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The primary objective of portfolio management is to allocate capital into different asset classes in order to maximize risk-adjusted returns. To achieve this goal, we will use PCA on a dataset of stocks. The PCA is a method used to reduce dimensionality at the expense of losing information because, depending on our chosen cut-off point, we pick the number of components and lose as much information as how many components we left off.
The dataset to be used for this case study is the Dow Jones Industrial Average (DJIA) index and its respective 30 stocks. The return data used will be from the year 2020 onwards. I will also compare the performance of the hypothetical portfolios against a benchmark and backtest the model to evaluate the effectiveness of the approach.