.

Reaction speed

A separate skill: the delay between recognising a change and acting.

Most of what looks like fast reaction is actually prepared response. Experienced traders have already decided what to do if volatility spikes or if they are lifted three times running, so the moment requires recognition rather than deliberation. That is trainable by rehearsing scenarios, not by trying to think faster.

What speed does not do

It does not create edge. A fast trader with a wrong fair value loses money faster than a slow one.

The ordering matters: get the price right, then get it right quickly. Candidates who optimise for speed at the cost of accuracy do poorly in interviews, because a confidently wrong quote is worse than a slightly slow correct one.

Practising

Little and often, because these skills decay. Ten minutes daily does more than an hour once a week.