PRACTICE GUIDE FIVE RINGS
Five Rings Stochastic Processes Practice Test
Five Rings does not publish the shape of its stochastic processes screen, and candidates describe it as 10 to 15 questions in 30 to 60 minutes, roughly two to five minutes per question, answered by picking one of the options.
Those are ranges across firms running this format rather than Five Rings's own figures, so treat them as the shape to train against and check the instruction screen on the day for the marking rule.
Outcry is not affiliated with Five Rings 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 Five Rings’s own.
What it screens
A proprietary trading firm in New York known for a heavily games- and puzzle-based interview style.
- ✓Martingale arguments and optional stopping applied to games
- ✓Gambler's ruin: absorption probabilities and expected duration
- ✓Recognising when a process is a martingale (and when the argument breaks)
- ✓Random-walk intuition: recurrence, drift, and scaling
Where it sits at Five Rings
A proprietary trading firm in New York known for a heavily games- and puzzle-based interview style. What that means for the screen is that the questions tend to be drawn from the work rather than from a textbook, so the format below is the shape to train against rather than a syllabus.
Candidates also report 3 other screens at Five Rings, covered separately on this site. Where a firm runs several, they usually sit in one round rather than spread across the process, so the pacing of the whole set matters more than any single section.
The format
Five Rings does not publish this screen's shape, and it varies between firms, so these are the ranges candidates report rather than exact figures.
| Questions | 10 to 15 |
|---|---|
| Time | 30 to 60 minutes |
| Per question | two to five minutes |
| Negative marking | No |
| Answer style | Multiple choice or short typed answer |
| Where it sits | Research-track screen, before the technical interviews |
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 Five Rings’s.
Markov chains
Transition matrices, absorbing states, and expected time to absorption.
Example
Two venues fill orders as independent Poisson processes, 5 and 3 per minute. Each fill is front-month with probability 0.5, independently of everything else. What is the arrival rate of front-month fills per minute?
- 8
- 4
- 2.5
- 2
Answer 4
Superposition: two independent Poisson streams merge into one Poisson stream at 5 + 3 = 8 per minute. Thinning by an independent coin keeps it Poisson, at 8 × 0.5 = 4 per minute. The rates add - they are not averaged, and the quiet venue does not drop out.
Random walks and martingales
Stopping times, the optional stopping theorem, and gambler's ruin.
Example
You draw 5 values independently and uniformly from [0, 1]. What is the expected value of the maximum?
- 1/5
- 4/5
- 1/2
- 5/6
Answer 5/6
For the maximum of n iid Uniform(0,1) draws, E[max] = n/(n+1) = 5/6.
Inference and research integrity
What a result means, and what it would take for it to mean nothing.
Example
A universe is built from firms currently in the index. What does this omit?
- Firms with high volatility
- Firms that were delisted or went bankrupt
- Firms that outperformed
- Nothing - the index is complete
Answer Firms that were delisted or went bankrupt
Survivorship bias: the losers left the index and dropped out of the sample, inflating measured returns.
Applied statistics
Regression identities, standard errors, and reading a coefficient correctly.
Example
A strategy has a true annual Sharpe ratio of 0.8. How many years of returns are needed before its t-statistic against zero reaches 2.5?
Answer 9.8
The t-statistic of a mean return over T years is the Sharpe ratio times √T, so T = (t/S)² = (2.5/0.8)² = 9.8 years. The argument: a Sharpe ratio IS a t-statistic per unit of time, which is why the sample size needed scales with the inverse square of it. At Sharpe 0.8 the answer is 9.8 years, and that is under the generous assumptions - returns independent, the edge constant, no regime change, and nobody looking at the data until the end. Any of those failing pushes the requirement up. This is the arithmetic that makes track records nearly useless as evidence at low Sharpe, and it is the reason research groups reach for higher-frequency data where the same edge produces many more independent observations per year.
Stating assumptions
Research screens mark the assumption you named as much as the number you produced.
Conditional expectation
Tower property and the expectation of a stopped process, which is most of what these rounds ask.
Example
Fills arrive at a mean of 12 per hour. Each fill is 2 lots or 4 lots with equal probability, independent of how many fills arrive. What is the expected total lots in an hour?
Answer 36
Condition on the number of fills N. Each fill averages (2 + 4)/2 = 3 lots, so E[lots | N = n] = 3n. The tower rule takes the expectation of that: E[lots] = 3 × E[N] = 3 × 12 = 36.
What a good score looks like
Research screens are marked by a person more often than a machine, so a numeric cutoff is rarely visible. Candidates consistently report that a wrong answer with a stated assumption scores better than a right answer with none.
How to train for it
- 01Practise writing the assumption down first. It is the part these screens grade and the part people skip.
- 02Say what would falsify the result. Research screens are looking for the person who reaches for that first, and it is the cheapest habit to build.
- 03Get comfortable with conditional expectation specifically. More of these rounds reduce to the tower property than to anything else.
TRAIN IT HERE
The drills that match each section
Martingale Mutiny
Optional stopping played as a game. Try to find a betting strategy that beats a fair coin.
Ruin Walker
Gambler's ruin with live absorption probabilities.
Distribution Lab
Recognise a distribution from how its samples behave.
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 Five Rings
Common questions
- Is the Five Rings stochastic processes test multiple choice?
- Reported as multiple choice or short typed answer. Formats move, so treat this as the shape rather than a guarantee.
- How long is the Five Rings stochastic processes test?
- Candidates report 10 to 15 questions in 30 to 60 minutes, roughly two to five minutes per question.
- Is there negative marking on the Five Rings stochastic processes 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.