Performance metrics#

exception sigtech.framework.analytics.performance.metrics.MetricsError

A class implementing exceptions raised when metrics-related errors occur.

sigtech.framework.analytics.performance.metrics.annualised_return(ts: pandas.core.series.Series, start: Optional[datetime.date] = None, use_returns: Optional[bool] = True) → float

Calculate the annualised return (only annualised if over 1 year).

Parameters

  • ts – TimeSeries of levels.

  • start – Starting date (optional).

  • use_returns – Set to use the percentage returns rather than profit (default is 'True').

Returns

Annualised return for history provided.

sigtech.framework.analytics.performance.metrics.risk_annualised_return(ts: pandas.core.series.Series, risk_factor: float, use_returns: Optional[bool] = True) → float

Calculate the risk annualised return (only annualised if over 1 year).

Parameters

  • ts – TimeSeries of levels.

  • risk_factor – Factor used to annualise.

  • use_returns – Set to use the percentage returns rather than profit (default is 'True').

Returns

Annualised return for history provided.

sigtech.framework.analytics.performance.metrics.excess_return_series(ts: pandas.core.series.Series, cash: pandas.core.series.Series) → pandas.core.series.Series

Calculate the excess return timeseries.

Parameters

  • ts – Timeseries of cumulative total return.

  • cash – Cash timeseries of cumulative cash return.

Returns

Cumulative excess returns.

sigtech.framework.analytics.performance.metrics.risk_excess_return_series(ts: pandas.core.series.Series, cash: pandas.core.series.Series) → pandas.core.series.Series

Calculate the risk excess return timeseries using division of return rather than subtraction (see excess_return_series()).

Parameters

  • ts – Timeseries of cumulative total return.

  • cash – Cash timeseries of cumulative cash return.

Returns

Cumulative excess returns.

sigtech.framework.analytics.performance.metrics.frequency(ts: pandas.core.series.Series) → str

Estimate the frequency of a timeseries by the number of elements compared to day count fraction.

Parameters

ts – Input timeseries.

Returns

Frequency identifier.

sigtech.framework.analytics.performance.metrics.drawdown_series(ts: pandas.core.series.Series, use_returns: Optional[bool] = True) → pandas.core.series.Series

Calculate the rolling max drawdown.

Parameters

  • ts – Timeseries of values.

  • use_returns – Set to use the percentage returns rather than profit (default is 'True').

Returns

Drawdown timeseries.

sigtech.framework.analytics.performance.metrics.resample(df: pandas.core.frame.DataFrame, freq: Optional[str] = None, how: str = 'last') → pandas.core.frame.DataFrame

Re-sample the values in a given DataFrame to the requested frequency.

Parameters

  • df – DataFrame of values.

  • freq – Frequency identifier.

  • how – Resampling mode (default is 'last').

Returns

DataFrame of re-sampled data.

sigtech.framework.analytics.performance.metrics.resample_single(ts: pandas.core.series.Series, freq: Optional[str] = None, how: str = 'last') → pandas.core.series.Series

Re-sample the values in a given Timeseries to the requested frequency.

Parameters

  • ts – Timeseries of values.

  • freq – Frequency identifier.

  • how – Resampling mode (default is 'last').

Returns

Timeseries of re-sampled values.

sigtech.framework.analytics.performance.metrics.periods_per_year(ts: pandas.core.series.Series) → int

Number of periods per year based on the estimated frequency of a timeseries.

Parameters

ts – Timeseries of values.

Returns

Integer number of periods per year.

sigtech.framework.analytics.performance.metrics.year_to_dates_single(ts: pandas.core.series.Series) → pandas.core.series.Series

Evaluate yearly returns from Timeseries.

Parameters

ts – Timeseries of cumulative return.

Returns

Timeseries of yearly returns.

sigtech.framework.analytics.performance.metrics.year_to_dates(df: pandas.core.frame.DataFrame) → pandas.core.frame.DataFrame

Evaluate yearly returns of DataFrame.

Parameters

df – DataFrame of cumulative returns.

Returns

DataFrame of yearly returns.

sigtech.framework.analytics.performance.metrics.geometric_average_return(price_series: pandas.core.series.Series, risk_factor: float) → float

Calculate the geometric average return from the supplied price series. We protect the calculation from zero division and ensure the geometric mean is not complex.

