Backtesting

Shift Daily Returns Data

The variable frames contains the data from daily_return and data correctly shifted.

Build Universe of Stocks

The function get_universe correctly creates a stock universe by selecting only those companies that have a market capitalization of at least 1 billion dollars (1e9) OR that are in the previous day's holdings, even if on the current day, the company no longer meets the 1 billion dollar criteria.

They should use the .copy() attribute to create a copy of the data and they should drop the column containing the daily return from the universe dataframe.

The returned universe dataframe should have a shape of (2265, 93)

Create the factor covariance matrix

The function diagonal_factor_cov correctly creates the factor covariance matrix. The factor matrix must be scaled by (0.01**2). They must use the given colnames function to get the column names from X and use the statement 'covariance[date]' to get the covariances for the given date .

The returned factor covariance matrix should have shape (77, 77)

create a matrix of alpha factors

The function get_B_alpha correctly creates a matrix of alpha factors. They must use the given get_formula and model_matrix functions.

The returned B_alpha should be of type patsy.design_info.DesignMatrix and it should have shape (2265, 4). The 4 columns of this matrix should correspond to the 4 alpha factors chosen at the beginning, namely:

"USFASTD_1DREVRSL"
"USFASTD_EARNYILD"
"USFASTD_VALUE"
"USFASTD_SENTMT"

Create an alpha vector

The function get_alpha_vec correctly creates a vector of alpha factors. To do this, they must add the rows of the Matrix of Alpha Factors and multiply the result by 1e-4.

The returned alpha_vac should have shape (2265,)

Create the objective function to be minimized

The obj_func(h) function correctly implements the objective function. The equation of the objective function is given in the notebook.

Create the gradient of the objective function

The grad_func(h) function correctly implements the gradient of the objective function. The equation of the gradient of the objective function is given in the notebook.

Optimize the objective function

The function get_h_star correctly optimizes the objective function using the following functions obj_func , grad_func , and scipy.optimize.fmin_l_bfgs_b .

The returned h_star should have shape (2265,)

Calculate the portfolio's Risk Exposure

The function get_risk_exposures correctly calculates the portfolio's risk exposures

The returned risk_exposures Pandas series should have shape (77,). The index of this Pandas Series should correspond to the risk factors such as 'USFASTD_AERODEF', 'USFASTD_AIRLINES', 'USFASTD_ALUMSTEL', ……

Calculate the portfolio's Alpha Exposure

The function get_portfolio_alpha_exposure correctly calculates the portfolio's alpha exposures.

The returned portfolio_alpha_exposure Pandas series should have shape (4,). The index of this Pandas Series should should correspond to the 4 alpha factors chosen at the beginning, namely:

"USFASTD_1DREVRSL"
"USFASTD_EARNYILD"
"USFASTD_VALUE"
"USFASTD_SENTMT"

Calculate Total Transaction Costs

The function get_total_transaction_costs correctly calculates the total transaction costs according to the equation given in the notebook.

Profit and Loss attribution

Correctly calculate the PnL attributed to the alpha factors, the PnL attributed to the risk factors, and attribution to cost.

To calculate the alpha and risk exposures they must use the provided partial_dot_product function

build portfolio characteristics

Correctly calculates the sum of long positions, short positions, net positions, gross market value, and amount of dollars traded.