Optiver Quantitative Finance Internship Online Test: First Round Coding Questions

3 coding questions, 1.5 hours The following content requires a score higher than 200. You can already view it. Q1: Given n, k, m; n is the number of shares you want to hold, k is the number of shares

3 coding questions, 1.5 hours The following content requires a score higher than 200. You can already view it. Q1: Given n, k, m; n is the number of shares you want to hold, k is the number of shares you already hold, and m is the number of times you can buy and sell 1 share. Calculate the maximum number of different ways to convert k shares to n shares. Example: You have 1 share and want to convert it to 2 shares. You are allowed 3 buy/sell operations: 1. buy 2. buy buy sell 3. buy sell buy 4. sell buy buy (four ways in total). Q2: You have N stock weights called allocations, which are arrays of N numbers. You also have T days' worth of price data for N stocks, which is an N*T array of timesseries. You need to keep the weights as specified by allocations each day. How do you calculate the average daily log return and standard deviation over T days? Q3: Stock prices follow a uniform distribution [a, b]. You have k opportunities to buy stocks at price p. You need to buy n stocks. What is the expected cost of your stock purchases in the optimal scenario?