Parameters

  • price_series – pd.Series of strategy prices.

  • risk_factor – Modifier for the frequency of the returns. If daily returns (365.25 per year) then / risk_factor = 1.

Returns

Geometric mean return

sigtech.framework.analytics.performance.metrics.summary_single(ts: pandas.core.series.Series, cash: Optional[pandas.core.series.Series] = None, complete_summary: Optional[bool] = True) → dict

Calculate summary statistics using the relative returns.

These statistics include:

  • Annualised Return

  • Annualised Excess Return

  • Annualised Standard Deviation

  • Annualised Sharpe Ratio (0%)

  • Annualised Sharpe Ratio (vs Cash)

  • Annualised Sortino Ratio (0%)

  • Annualised Sortino Ratio (vs Cash)

  • Drawdown

  • Max Drawdown

  • Annualised Downside Deviation (0%)

  • Annualised Downside Deviation (vs Cash)

  • Annualised Upside Deviation (0%)

  • Annualised Upside Deviation (vs Cash)

  • 1 Month Return

  • 1 Year Return

  • 3 Month Return

  • 3 Year Return (Annualised)

  • Mean

  • Standard Deviation

  • Kurtosis

  • Skewness

  • Daily Var 95%

  • Daily Var 99%

  • Daily CVar 95%

  • Daily CVar 99%

  • Best Return

  • Worst Return

  • Mean Positive Return

  • Mean Negative Return

  • Proportion Positive Returns

  • Series Start Date

  • Series End Date

  • Series Length

  • Series Start Value

  • Series End Value

  • Frequency

  • Annualisation Factor

  • Max Drawdown Start Date

  • Max Drawdown End Date

  • Max Drawdown Period

  • Max Drawdown Period Units

  • Max Drawdown Recovery Date

  • Max Drawdown Recovery Period

  • Max Drawdown Recovery Period Units

  • MAR Ratio

  • Risk Annualised Return

  • Risk Annualised Excess Return

  • Risk Annualised Standard Deviation

  • Risk Annualised Excess Standard Deviation

  • Risk Information Ratio

  • Risk Sharpe Ratio

  • Max DD/Vol

Parameters

  • ts – Timeseries of cumulative total returns.

  • cash – Timeseries of cumulative cash returns.

  • complete_summary – Calculate VaR, CVaR, MaR and Calmar as well as Risk return metrics if true.

Returns

dict of statistics.

sigtech.framework.analytics.performance.metrics.summary_single_ccy(ts: pandas.core.series.Series, complete_summary: Optional[bool] = True) → dict

Calculate summary statistics that are based on the strategies absolute returns i.e. profit in the strategy currency.

These statistics include:

  • Total Return

  • Annualised Return

  • Annualised Standard Deviation

  • Annualised Sharpe Ratio (0% Cash)

  • Annualised Sortino Ratio (0% Cash)

  • Drawdown

  • Max Drawdown

  • Annualised Downside Deviation

  • Annualised Upside Deviation

  • 1 Month Return

  • 1 Year Return

  • 3 Month Return

  • 3 Year Return (Annualised)

  • Mean

  • Standard Deviation

  • Kurtosis

  • Skewness

  • Daily Var 95%

  • Daily Var 99%

  • Daily CVar 95%

  • Daily CVar 99%

  • Best Return

  • Worst Return

  • Mean Positive Return

  • Mean Negative Return

  • Proportion Positive Returns

  • Series Start Date

  • Series End Date

  • Series Length

  • Series Start Value

  • Series End Value

  • Frequency

  • Annualisation Factor

  • Max Drawdown Start Date

  • Max Drawdown End Date

  • Max Drawdown Period

  • Max Drawdown Period Units

  • Max Drawdown Recovery Date

  • Max Drawdown Recovery Period

  • Max Drawdown Recovery Period Units

  • MAR Ratio

  • Calmar Ratio

  • Max DD/Vol

Parameters

  • ts – Timeseries of cumulative total returns.

  • complete_summary – Calculate VaR, CVaR, MaR and Calmar metrics if true.

