FactSet Quantitative Analyst interview questions

Portfolio Optimization Let us investigate a hypothetical setup in the framework of Markowitz portfolio optimization. We have n=5 assets under consideration and m=7 observations of returns for each of them. These observations are collected in the table below, where data is given in percentage format and each row contains the different simulations of each single asset (columns are the joint realization of all 5 assets’ returns): 2.2 0.1 -0.77 0.6 1.1 0.5 0 0 1.1 -1.2 2.2 -0.56 -0.012 0.21 -0.5 -1.6 1.1 -0.3 -4.05 1.2 0.8 -0.45 2.2 -2.3 1.1 1.3 1.4 0.2 1.1 0.11 -0.2 4.12 2.2 1.8 0.9 In what follows, we denote by wi the proportion of our wealth invested in asset i (whose simulations are recorded in row i). 1. Find the portfolio that minimizes variance in the above setup under the following weight constraints: