WalzoneInterview Prep
📞 Interviewing soon? Practice with a realistic AI mock phone interview — it calls you, then scores you. First 15 min FREE →

155 Wall Street Quant Interview Questions and Answers

Quant & Finance · 155 questions, each with a full written answer — free, no sign-up.

Reading is step one. Saying it out loud is the interview. Our AI interviewer calls your phone and runs a realistic Wall Street Quant interview — then scores it.
📞 Practice Wall Street Quant — free 15 min
📕 Buy this interview preparation book: 155 Wall Street Quant questions & answers — PDF + EPUB for $5
Puzzles & Problems 49Linear Algebra 25Probability 25Financial Models 56

Puzzles & Problems

  1. What is the probability of rolling a sum of 7 with two dice?
  2. There are 5 white, 3 black, and 2 red marbles in a bag. What is the probability of drawing a black marble?
  3. If an elevator stops at 10 floors, how many ways can it stop at any three distinct floors?
  4. If you toss a fair coin three times, what is the probability of getting at least one head?
  5. If there are 23 people in a room, what is the probability that at least two people share the same birthday?
  6. If a stock price goes up by 5% one day, then goes down by 5% the next day, is the final price higher, lower, or the same as the original price?
  7. How many Pythagorean triangles with sides of integer length exist where the longest side is less than or equal to 100?
  8. Two trains start from two cities 200 miles apart and travel toward each other at constant speeds. One goes 40 mph, and the other goes 60 mph. How long does it take for them to meet?
  9. If you drive at 60mph for 1 hour, then 70mph for another hour, what was your average speed?
  10. How many squares (of all sizes) are there in an 8x8 chessboard?
  11. You’re on a game show with three doors. Behind one is a car, behind the others, goats. You pick a door - say, Door 1 - and the host, who knows what’s behind all the doors, opens another door - say, Door 3 - which has a goat. He then asks you if you want to switch your choice to the remaining door, Door 2. Is it in your interest to switch?
  12. In a simple random walk with an equal probability of moving up or down, starting from 0, what’s the probability of hitting +3 before hitting -2?
  13. If a quantity grows by 7% per year, how long will it take to double?
  14. A fair six-sided die is rolled. What is the expected value of the number rolled?
  15. If the weights of five people are 50, 60, 70, 80, and 90 kg, what is the standard deviation of their weights?
  16. If you have $100 and bet $1 on an even-money game, what’s the probability that you reach $200 before going broke?
  17. Suppose there’s a rare disease (1 in 10,000) that you’re testing for. Your test is 99% accurate. If someone tests positive, what’s the probability they actually have the disease?
  18. What is the probability of getting a flush (five cards of the same suit) in a five-card poker hand in a standard 52-card deck?
  19. In a class of 100 students, 70 like math, 60 like physics, and 50 like both. How many students don’t like either subject?
  20. Four people need to cross a bridge at night which only supports two people at the same time. They have one torch and the bridge is too risky to cross without the torch. They all walk at different speeds, one can cross the bridge in 1 minute, another in 2 minutes, the third in 5 minutes and the last takes 10 minutes to cross. When two people cross the bridge together, they must walk at the slower person’s pace. What is the least amount of time in which all people can cross the bridge?
  21. You have 7 marbles that are identical in size. Six of them weigh the same but one is heavier. Using a balance scale only twice, how can you find the heavier marble?
  22. You are given three points in a plane. Construct an algorithm to determine the center and radius of the unique circle that passes through all three points.?
  23. You have an array that represents the price of a stock each day for a period of n days. You can make as many transactions as you like, but you can’t engage in multiple transactions at the same time (you must sell the stock before you buy again). Design an algorithm to find the maximum profit.?
  24. A frog can jump over one stone or two at a time. If there are N stones in a line, how many different ways can the frog traverse the path?
  25. You have an infinite supply of coins and you need to make a pyramid with a base of N coins on each side. How many coins do you need?
  26. Write a function that takes a positive integer n as an input and performs the following steps. If n is even, divide it by 2, if n is odd, multiply it by 3 and add 1. Repeat the process (which has been called "Half Or Triple Plus One") indefinitely. The conjecture is that no matter what number you start with, you will always eventually reach 1. What is the smallest number that has not been proven to reach 1?
  27. You are one of 100 prisoners. The warden, who is a bit eccentric, makes the following announcement. You may meet together today and plan a strategy, but after today you will be in isolated cells and will have no communication with one another. I have a fair coin and a light switch in a special cell. The coin flip will determine whether the switch is initially on or off. Each day, I will choose one of you at random and escort you to the special cell. There, you can toggle the switch if you wish, or you can leave it as it is. But you may do nothing else. If at any point any one of you declares to me, "We have all visited the special cell," and this statement is true, then you will all be set free. If the statement is false (that is, if one or more of you have not yet visited the special cell), then you will all be executed. You see the switch, but you do not see whether it changes day-to-day. What is your plan?
