Back-test result

This module defines cvxportfolio.BacktestResult.

This is the object that is returned by the cvxportfolio.MarketSimulator.backtest() method, and also by the same method in derived classes of cvxportfolio.MarketSimulator. It contains all relevant information from a back-test and implements the logic to compute various performance metrics, in addition to the BacktestResult.plot() method for producing plots and __repr__ magic method, which is invoked when the user prints an instance.

class cvxportfolio.BacktestResult(universe, trading_calendar, costs)

Store the data from a back-test and produce metrics and plots.

Parameters:

• universe (pandas.Index) – Best initial guess of the trading universe.

• trading_calendar (pandas.DatetimeIndex) – Best initial guess of the trading calendar.

• costs (list) – Simulator cost objects whose value is logged.

property cash_key

The name of the cash unit used (e.g., USDOLLAR).

Returns:

Name of the cash accounting unit.

Return type:

str

property periods_per_year

Average trading periods per year in this backtest (rounded).

Returns:

Average periods per year.

Return type:

int

property v

The total value (or NAV) of the portfolio at each period.

Returns:

Total value at each period.

Return type:

pandas.Series

property profit

The total profit (PnL) in this backtest.

Returns:

Total profit.

Return type:

float

property w

The weights of the portfolio at each period.

Returns:

Portfolio weights at each period.

Return type:

pandas.DataFrame

property h_plus

The post-trade portfolio (holdings) at each period.

Returns:

Post-trade holdings at each period.

Return type:

pandas.DataFrame

property w_plus

The post-trade weights of the portfolio at each period.

Returns:

Post-trade weights at each period.

Return type:

pandas.DataFrame

property leverage

Leverage of the portfolio at each period.

This is defined as:

\[\| {(h_t)}_{1:n} \|_1 / v_t,\]

where \(h_t\) is the portfolio (the holdings) at time \(t\), we exclude the cash account from the \(\ell_1\) norm, and \(v_t\) is the total value (NAV) of the portfolio at time \(t\).

Returns:

Leverage at each period.

Return type:

pandas.Series

property turnover

The turnover of the portfolio at each period.

This is defined as:

\[\| {(u_t)}_{1:n} \|_1 / (2 v_t),\]

where \(u_t\) are the portfolio trades at time \(t\), we exclude the cash account from the \(\ell_1\) norm, and \(v_t\) is the total value (NAV) of the portfolio at time \(t\).

Returns:

Turnover at each period.

Return type:

pandas.Series

property returns

The portfolio returns at each period.

This is defined as:

\[R_t^\text{p} = \frac{v_{t+1} - v_t}{v_t}\]

in terms of the portfolio value (NAV).

Returns:

Portfolio returns at each period.

Return type:

pandas.Series

property average_return

The average realized return \(\overline{R^\text{p}}\).

Returns:

Average portfolio return.

Return type:

float

property annualized_average_return

The average realized return, annualized.

Returns:

Average portfolio return, annualized.

Return type:

float

property growth_rates

The growth rate (or log-return) of the portfolio at each period.

This is defined as:

\[G^\text{p}_t = \log (v_{t+1} / v_t) = \log(1 + R^\text{p}_t).\]

Returns:

Growth rate of the portfolio value at each period.

Return type:

pandas.Series

property average_growth_rate

The average portfolio growth rate \(\overline{G^\text{p}}\).

Returns:

Average growth rate.

Return type:

float

property annualized_average_growth_rate

The average portfolio growth rate, annualized.

Returns:

Average growth rate, annualized.

Return type:

float

property volatility

Realized volatility (standard deviation of the portfolio returns).

Returns:

Volatility.

Return type:

float

property annualized_volatility

Realized volatility, annualized.

Returns:

Volatility, annualized.

Return type:

float

property quadratic_risk

Quadratic risk, square of the realized volatility.

Returns:

Quadratic risk.

Return type:

float

property annualized_quadratic_risk

Quadratic risk, annualized.

Returns:

Quadratic risk, annualized.

Return type:

float

property excess_returns

Excess portfolio returns with respect to the cash returns.

Returns:

Excess returns at each period.

