Multivariate Volatility Models and PCA
1. PCA and Orthogonal GARCH
(a) Get historical prices for: Google, Facebook, Mastercard and Visa, from 04-04-2014 to 28-10-2022, convert into log returns.
(b) Estimate the 4 Principal Components (PCs) and decide how many to use.
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(c) Build your in-sample variance covariance matrix with your chosen PCs from the pre- vious question.
(d) Compare the estimated correlations for 12-04-2017 and 30-03-2020.
2. PCA – Interest rates
(a) Using the provided data on interest rates (Treasury Yields.csv) perform a principal component analysis.
(b) What fraction of the total variance is explained by each component.
(c) How would you interpret the first three principal components?
3. PCA – Currency returns
(a) Using the provided data on currency excess returns perform PCA analysis. Cur- rency Excess Returns.csv contains monthly excess returns for nine currencies from the perspective of a USD-based investor.
(b) What fraction of the total variance is explained by each component.
(c) How many components would you choose in a multivariate volatility model for cur- rencies?
London School of Economics
FM 321 Classwork Lecture 6
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