statistics package

Submodules

statistics.VaR module

Value at risk functions here/ no need for class

quant_risk.statistics.VaR.conditional_value_at_risk(price: pandas.core.series.Series, threshold: float = 0.05) → float

Calculates Conditional Value at Risk for given price series

Parameters

price (pd.Series) – historical prices of a given security

Returns

Conditional Value at Risk (VaR value) for given price

Return type

float

quant_risk.statistics.VaR.value_at_risk(price: pandas.core.series.Series, threshold: float = 0.05) → float

Calculates Value at Risk for given price series

Parameters

price (pd.Series) – historical prices of a given security

Returns

Value at Risk (VaR value) for given price

Return type

float

statistics.annualize module

This file implements different functions for annualising volatility and returns from a given dataframe of returns

quant_risk.statistics.annualize.annualised_returns(returns: pandas.core.frame.DataFrame, periodsPerYear: int = 252)

This function returns the annualised returns of a given dataframe of returns. If the freq of the data is not daily, the annualisation factor must be specified. The function returns nan if the value computed is too small

Parameters

• returns (pd.DataFrame) – dataframe of returns

• periodsPerYear (int, optional) – freq of returns in a year, by default 252

Returns

Returns the annualised return for each column in the dataframe

Return type

Annualised Returns

quant_risk.statistics.annualize.annualised_volatility(returns: pandas.core.frame.DataFrame, periodsPerYear: int = 252)

This function returns the annualised volatility of a given dataframe of returns. If the freq of the data is not daily, the annualisation factor must be specified

Parameters

• returns (pd.DataFrame) – dataframe of returns

• periodsPerYear (int, optional) – freq of returns in a year, by default 252

Returns

Returns the annualised volatility for each column in the dataframe

Return type

Annualised Returns

statistics.financial_ratios module

Put all financial ratios here, no need for class I think

quant_risk.statistics.financial_ratios.calmar_ratio(price: Union[pandas.core.frame.DataFrame, pandas.core.series.Series], periodsPerYear: Union[float, int] = 252, riskFreeRate: float = 0.0) → float

Calculates annualised calmar ratio for given set of prices and risk free rate

Parameters

• price (Union[pd.DataFrame, pd.Series]) – historical prices of a given security

• periodsPerYear (Union[float, int]) – periodicity of the returns data for purposes of annualising

Returns

annualised calmar ratio

Return type

float

quant_risk.statistics.financial_ratios.omega_ratio(price: Union[pandas.core.frame.DataFrame, pandas.core.series.Series], riskFreeRate: float = 0.0, periodsPerYear: Union[float, int] = 252) → float

Calculates annualised omega ratio for given set of prices and risk free rate

Parameters

• price (Union[pd.DataFrame, pd.Series]) – historical prices of a given security

• riskFreeRate (float) – given constant risk free rate throughout the period

• periodsPerYear (Union[float, int]) – periodicity of the returns data for purposes of annualising

Returns

annualised omega ratio

Return type

float

quant_risk.statistics.financial_ratios.sharpe_ratio(price: Union[pandas.core.frame.DataFrame, pandas.core.series.Series], riskFreeRate: float = 0.0, periodsPerYear: Union[float, int] = 252) → float

Calculates annualised sharpe ratio for given set of prices and risk free rate

Parameters

• price (Union[pd.DataFrame, pd.Series]) – historical prices of a given security

• riskFreeRate (float) – given constant risk free rate throughout the period

• periodsPerYear (Union[float, int]) – periodicity of the returns data for purposes of annualising

Returns

annualised sharpe ratio

Return type

float

quant_risk.statistics.financial_ratios.sortino_ratio(price: Union[pandas.core.frame.DataFrame, pandas.core.series.Series], periodsPerYear: Union[float, int] = 252, reqReturn: float = 0) → float

Calculates annualised sortino ratio for given set of prices and risk free rate

Parameters

• price (Union[pd.DataFrame, pd.Series]) – historical prices of a given security

• periodsPerYear (Union[float, int]) – periodicity of the returns data for purposes of annualising

• reqReturn (float, optional) – the minimum acceptable return by investors, by default 0

Returns

annualised sortino ratio

Return type

float

quant_risk.statistics.financial_ratios.tail_ratio(price: Union[pandas.core.frame.DataFrame, pandas.core.series.Series]) → float

Calculates annualised tail ratio for given set of prices and risk free rate

Parameters

price (Union[pd.DataFrame, pd.Series]) – historical prices of a given security

Returns

annualised tail ratio

Return type

float

statistics.statistics module

Put summary function here that prints or returns a dataframe

quant_risk.statistics.statistics.calculate_kurtosis(price: Union[pandas.core.series.Series, pandas.core.frame.DataFrame], test: bool = False, **kwargs) → Union[float, pandas.core.series.Series]

Calculates the kurtosis for a given set of prices

Parameters

price (Union[pd.DataFrame,pd.Series]) – historical prices of a given security

Returns

kurtosis for a given set of prices

Return type

Union[float,pd.Series]

quant_risk.statistics.statistics.calculate_skewness(price: Union[pandas.core.frame.DataFrame, pandas.core.series.Series], test: bool = False, **kwargs) → Union[float, pandas.core.series.Series]

Calculates the skewness for a given set of prices

Parameters

price (Union[pd.DataFrame,pd.Series]) – historical prices of a given security

Returns

skewness for a given set of prices

Return type

Union[float,pd.Series]

quant_risk.statistics.statistics.covariance_shrinkage(price: pandas.core.frame.DataFrame, delta: float = 0.5, **kwargs)

This function computes the covariance matrix using the Ledoit-Wolf covariance shrinkage method taking a linear combination of the Constant Correlation matrix, acting as our prior and the Sample covariance matrix. The posterior covariance matrix is then computed.

