Using the covariance matrix V from exercise 1:
(a) Perform a spectral decomposition: VW = WΛ.
(b) Form an array 𝜀 by drawing N random numbers from a U[0, 1] distribution.
(c) Form an NxN matrix where
(e) Repeat exercise 2, this time using Ṽ as covariance matrix. What allocation method has been most impacted by the re-scaling of spectral variances?
Using the clustered covariance matrix V from exercise 1:
(a) Compute the HRP allocations.
(b) Compute the CLA allocations.
(c) Compute the IVP allocations.
Given the PnL series on N investment strategies:
(a) Align them to the average frequency of their bets (e.g., weekly observations for strategies that trade on a weekly basis).
(b) Compute the covariance of their returns, V.
(c) Identify the hierarchical clusters among the N strategies.
(d) Plot the clustered correlation matrix of the N strategies.