  28. You are at a race track with 25 horses. You want to find out the fastest 3 horses, but the track only allows 5 horses to race at a time. What is the minimum number of races you need to conduct to find out the top 3 horses?
  29. You are given two indistinguishable envelopes, each containing money, one contains twice as much as the other. You may pick one envelope and keep whatever is inside. You pick one envelope at random but before you open it you are given the chance to take the other envelope instead. Is it in your interest to switch envelopes?
  30. How many ways are there to tile a 3xn rectangle with 2x1 dominoes?
  31. You’ve got someone working for you for seven days and a gold bar to pay them. The gold bar is segmented into seven connected pieces. You must give them a piece of gold at the end of every day. If you are only allowed to make two breaks in the gold bar, how do you pay your worker?
  32. You have 100 doors in a row that are all initially closed. You make 100 passes by the doors starting with the first door every time. The first time through you visit every door and toggle the door (if the door is closed, you open it; if it is open, you close it). The second time you only visit every 2nd door (door #2, #4, #6, ...). The third time, every 3rd door (door #3, #6, #9, ...), etc, until you only visit the 100th door. After your last pass, which doors are open and why?
  33. On an 8x8 chessboard, a knight starts at any square and moves in legal chess moves (an L shape). Can the knight tour the entire board, visiting every square exactly once, and return to the original square?
  34. You have two ropes and a lighter. Each rope takes exactly one hour to burn but they do not burn at a consistent rate (i.e., half the rope length-wise might burn in 20 minutes, while the other half might take 40 minutes). Using these two ropes, how do you measure exactly 45 minutes?
  35. You have 1000 bottles of juice. One contains poison and the others do not. The poison is lethal and will kill anyone who ingests even a tiny amount. You have 10 lab rats to test the bottles. How can you find out which bottle contains poison?
  36. You have 5 coins, one of which is counterfeit and is slightly lighter than the other four, which are identical. With a balance scale, how can you determine which coin is counterfeit in just two weighings?
  37. You have 8 identical-looking coins, and one of them is known to be heavier or lighter than the rest. Using a balance scale only twice, how can you determine which coin is counterfeit and whether it’s heavier or lighter?
  38. There are 100 prisoners in separate cells, and each cell has a light bulb that can be either on or off. The prisoners cannot communicate with each other, but they have a chance to come up with a strategy beforehand. How can they ensure that eventually all the prisoners know that all of them have visited their own cells, while minimizing the number of times the light bulbs are switched? How many days does it take?
  39. You have a 5-liter jug and a 3-liter jug. How can you measure exactly 4 liters of water using only these two jugs?
  40. You are given an array of integers from 1 to 100, and two numbers are missing. How can you efficiently find the two missing numbers?
  41. You have two identical eggs and a 100-story building. The eggs may break when dropped from a certain floor or may survive the fall. What is the minimum number of drops needed to determine the highest floor from which an egg can be dropped without breaking, using the fewest number of egg drops possible?
  42. A train crosses a bridge that is 1 mile long in 1 minute. How long does it take to cross the same bridge if there is a constant speed decrease and increase so that the train is stationary at the midpoint of the bridge for 10 seconds?
  43. You draw two cards from a standard deck without replacement. What is the probability that both cards are hearts?
  44. In a room with N people, what is the minimum value of N such that the probability of two people having the same birthday is greater than 50%?
  45. An ant is on one corner of a empty cube. What is the shortest distance the ant must travel to get to the opposite corner of the cube?
  46. A standard 8x8 chessboard has two diagonally opposite corners removed. Is it possible to cover the remaining 62 squares with 31 dominos, each covering exactly two adjacent squares?
  47. You have three coins. What is the probability of getting at least two heads when flipping all three coins simultaneously?
  48. You are given a deck of 52 shuffled cards. What is the minimum number of times you need to sort the cards in order to return them to their original sorted order?
  49. An office manager needs to hire a new secretary. He arranges to interview ’n’ candidates. He decides to hire a secretary according to the following strategy: He will interview the first ’n/2’ candidates and then hire the next candidate who is better than all the candidates interviewed so far. If no such candidate appears, he will hire the last candidate. What is the probability that he hires the best secretary?

