Today’s Selection of Questions (Technical) Which company has higher beta, Johnson and Johnson or Google? Describe a coding project you have done recently. What do you think is the disadvantage and advantage of different coding languages (like R and C++)? How will you invest your money on different kinds of assets if you have 1 billion? How to invest your customer's money if he couldn’t take too much risk? Why? What is the probability of at least one head in three tosses of a coin? What is the density of the standard normal distribution? How would you use residuals to check the fit of a linear regression? If I have two random variables which are uncorrelated, what does this say about their independence? In what case would uncorrelated imply independent? What is the Taylor series expansion of e^x? What is your view of the US equity market? How can you replicate the payoff of a forward contract by using two option contracts? Mock Interviews – Class of 2015 interviewing Class of 2016 3 5/8/2015
Mock Interviews 4 11-3-14 Other Technical Interview Questions What does R^2 tell you in a linear regression? What is the Kurtosis of a distribution? Find lim x-> 0 (e^x - 1)/x What two theoretical properties must all covariance matrices have? If I have an infinitely long random sequence of letters and numbers what is the probability the complete works of Shakespeare are contained in this sequence? If you were running in a race and passed the person in 2nd place, what place would you now be in? x^x^x^x^.... = 2 solve for x Find the derivative of x^x Find the integral of ln(x) derive Black Scholes formula. define Brownian Motion solve some ode, sde, pde.... define Var, Expected shortfall/ What is your opinion on interest rates today ? How do you derive the Black Scholes price of a call? What's a GARCH and ARIMA model?
Mock Interviews 5 11-3-14 Other Technical Interview Questions Probability If you get paid on every last week day of the month, what is the probability that you get paid on Friday? What’s the average number of tosses you need for a fair coin to have two heads in a row? Algorithm There’s a stairs with n levels, you can either go up one level with one step or go up two levels with one step. For a n-level stairs, how many ways do you have to get to the top? Can you code it? What does your methodology called in computer science? Can you describe an abstract data structure that’s related to it? What’s the complexity of your algorithms? Can you make the programs more efficient? You have a function f(x) that takes value of x in the region of [0,2^32], now there’s a value y such that: If you give a value x>y to function f(x), it takes the function 3 seconds to print 1 If you put a value x<7 to function f(x), it takes the function 1 second to print 0 Design a method to find y, consider the efficiency of the program. How many loops you need?
Mock Interviews 6 11-3-14 Other Technical Interview Questions Trader’s Instinct You got a coin from the grocery store, you have no idea whether this coin is fair or not, you tossed it 10 times and had 10 heads in a row, what’s the probability of getting head next toss? (open question, no definite answer) You have a pack of cards, 52 cards except the Jokers. The cards are fully shuffled, you start to draw card from the top, you’re searching for an ACE, before you get an ACE, any card you get is meaningless. After that you search for a 2, then a 3, so on and so forth. When the 52 cards are all drawn, the biggest number you have reached is your score, ACE for 1, 2 for 2, 3 for 3, so on and so forth. (Don’t try to solve this problem with brutal force, you just need to make a calculated guess) What is the expected score for this game? Is the distribution for the score skewed? If yes, it’s positive skewed or negative skewed? Can you name a distribution that has similar shape? Why does the CDS market shrink dramatically after the crisis? Data Science What can you do when you have missing values in your data? (You’ll be asked to explain every single method you use)
Mock Interviews 7 11-3-14 Other Technical Interview Questions Math Finance What is put-call parity? What’s the contract you get by longing a call and shorting a put with same underlying stock and same strike? How to price a Barrier Option? Why people usually don’t exercise American Call? What will make you exercise your American call before maturity? In a binomial tree model, why isn’t the price of the option the expected discounted payoff? Why is the expected return of stocks not appearing in Black-Scholes formula? Brain Teaser How tall is John Hancock Tower? (The mirror building at Copley, Boston) How many Macdonald’s are there in Boston? You have 1000 stones at hand, now you divide them into two groups. And you multiply the number to these two groups. For example, if you decided to divide the 1000 stones into 500 and 500, then you multiply 500 with 500 to get 250,000. Then you divide each of the group you have into another two groups and multiply the number of the stones, so on and so forth until you have divide the 1000 stones into 1000 groups. You sum all the products you have through the process. Now I convince you, no matter how you divide the stones, the sum of the products is a constant. Then: What is this sum? How do you prove this result? (Just describe the method)
Mock Interviews 8 11-3-14 Other Resources Books: "fifty challenging problems in probability" "heard on the street" by crack
9 11/3/14 Questions? Help? What do you do if you get into a jam or need help? Schedule an appointment with me! firstname.lastname@example.org@bu.edu or 617-358-0542