PRACTICE GUIDE BELVEDERE TRADING
Belvedere Trading Probability and Logic: what the test is, and how to train for it
The Belvedere Trading probability and logic screen is 14 questions in 25 minutes - about 1.8 minutes each - answered by typing the number, with no calculator. There is no negative marking, so leaving an item blank gains you nothing over guessing.
Where it sits: Probability and logic section. The practice sitting on this page runs the same item count, the same clock and the same marking rule, with questions generated by Outcry rather than taken from Belvedere Trading.
Outcry is not affiliated with Belvedere Trading and has no access to their assessment content. This guide describes an assessment format that candidates report publicly; the questions here are generated by Outcry and are not Belvedere Trading’s own.
What it screens
A Chicago-based proprietary trading firm specialising in options market making and derivatives strategies.
- ✓Expected value computed fast and used to make a decision
- ✓Conditional probability and Bayes updates without formal notation
- ✓Ranking likelihoods rather than computing them exactly
- ✓Fermi estimation: decomposing an impossible question into three easy ones
Where it sits at Belvedere Trading
This section does not arrive on its own. It opens the paper, and the sitting around it runs 55 minutes and 16 items in total, with Coding challenge on the same continuous clock. Candidates who prepare only for this round tend to be caught by the pacing of the rest.
There is no going back. You answer or skip, and the next item loads, which means the decision to leave an item is final at the moment you make it.
The format
These are the numbers the Belvedere Trading sitting on this site runs on, matching the format candidates report.
| Questions | 14 |
|---|---|
| Time | 25 minutes |
| Per question | 1.8 minutes |
| Negative marking | No |
| Answer style | Typed numeric answer, no calculator |
| Where it sits | Probability and logic section |
What it tests, with a worked example
Every example below is generated by Outcry, drawn from the same question generators the timed drills run. None of them is Belvedere Trading’s.
Expected value and odds
Pricing a bet, converting between odds and probabilities, and deciding whether to take it.
Example
You roll a fair die 3 times. Probability of at least one six?
- 50%
- 32.1%
- 42.1%
- 0.5%
Answer 42.1%
Complement: 1 − (5/6)^3 = 42.1%. Adding 1/6 each time double-counts.
Conditional probability
Bayes' rule in disguise: a test result, a signal, a drawn card, and what it implies.
Example
A strategy's daily returns over n days average x̄ with sample standard deviation s. Which statistic tests whether the true mean return is zero?
- x̄ / (s/√n)
- x̄·√n / s²
- (x̄ − s) / n
- x̄ / s
Answer x̄ / (s/√n)
The one-sample t-statistic divides the observed mean by its standard error s/√n. Dividing by s alone ignores how the estimate sharpens with n.
Estimation under uncertainty
A number nobody knows exactly, reasoned to the right order of magnitude out loud.
Example
4 crates arrive at a receiving dock holding spacers, shims, gaskets and bolts, one content each. Each crate carries a label naming one of those 4 contents, no two labels the same, and every label is on the wrong crate. Opening a crate shows what is in it. How many crates must be opened, in the worst case, to relabel all 4 correctly?
Answer 2
The label-to-contents map is a permutation with no fixed point, and there are 9 of those on 4 items. Opening a crate reveals its contents and splits the live set; picking the next crate after seeing the last result, a minimax search over every opening order gives 2 as the worst case. With 4 = 3 the two possible arrangements are the two rotations, and one look separates them. The general pattern: the last two crates settle themselves only when the two contents left both clash with their own labels.
Ranking outcomes
Ordering several events by likelihood, where only the exact order scores.
Example
An index fund charges 5 basis points a year and keeps 3.0% of assets in non-interest-bearing cash. The index returns 6.0% over the year. What is the tracking difference in basis points, as a signed number?
Answer -23
Tracking difference is the fund's return less the index's. The invested 97.0% earns the index return and the cash earns nothing, so the drag is 3.0% x 6.0% = 0.1800%, or 18.00 basis points. The fee takes another 5 basis points. Together the fund returns 6.0% - 0.05% - 0.1800% = 5.7700%, a tracking difference of -23.00 basis points. Cash drag hurts in a rising market and the fee is the only part that costs the same whatever the market does. Tracking difference is the realised gap; tracking ERROR is the volatility of that gap and is a different number.
Waiting times and repeated trials
How long until the first success, and why the answer is rarely the average you expected.
Example 1
How many digits does 50! have?
Answer 65
Stirling: log10(50!) ≈ 50·log10(50/e) + ½·log10(2π·50) = 63.23 + 1.25 = 64.48, so 65 digits.
Example 2
How many observations are needed for a 95% confidence interval of half-width 2.5, when the standard deviation is 25?
Answer 385
n = (1.96σ/w)². Call it 2: (2 × 25/2.5)² = 400, which overshoots by 4%.
Example 3
A trading floor has 40 people on it. What is the chance that at least two share a birthday, as a percentage?
Answer 89
There are C(40,2) = 780 pairs, each matching with probability 1/365. P(none) ≈ e^−2.14 ≈ 0.12, so about 88%.
Symmetry arguments
Questions that collapse to one line once you notice the two cases are mirror images.
Example
Three fair dice are rolled. How many of the 216 ordered outcomes total 7?
Answer 15
Counting ordered triples summing to 7 gives 15, so the chance is 15/216 = 6.9%.
What a good score looks like
On a paper of 14 questions with no penalty for a wrong answer, the only thing an unanswered question can do is cost you. Probability rounds are usually marked as part of a wider battery, so a standalone threshold is rarely reported. Where candidates do describe one it clusters around getting two thirds of the items right, with the caveat that these sections are short enough that two mistakes move you a long way.
How to train for it
- 01Practise setting up before calculating. Most wrong answers on these are a correct calculation of the wrong quantity.
- 02Sanity-check the magnitude before committing. A probability above one or an expectation outside the range of outcomes is a caught error, and these papers plant both as options.
- 03Work the complement first whenever the question says at least or at most. It is usually the shorter route and it is almost always the intended one.
TRAIN IT HERE
The drills that match each section
Likelihood Ranking
Order events from most to least likely - the exact screen-question format.
Fermi Estimation
Piano tuners in Chicago, atoms in a body - scored on order of magnitude.
Quitters Never Lose
A casino stopping-strategy game that is secretly a martingale lesson.
Tail Risk
Rare events and fat tails, and what they do to a plain expected-value estimate.
SIT THE FULL BATTERY
All the sections back to back on one clock, marked the way the real screen marks them, with a by-skill breakdown at the end. Included with any pass.
Also reported at Belvedere Trading
Common questions
- Is the Belvedere Trading probability and logic test multiple choice?
- Typed numeric answer, no calculator. You type the number, so there is nothing to eliminate your way to.
- How long is the Belvedere Trading probability and logic test?
- 14 questions in 25 minutes, which is about 1.8 minutes each.
- Is there negative marking on the Belvedere Trading probability and logic test?
- No. A wrong answer costs nothing beyond the mark you would have earned, so leaving an item blank is never better than guessing at it.
- How do I practise for it free?
- Every drill linked on this page is free to play, with no account, inside a daily run cap. Questions are generated fresh each run, so there is nothing to memorise between attempts. The full Belvedere Technical Challenge sitting puts the sections back to back on one clock.