oc... Optimization Exo (1) - Saved to my Mac Home Insert Draw Design Layout References Mailings Review View Tell me Share Comments Calibri (Bo... 11 A A Aay A Aalboc de Abc dle EEE 2! == AaBbccdc Anbucetat Aalbi Pealid Normal B B ! | x 33 x x AOA Nu Sparing Heading Haning Title Dictate 3 Sensitivity Editor Styles Pane In the following exercise, we focus on the core mathematical problem in Asset Management and Machine Learning: Optimization. Suppose that we have financial assets R with: Expected Return: = E(R) Covariance Matrix: And other higher order statistics: skew, kurt, Var(a), etc. We would like to decide the best way to invest in those assets quantitatively with this information. Questions: Q1. (theoretical) ( As an asset manager, how can you decide how much to invest in each assets? Explain briefly the well-known Mean Variance Framework and other methods (if possible). Q2. (practical) ) Recall the Mean Variance Framework Optimization. Simulate (4,2) above with the number of assets n = 3 and do the simulation in the programming language that you prefer. You can do a notebook or presentation (pptx/latex + script), etc. - Hint 1: You would like to give some reasonable theoretical values of (H. E) Hint 2: Then, simulate the data (random walk) of those assets based on the theoretical parameters. You also want to split the simulated data into train set and test set. Hint 3: Then, the re-estimation of empirical parameters and optimization will be done on train set and evaluate the performance of the investment solution on test set. Evaluate the performance of this solution - Hint 4: you may want to try 3 versions of optimization: (C1): Only constraint: osset weights' sum is equal to 1 (C2): C1 + no short selling constraint (C3): C1 + Number of optimized assets is less than 2 Hint 5: Don't forget to: o Plot the simulated series Calculate the usually used statistics of the simulated series/ solution in train and test period. Page 1 of 2 218 words IE English (United States Focus 3 + % 134%