Multi-factor Model

Statistical Risk Model

Criteria	Meet Specification
Fit PCA	The function `fit_pca` fits the PCA model with returns.
Factor Betas	The function `factor_betas` gets the factor betas from the PCA model.
Factor Returns	The function `factor_returns` gets the factor returns from the PCA model.
Factor Covariance Matrix	The function `factor_cov_matrix` gets the factor covariance matrix.
Idiosyncratic Variance Matrix	The function `idiosyncratic_var_matrix` gets the idiosyncratic variance matrix.
Idiosyncratic variance Vector	The function `idiosyncratic_var_vector` gets the idiosyncratic variance vector.
Predict using the Risk Model	The function `predict_portfolio_risk` gets the predicted portfolio risk.

Create Alpha Factors

Criteria	Meet Specification
Mean Reversion 5 Day Sector Neutral Factor	The function `mean_reversion_5day_sector_neutral` generates the mean reversion 5 day sector neutral factor.
Mean Reversion 5 Day Sector Neutral Smoothed Factor	The function `mean_reversion_5day_sector_neutral_smoothed` generates the mean reversion 5 day sector neutral smoothed factor.

Evaluate Alpha Factors

Criteria	Meet Specification
Sharpe Ratio of the Alphas	The function `sharpe_ratio` gets the sharpe ratio for each factor for the entire period.
What do you think would happen if we smooth the momentum factor?	The student correctly mentions what would happened if you smooth the momentum factor and why.

Optimal Portfolio Constrained by Risk Model

Criteria	Meet Specification
Objective Function	The function `OptimalHoldings._get_obj` returns the correct objective function.
Constraints Function	The function `OptimalHoldings._get_constraints` returns the correct list of constraints.
Optimize with a Regularization Parameter	The function `OptimalHoldingsRegualization._get_obj` returns the correct objective function.
Optimize with a Strict Factor Constraints and Target Weighting	The function `OptimalHoldingsStrictFactor._get_obj` returns the correct objective function.