Linear Algebra

  1. What is the rank of a matrix and how is it useful?
  2. Can you describe how Gaussian elimination works?
  3. What is the determinant of a matrix and what does it tell you?
  4. How do you calculate eigenvalues and eigenvectors of a matrix?
  5. What are the properties of transpose of a matrix?
  6. What is the difference between the L1 and L2 norms?
  7. Can you explain the concept of linear independence and dependence?
  8. What are singular value decomposition (SVD) and its applications in finance?
  9. What does it mean if a matrix is positive definite?
  10. What is the orthogonality principle in terms of projections?
  11. How would you solve a system of linear equations using matrices?
  12. What is the geometric interpretation of a matrix?
  13. What is the difference between the dot product and the cross product?
  14. What is the difference between an eigenvector and a principal component?
  15. Can you describe the Least Squares method?
  16. How would you use linear algebra in solving simultaneous linear equations?
  17. Can you explain the Gram-Schmidt process?
  18. What is the trace of a matrix?
  19. What is the Kronecker product?
  20. How do you find the inverse of a matrix?
  21. What are the conditions for a matrix to be invertible?
  22. What is a Hilbert space?
  23. Explain the concept of a basis in linear algebra.?
  24. What is the use of the Cholesky decomposition in finance?
  25. What is a tensor and how is it different from a matrix?

Probability

  1. What is a random variable?
  2. What is the difference between a PDF and a CDF?
  3. Can you define and provide examples of discrete and continuous random variables?
  4. What is the Law of Large Numbers?
  5. Can you explain the Central Limit Theorem?
  6. Define and provide examples of conditional and joint probabilities.?
  7. What are Bayes’ theorem and its applications?
  8. Can you define expectation, variance, and covariance?
  9. What are moment generating functions?
  10. What is the difference between correlation and covariance?
  11. Explain the concept of statistical independence.?
  12. What is a Bernoulli process?
  13. What are Markov chains and Markov processes?
  14. Can you explain what a Poisson process is?
  15. What is the exponential distribution and where is it used?
  16. What is a normal distribution and why is it important in finance?
  17. How do you estimate the parameters of a probability distribution from data?
  18. What is the concept of a confidence interval?
  19. Can you explain Type I and Type II errors?
  20. What is a t-test and when would you use it?
  21. Explain the principles of Maximum Likelihood Estimation (MLE).?
  22. What is the difference between a prior and posterior distribution?
  23. What is the difference between marginal and conditional probability?
  24. Can you describe the Uniform and Binomial distributions?
  25. What is the concept of entropy in information theory?

