Pilot Macro Advisors

User: Retrieve the ftse equity index factors, store the results in a variable named ftse_factors. Then perform a PCA on these ftse_factors. Tell me what the results mean.

Miura: To retrieve the FTSE equity index factors, I will use the getEquityIndexFactors action with the index set to “ftse” and the factors set to [“Value”, “Quality”, “Size”, “Vol”, “Yield”, “Momo”]. I will store the results in a variable named “ftse_factors”. After that, I will perform a Principal Component Analysis (PCA) using the calculatePca action with the tickers set to the output of the getEquityIndexFactors action. The results of the PCA will provide insights into the underlying structure of the data and help identify patterns or relationships among the factors.

Data…

forecast  previous  residual  residual%   ticker

0  1.105525  1.105308 -0.000217  -0.019624    value

1  1.129802  1.128800 -0.001002  -0.088762  quality

2  1.106535  1.106950  0.000415   0.037516     size

3  1.092824  1.091434 -0.001390  -0.127329      vol

4  1.116901  1.118090  0.001189   0.106302    yield

5  1.199155  1.201612  0.002457   0.204492     momo

…

Miura: The PCA analysis reveals that the six equity factors – value, quality, size, volatility, yield, and momentum (momo) – can be represented as linear combinations of the principal components (PC1, PC2, and PC3). The principal components explain a significant portion of the total variance in the data. In this case, PC1 explains approximately 90.13% of the variance, while PC2 and PC3 explain smaller proportions of 5.88% and 3.23%, respectively.

The factor loadings represent the relationship between each factor and the principal components. A high absolute value indicates a strong relationship between the factor and the principal component. For example, the value factor has a strong negative relationship with PC1, while the size factor has a strong positive relationship with PC3. Understanding these relationships can help in interpreting the results and identifying the underlying structure of the data.

The feature vectors represent the transformed data points in the new coordinate system defined by the principal components. These vectors can be used for further analysis, such as clustering or classification. The PC1:2 neutral weightings provide the optimal weights for each factor to achieve a neutral position in the new coordinate system. These weights can be used as a benchmark for evaluating the performance of investment strategies based on these factors.