Fast Quant Interview Drill
This conversation was generated using Cook'd AI's career assistant and reviewed by Fallon Han from our editorial team for accuracy.
I want a fast-paced quant-style oral exam for a sales and trading internship. I'm a third-year math student in India, open to relocation, and I want to be tested on probability, mental math, and market scenarios. Please keep it intense and make me explain my assumptions out loud.
Great. We'll run this like a desk-style screening for a global bank.
I will move quickly, and you should answer as if you are speaking to the interviewer. For each answer, state your assumptions first, then the calculation, then the conclusion.
Round 1: A trader says a stock has a 60 percent chance to rise 2 percent tomorrow and a 40 percent chance to fall 1 percent tomorrow. What is the expected return? Do it mentally and say your steps out loud.
Expected return is 0.6 times 2 percent plus 0.4 times negative 1 percent, so 1.2 percent minus 0.4 percent equals 0.8 percent. I assumed only two outcomes and ignored fees and slippage.
Good. You were fast and clear.
Follow-up: If the stock is currently at 100 and the market gives a 95 percent confidence interval for tomorrow's price change of plus or minus 3 percent, what range would you quote? Also tell me what that interval means in plain English.
At 100, plus or minus 3 percent means 97 to 103.
In plain English, I would say I expect tomorrow's move to land inside that range most of the time, but there is still a small chance of a larger move outside it. I know it does not guarantee anything.
Strong. Now a market scenario.
A global bank client wants to buy 25 million dollars of a stock basket, but volatility spikes before execution. The basket is up 1 percent in the morning and down 1.5 percent by noon. If you estimate the client will accept half the order immediately and wait on the rest, what is the rough average execution impact if the second half is filled at noon? Use simple arithmetic and speak your assumption clearly.
My assumption is the first half gets filled at the morning price and the second half at the noon price.
So the average move is 50 percent times 1 percent plus 50 percent times negative 1.5 percent, which is 0.5 percent minus 0.75 percent, so negative 0.25 percent. That means the average execution is about a quarter percent worse versus the morning level.
Good reasoning. Last drill.
A trader asks whether the stock's daily return is more likely to be above 1 standard deviation or above 2 standard deviations. Give the approximate probability under a normal assumption, then explain why that assumption may break in real markets. Keep it concise and confident.
Under a normal distribution, above 1 standard deviation is about 16 percent in the upper tail, and above 2 standard deviations is about 2.5 percent.
The normal assumption can break because markets have fat tails, jumps, and volatility clustering, so extreme moves happen more often than the model predicts. I would say that out loud before using the estimate.
Excellent. You were fast, structured, and you explained assumptions instead of hiding them.
Post-session evaluation:
- Calculation speed: Strong
- Accuracy: Strong
- Communication under pressure: Strong
- Market intuition: Good
- Assumption discipline: Strong
Main improvement point: when a question involves probability language, define whether you are using a normal approximation, event frequency, or conditional probability before you calculate. That will make your answer sound more senior.
For the next round, I would increase difficulty with:
- a quick Bayes question
- an order book imbalance scenario
- a mental math spread pricing drill