Financial Models

  1. Given a risk-free rate of 2%, a volatility of 30% and a strike price of $100, what is the price of a call option on a stock currently priced at $105 with 6 months to expiration?
  2. Use a two-step binomial model to calculate the price of an American call option with a strike price of $100, given that the current stock price is $100, the risk-free rate is 5%, the up-move potential is 20%, the down-move potential is -20%, and the time to expiration is 2 periods.?
  3. You have the expected returns, variances, and correlation for two assets. How would you construct the minimum variance portfolio?
  4. Given the expected returns and covariance matrix of 4 assets, use mean-variance optimization to determine the weights of assets in the portfolio.?
  5. What is the formula for the variance of a portfolio of two assets? And how would you calculate the variance of a portfolio composed of 40% asset A with an annual standard deviation of 15% and 60% asset B with an annual standard deviation of 25%, given that the correlation between the two assets is 0.4?
  6. How many options do you need to hedge a position in 1000 shares of a stock given a delta of the option of 0.75?
  7. Given the log returns of a portfolio, calculate the 1-day 99% VaR.?
  8. Write a Monte Carlo simulation in Python or R to price a European call option.?
  9. Calculate the Delta, Gamma and Vega of an option given the current stock price, strike price, time to expiration, risk-free rate, and the volatility.?
  10. Given a time series dataset, how would you test for stationarity? If the series is not stationary, how would you make it stationary?
  11. You have price data for a particular stock and a particular market index. Perform a linear regression to calculate the beta of the stock relative to the index.?
  12. Given a binary classification problem with an imbalanced dataset, which metrics would you use to evaluate the model’s performance? How would you adjust the model or data to improve the model’s performance?
  13. Is the stock price a martingale, sub-martingale or super-martingale? Justify your answer.?
  14. Apply Ito’s lemma to the Geometric Brownian Motion formula to derive the Black-Scholes formula.?
  15. Write down the SDE for Black-Scholes model and explain each of the terms.?
  16. How would you use Fourier transform methods to price options?
  17. If a bond has a face value of $1,000, a coupon rate of 5%, and matures in 10 years, what is its price given a yield to maturity of 4%?
  18. Calculate the Macaulay duration and convexity of the bond in the previous question.?
  19. How would you construct a factor model for a group of stocks?
  20. How would you use PCA in portfolio management?
  21. Calculate the expected shortfall given the returns distribution of a portfolio.?
  22. Calculate the expected return of a stock with a beta of 1.5, given a risk-free rate of 2% and expected market return of 7%.?
  23. How would you estimate the parameters of an AR(1) model?
  24. Given some time series data, estimate a GARCH(1, 1) model.?
  25. Construct a butterfly spread and determine the payoff.?
  26. If the yield curve is upward sloping, what does this imply about the market’s expectations of future interest rates?
  27. How would you price an interest rate swap?
  28. How do you construct a risk parity portfolio with 4 different assets?
  29. What are the steady-state probabilities of a given Markov Chain?
  30. Given price data for two historically cointegrated stocks, develop a statistical arbitrage strategy.?
  31. How would you use the bootstrap method to estimate the confidence interval of a sample mean?
  32. Perform a hypothesis test to determine if the average return of a stock is different from zero.?
  33. How would you use a Kalman filter in a pairs trading strategy?
  34. Given a certain volume of shares to be executed within a defined time period, describe an optimal execution strategy.?
  35. How can copulas be used to model the dependence structure between financial assets?
  36. How is the VIX index calculated?
  37. What is the leverage effect in financial markets? How could you quantify it?
  38. How would you modify the Black-Scholes model to incorporate jumps in the stock price?
  39. You have high-frequency price and volume data for a stock. How would you calculate the Volume Weighted Average Price (VWAP)?
  40. How would you use survival analysis in credit risk modeling?
  41. What is the volatility smile? What does it tell us about market expectations?
  42. How would you calculate the implied volatility of an option?
  43. If the spot price of oil is $50, the storage cost is $2, the risk-free rate is 5% and the futures contract expires in 6 months, what is the no-arbitrage price of the futures contract?
  44. How would you model the probability of default of a bond?
  45. How would you measure and manage liquidity risk in a portfolio?
  46. How would you set the bid and ask prices as a market maker?
  47. Given a specific utility function, how would you optimize the portfolio selection?
  48. How would you estimate the three factors in the Fama-French three-factor model?
  49. What is volatility clustering and how would you test for it in financial returns data?
  50. How would you test if stock prices follow a random walk?
  51. How would you incorporate transaction costs into a portfolio optimization problem?
  52. Given a data set that’s too large to fit into memory, how would you compute its mean and variance?
  53. Given the cash flows of a fixed income security, how would you compute its yield to maturity?
  54. Given the returns of a set of assets, how would you compute the covariance matrix?
  55. How would you price a derivative using the risk-neutral approach?
  56. Given the zero-coupon yield curve, how would you bootstrap the spot rate curve?
📕 Buy this interview preparation book: 155 Wall Street Quant questions & answers — PDF + EPUB for $5
Reading is step one. Saying it out loud is the interview. Our AI interviewer calls your phone and runs a realistic Wall Street Quant interview — then scores it.
📞 Practice Wall Street Quant — free 15 min
More in Quant & Finance: Quant FinanceQuant ProbabilityStochastic Processes