Returns

dict of statistics.

sigtech.framework.analytics.performance.metrics.summary(df: pandas.core.frame.DataFrame, cash: Optional[pandas.core.series.Series] = None, use_returns: Optional[bool] = True) → pandas.core.frame.DataFrame

Calculate the summary statistics for a DataFrame.

Parameters

  • df – DataFrame of cumulative total return series.

  • cash – Cumulative cash return timeseries.

  • use_returns – Provide relative returned based metrics rather than profit based.

Returns

DataFrame of statistics.

sigtech.framework.analytics.performance.metrics.sharpe_ratio(ts: pandas.core.series.Series, cash: Optional[pandas.core.series.Series] = None, sharpe_type: str = 'arithmetic') → float

Calculate the Sharpe Ratio of a timeseries.

Parameters

  • ts – Timeseries of cumulative total return.

  • cash – Cumulative cash total return (if None, a constant cash value is used).

  • sharpe_type – 'arithmetic' or 'compounding' , mode to determine whether compounding returns are used (default is 'arithmetic').

Returns

Sharpe Ratio.

sigtech.framework.analytics.performance.metrics.mar_ratio(ts: pandas.core.series.Series, start: Optional[datetime.date] = None, use_returns: Optional[bool] = True) → float

Calculate the MAR ratio of a timeseries. Can be used to compute Calmar Ratio with start date 3Y prior.

Parameters

  • ts – Timeseries of cumulative total return.

  • start – Starting date (optional).

  • use_returns – Set to use the percentage returns rather than profit (optional).

Returns

MAR Ratio.

sigtech.framework.analytics.performance.metrics.deflated_sharpe_ratio(df: pandas.core.frame.DataFrame, cash: Optional[pandas.core.series.Series] = None, sharpe_type: str = 'arithmetic') → float

Calculate the deflated Sharpe Ratio based on trial data, implemented according to the Bailey-de Prado paper.

Parameters

  • df – Trial data in DataFrame, last column is the target strategy.

  • cash – Cash history to calculate excess return.

  • sharpe_type – 'arithmetic' or 'compounding' , mode to determine whether compounding returns are used (default is 'arithmetic').

Returns

Deflated Sharpe Ratio percentile.

sigtech.framework.analytics.performance.metrics.deflated_sharpe_ratio_raw(sr: float, n: int, variance: float, t: int, skewness: float, kurtosis: float) → float

Calculate the deflated Sharpe Ratio based on statistics, implemented according to the Bailey-de Prado paper.

Parameters

  • sr – Sharpe Ratio of the strategy.

  • n – Number of independent trials carried out.

  • variance – Variance of the backtest results of sharpe ratios.

  • t – Sample length.

  • skewness – Skewness of the returns.

  • kurtosis – Kurtosis of the returns.

Returns

Deflated Sharpe Ratio percentile.

sigtech.framework.analytics.performance.metrics.adjusted_sharpe_ratio(ts: pandas.core.series.Series, cash: pandas.core.series.Series, independent_trials: int) → float

Calculate a Sharpe Ratio adjusted for the number of independent trials, implemented according to the Harvey-Liu paper.

Parameters

  • ts – Timeseries of cumulative total returns.

  • cash – Timeseries of cumulative cash returns.

  • independent_trials – Number of independent trials.

Returns

Adjusted Sharpe Ratio.

sigtech.framework.analytics.performance.metrics.summary_rolling_series(ts: pandas.core.series.Series, cash: Optional[pandas.core.series.Series] = None, period: int = 756, compound_metrics: bool = False, min_periods: Optional[int] = None) → pandas.core.frame.DataFrame

Calculate the rolling statistics, including:

  1. Annualised Return

  2. Annualised Excess Return

  3. Volatility

  4. Drawdown

  5. Sharpe (vs 0%)

  6. Sharpe (vs Cash)

  7. Sortino (vs 0%)

  8. Sortino (vs Cash)

Parameters

  • ts – Timeseries of cumulative total return.

  • cash – Timeseries of cumulative cash return.

  • period – Period window to calculate the rolling statistics over.

  • compound_metrics – Whether to compound metrics (as for a fund) or not (default = False).

