PRACTICE GUIDE TOWER RESEARCH
Tower Research Stochastic Processes Practice Test
This guide offers stochastic processes preparation for readers interested in Tower Research Capital. The general practice ranges below are not a verified assessment specification for that employer.
Those are ranges across firms running this format rather than Tower Research Capital's own figures, so treat them as the shape to train against and check the instruction screen on the day for the marking rule.
These are Outcry preparation topics, not a verified current firm assessment specification. Check your role-specific invitation for the test, timing, tools and recruitment stage.
Outcry is not affiliated with Tower Research Capital 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 Tower Research Capital’s own.
What it screens
A quantitative trading firm whose public careers material covers trading, research and engineering.
- ✓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 Tower Research Capital
A quantitative trading firm whose public careers material covers trading, research and engineering. The topics here are Outcry preparation suggestions, not a verified firm syllabus or recruiting stage.
Outcry also has 2 other topic guides for readers interested in Tower Research Capital. Their presence does not mean applicants must sit that many tests or that they belong to one recruiting round.
The format
These are general practice ranges, not a verified current assessment specification for Tower Research Capital. Check the employer’s invitation for the actual format.
| 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 | Preparation topics · employer round unconfirmed |
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 Tower Research Capital’s.
Markov chains
Transition matrices, absorbing states, and expected time to absorption.
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.
Inference and research integrity
What a result means, and what it would take for it to mean nothing.
Example
A Monte Carlo estimate uses 900 paths. Roughly how many are needed to halve the standard error?
- 3600
- 1800
- 14400
- 450
Answer 3600
Standard error scales as 1/√n, so cutting it in half needs four times the paths: 3600.
Applied statistics
Regression identities, standard errors, and reading a coefficient correctly.
Example
A research group tests signals of which 5% are genuinely predictive. The tests run at the 5% level and have 60% power against the effects that are real. Of the signals that come back significant, what percentage are genuinely predictive? Answer as a percentage.
Answer 39
Take 1,000 signals. 50 are real and 30 of those are detected. 950 are null and 48 of those are flagged anyway. The significant pile holds 78 signals, of which 30 are real: 39%. The argument: the 5% level controls P(flag | null), which is not what anyone wants to know. What matters is P(real | flag), and turning the conditional round needs the base rate. When only 5% of the hypotheses are true, the null pool is 19 times larger, so even a small false positive rate on a large pool competes with a good detection rate on a small one. Raising power helps the numerator; lowering the level or testing better hypotheses helps more, because both attack the denominator.
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
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.
Overfitting and multiple testing
Why a result at the five per cent level means very little after the twentieth test.
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.
What a good score looks like
No current employer cutoff is verified for these general practice ranges. Use the worked examples to identify what to study and check your role-specific invitation for the actual assessment rules.
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 Tower Research Capital
Common questions
- Is the Tower Research stochastic processes test multiple choice?
- This guide uses multiple choice or short typed answer for practice. The employer’s current answer format was not verified here.
- How long is the Tower Research stochastic processes test?
- This guide uses general practice ranges of 10 to 15 questions in 30 to 60 minutes. They are not a verified current employer format.
- Is there negative marking on the Tower Research 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?
- The warm-up drills are free with no account, and every pass opens the rest of the drills linked on this page. Questions are generated fresh each run, so there is nothing to memorise between attempts.