Return type:

pandas.Series

property excess_volatility

Excess volatility (standard deviation of the excess returns).

Returns:

Average excess volatility.

Return type:

float

property average_excess_return

The average excess return \(\overline{R^\text{e}}\).

Returns:

Average excess portfolio return.

Return type:

float

property annualized_average_excess_return

The average excess return, annualized.

Returns:

Average excess portfolio return, annualized.

Return type:

float

property annualized_excess_volatility

Annualized excess volatility.

Returns:

Average excess volatility, annualized.

Return type:

float

property active_returns

Portfolio returns minus benchmark returns (if defined by policy).

Returns:

Active returns at each period if benchmark is defined, else nan.

Return type:

pandas.Series

property active_volatility

Active volatility (standard deviation of the active returns).

Returns:

Average active volatility if benchmark is defined, else nan.

Return type:

float

property average_active_return

The average active return \(\overline{R^\text{a}}\).

Returns:

Average active portfolio return if benchmark is defined, else nan.

Return type:

float

property annualized_average_active_return

The average active return, annualized.

Returns:

Average active portfolio return, annualized. If benchmark is not defined, nan.

Return type:

float

property annualized_active_volatility

Annualized active volatility.

Returns:

Average active volatility, annualized. If benchmark is not defined, nan.

Return type:

float

property sharpe_ratio

Sharpe ratio (using annualized excess portfolio returns).

This is defined as

\[\text{SR} = \overline{R^\text{e}}/\sigma^\text{e}\]

where \(\overline{R^\text{e}}\) is the average excess portfolio return and \(\sigma^\text{e}\) its standard deviation. Both are annualized.

Returns:

Sharpe Ratio.

Return type:

float

property information_ratio

Information ratio (using annualized active portfolio returns).

This is defined as

\[\text{IR} = \overline{R^\text{a}}/\sigma^\text{a}\]

where \(\overline{R^\text{a}}\) is the average active portfolio return and \(\sigma^\text{a}\) its standard deviation. Both are annualized.

Returns:

Information Ratio, nan if benchmark is not defined.

Return type:

float

property excess_growth_rates

The growth rate of the portfolio, relative to cash.

This is defined as:

\[G^\text{e}_t = \log(1 + R^\text{e}_t)\]

where \(R^\text{e}_t\) are the excess portfolio returns.

Returns:

Excess growth rates at each period.

Return type:

pandas.Series

property average_excess_growth_rate

The average excess growth rate \(\overline{G^\text{e}}\).

Returns:

Average excess portfolio growth rates.

Return type:

float

property annualized_average_excess_growth_rate

The average excess growth rate, annualized.

Returns:

Average excess portfolio growth rates, annualized.

Return type:

float

property active_growth_rates

The growth rate of the portfolio, relative to benchmark.

This is defined as:

\[G^\text{a}_t = \log(1 + R^\text{a}_t)\]

where \(R^\text{a}_t\) are the active portfolio returns.

Returns:

Active growth rates at each period. If benchmark is not defined, nan.

Return type:

pandas.Series

property average_active_growth_rate

The average active growth rate \(\overline{G^\text{a}}\).

Returns:

Average active portfolio growth rates. If benchmark is not defined, nan.

Return type:

float

property annualized_average_active_growth_rate

The average active growth rate, annualized.

Returns:

Average active portfolio growth rates, annualized. If benchmark is not defined, nan.

Return type:

float

property drawdown

The drawdown of the portfolio value over time.

Returns:

Drawdown of portfolio value at each period.

Return type:

pandas.Series

property policy_times

The computation time of the policy object at each period.

Returns:

Policy time in seconds at each period.

Return type:

pandas.Series

property simulator_times

The computation time of the simulator object at each period.

Returns:

Simulator time in seconds at each period.

Return type:

pandas.Series

plot(show=True, how_many_weights=7)

Make plot and show it.

Parameters:

• show (bool) – if True, call matplotlib.Figure.show, helpful when running in the interpreter.

• how_many_weights (int) – How many assets’ weights are shown in the weights plots. The ones with largest average absolute value are chosen.