  • min_periods – Minimum number of observations in window required to have a value (if not set, period value will be used).

Returns

DataFrame of rolling statistics.

sigtech.framework.analytics.performance.metrics.summary_rolling_ccy_series(ts: pandas.core.series.Series, cash: Optional[pandas.core.series.Series] = None, period: int = 756, compound_metrics: bool = False, min_periods: Optional[int] = None) → pandas.core.frame.DataFrame

Calculate the rolling statistics, in the strategy currency, including:

  1. Annualised Return

  2. Annualised Excess Return

  3. Volatility

  4. Drawdown

  5. Sharpe (vs 0%)

  6. Sortino (vs 0%)

Parameters

  • ts – Timeseries of cumulative total return.

  • cash – Timeseries of cumulative cash return (deprecated).

  • period – Period window to calculate the rolling statistics over.

  • compound_metrics – Whether to compound metrics (as for a fund) or not (default = False).

  • min_periods – Minimum number of observations in window required to have a value (if not set, period value will be used).

Returns

DataFrame of rolling statistics.

sigtech.framework.analytics.performance.metrics.summary_rolling_averages(df: pandas.core.frame.DataFrame, cash: Optional[pandas.core.series.Series] = None, period: int = 756) → pandas.core.frame.DataFrame

Calculate the statistics of the rolling metric series, including:

  • Mean Annualised Return

  • Mean Annualised Excess Return

  • Mean Volatility

  • Mean Drawdown

  • Mean Sharpe(0%)

  • Mean Sharpe(vs Cash)

  • Mean Sortino(0%)

  • Mean Sortino(vs Cash)

  • Median Annualised Return

  • Median Annualised Excess Return

  • Median Volatility

  • Median Drawdown

  • Median Sharpe(0%)

  • Median Sharpe(vs Cash)

  • Median Sortino(0%)

  • Median Sortino(vs Cash)

  • 10th Percentile Annualised Return

  • 10th Percentile Annualised Excess Return

  • 10th Percentile Volatility

  • 10th Percentile Drawdown

  • 10th Percentile Sharpe(0%)

  • 10th Percentile Sharpe(vs Cash)

  • 10th Percentile Sortino(0%)

  • 10th Percentile Sortino(vs Cash)

  • 90th Percentile Annualised Return

  • 90th Percentile Annualised Excess Return

  • 90th Percentile Volatility

  • 90th Percentile Drawdown

  • 90th Percentile Sharpe(0%)

  • 90th Percentile Sharpe(vs Cash)

  • 90th Percentile Sortino(0%)

  • 90th Percentile Sortino(vs Cash)

Parameters

  • df – DataFrame of cumulative total return series.

  • cash – Timeseries of cumulative cash return.

  • period – Period window to use for rolling metrics.

Returns

DataFrame of statistics.

sigtech.framework.analytics.performance.metrics.monthly_returns(rets: pandas.core.series.Series)

Evaluate compounded returns for each calendar month based on a daily return series.

Parameters

rets – Series of daily returns.

Returns

Series of monthly returns.

sigtech.framework.analytics.performance.metrics.upside_downside_capture(rets, bmk_rets)

Calculate upside/downside ratios vs a benchmark series.

Parameters

  • rets – Series of daily returns.

  • bmk_rets – Series of benchmark.

Returns

pandas Series.

sigtech.framework.analytics.performance.metrics.win_ratio_returns(ts, freq='daily')

Calculate the proportion of positive returns for a given frequency.

Parameters

  • ts – Daily returns.

  • freq – Frequency, i.e. 'daily', 'monthly'. Default is 'daily'.

Returns

Proportion of positive returns.

sigtech.framework.analytics.performance.metrics.benchmark_metrics(cumulative_return_df, cumulative_benchmark_return)

Calculate benchmark statistics, including:

  • information_ratio

  • 1_year_upside_capture

  • 1_year_downside_capture

  • 3_year_upside_capture

  • 3_year_downside_capture

  • full_year_upside_capture

  • full_year_downside_capture

Parameters

  • cumulative_return_df – DataFrame of cumulative return series.

  • cumulative_benchmark_return – Timeseries of cumulative benchmark returns.

Returns

DataFrame of statistics.