PRACTICE GUIDE HRT
HRT Stochastic Processes Practice Test
Hudson River Trading 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 Hudson River Trading'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 Hudson River 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 Hudson River Trading’s own.
What it screens
An automated trading firm known for research-driven strategies and a heavy C++ and algorithms bar.
- ✓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 Hudson River Trading
An automated trading firm known for research-driven strategies and a heavy C++ and algorithms bar. 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 2 other screens at Hudson River Trading, 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
Hudson River Trading 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 Hudson River Trading’s.
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.
Estimation and its failure modes
Bias, variance, and the ways a backtest lies to you.
Example
A strategy has a daily Sharpe ratio of 0.1. What is the annualised Sharpe, using 252 trading days?
- 25.2
- 1.2
- 1.59
- 0.1
Answer 1.59
Mean scales with the number of days and standard deviation with its square root, so the ratio scales with √252 ≈ 15.87: 0.1 × 15.87 = 1.59. Multiplying by 252 scales the numerator only and overstates the ratio by a factor of 15.87.
Applied statistics
Regression identities, standard errors, and reading a coefficient correctly.
Example
Daily P&L follows an AR(1) with lag-1 autocorrelation 0.1. The mean is tested against zero with the usual s/√n standard error, which assumes independence. By what factor is that standard error too small? Write the argument out.
Answer 1.11
For an AR(1), the variance of the sample mean is inflated by (1 + ρ)/(1 − ρ) = 1.1/0.9 = 1.22. The standard error is the square root of that, so it is understated by √1.22 = 1.11. The argument: s/√n counts n independent pieces of information, and positive autocorrelation means consecutive days partly repeat each other, so the true information content is nearer n/1.22 days. Every t-statistic built on the naive error is 1.11 times too large, which turns a t of 2.21 into a real t of 2. Note the direction: positive autocorrelation understates the error and manufactures significance, while NEGATIVE autocorrelation overstates it and hides real effects. Both are fixed by a HAC estimator, not by a bigger sample.
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
A trader starts with 3 chips and bets one chip at a time on a fair coin, stopping at 0 chips or at 16. What is the probability of reaching 16?
- 1/16
- 1/2
- 13/16
- 3/16
Answer 3/16
The chip count is a martingale under a fair bet and the stopping time is finite, so the expected value at the stop equals the start: P×16 + (1−P)×0 = 3. That gives P = 3/16 = 3/16 = 0.188. The coin being fair makes the game fair, not the two outcomes equally likely - the barriers are at different distances.
Overfitting and multiple testing
Why a result at the five per cent level means very little after the twentieth test.
Example
A return model fits 5 regressors on 120 observations and reports R² = 0.1. What is the adjusted R²?
- 0.138
- 0.1
- 0.058
- 0.061
Answer 0.061
Adjusted R² = 1 − (1 − R²)(n − 1)/(n − k − 1) = 1 − (1 − 0.1) × 119/114 = 0.061. R² can only rise when a regressor is added, however worthless, so the unadjusted 0.1 rewards throwing variables at the problem. The adjustment charges 5 degrees of freedom, and here it costs 0.039.
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
- 01Rebuild the standard results rather than memorising them - a two-state chain, gambler's ruin, the regression slope from correlation and standard deviations.
- 02Practise writing the assumption down first. It is the part these screens grade and the part people skip.
- 03Work under time, but slower than a trading screen. These reward a correct setup, not speed.
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 Hudson River Trading
Common questions
- Is the HRT 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 HRT 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 HRT 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.