Parameters

• price (pd.DataFrame) – Historical prices of a given security

• delta (float, optional) – Constant by which to weigh the priori matrix, by default 0.5

Returns

Returns a covariance matrix

Return type

pd.DataFrame

quant_risk.statistics.statistics.cumulative_returns(price: Union[pandas.core.frame.DataFrame, pandas.core.series.Series]) → float

Calculates cumulative returns for a given set of prices

Parameters

price (Union[pd.DataFrame, pd.Series]) – historical prices of a given security

Returns

cumulative returns for a given set of prices

Return type

float

quant_risk.statistics.statistics.elton_gruber_covariance(price: pandas.core.frame.DataFrame, **kwargs)

This function estimates the covariance matrix by assuming an implicit structure as defined by the Elton-Gruber Constant Correlation model.

Parameters

price (pd.DataFrame) – Historical prices of a given security

Returns

Returns a covariance matrix

Return type

pd.DataFrame

quant_risk.statistics.statistics.is_stable(price: pandas.core.series.Series) → float

Calculates stability for a given set of prices

Parameters

price (pd.Series) – historical prices of a given security

Returns

stability for a given set of prices

Return type

float

quant_risk.statistics.statistics.maximum_drawdown(price: pandas.core.series.Series) → float

Calculates maximum drawdown for a given set of prices

Parameters

price (pd.Series) – historical prices of a given security

Returns

maximum drawdown for a given set of prices

Return type

float

quant_risk.statistics.statistics.risk_contribution(portfolioWeights: Union[numpy.array, pandas.core.frame.DataFrame], covarianceMatrix: pandas.core.frame.DataFrame)

This function computes the contributions to the risk/variance of the constituents of a portfolio, given a set of portfolio weights and a covariance matrix

Parameters

• portfolioWeights (Union[np.array, pd.DataFrame]) – weights of our assets in our portfolio

• covarianceMatrix (pd.DataFrame) – the covariance matrix of our assets computed by any method

Returns

Returns the risk contribution of each asset

Return type

pd.DataFrame

statistics.summarize module

quant_risk.statistics.summarize.print_summary(price: pandas.core.series.Series, **kwargs)

This function returns a dataframe with the following characteristics: Financial Ratios: 1. Sharpe ratio 2. Sortino ratio 3. Calmar ratio 4. Omega ratio 5. Tail Ratio

Statistics: 1. Skewness 2. Kurtosis 3. Stability 4. Max Drawdown 5. Cumulative returns

Annualise: 1. Returns 2. Vol

Value at Risk 1. VaR 2. cVaR

statistics.tests module

Statistical tests

quant_risk.statistics.tests.ACF(series: pandas.core.series.Series, adjusted: bool = False, nLags: int = 20, qStat: bool = False, fft: bool = True, alpha: float = None, missing: str = 'none', plot: bool = True) → Union[numpy.ndarray, tuple]

Calculates the ACF, and optionally the confidence intervals, Ljung-Box Q-Statistic, and its associated p-values for a given series Check documentation here: https://www.statsmodels.org/stable/generated/statsmodels.tsa.stattools.acf.html#statsmodels.tsa.stattools.acf Note: series is only for one security

Parameters

• series (pd.Series) – time series data

• adjusted (bool, optional) – If True, then denominators for autocovariance are n-k, otherwise n, by default False

• nLags (int, optional) – Number of lags to return autocorrelation for, by default None

• qStat (bool, optional) – If True, returns the Ljung-Box q statistic for each autocorrelation coefficient, by default False

• fft (bool, optional) – If True, computes the ACF via FFT, by default None

• alpha (float, optional) – If a number is given, the confidence intervals for the given level are returned, by default None

• missing (str, optional) – A string in [“none”, “raise”, “conservative”, “drop”] specifying how the NaNs are to be treated, by default ‘none’

Returns

Returns the autocorrelation function of type np.ndarray, and

Confidence intervals for the ACF, if alpha is not None, of type np.ndarray The Ljung-Box Q-Statistic, if qStat is True, of type np.ndarray The p-values associated with the Q-statistics, if qStat is True, of type np.ndarray

Return type

Union[np.ndarray,tuple]

quant_risk.statistics.tests.PACF(series: pandas.core.series.Series, nLags: int = 20, method: str = 'ywadjusted', alpha: float = None, plot: bool = True) → Union[numpy.ndarray, tuple]

Calculates the PACF, and optionally the confidence intervals, for the returns of a given series Documentation: https://www.statsmodels.org/stable/generated/statsmodels.tsa.stattools.pacf.html#statsmodels.tsa.stattools.pacf Note: series is only for one security

Parameters

• series (pd.Series) – time series data

• nLags (int, optional) – The largest lag for which the PACF is returned, by default None

• method (str, optional) – Specifies which method for the calculations to use, full list in documentation, by default ‘ywadjusted’

• alpha (float, optional) – If a number is given, the confidence intervals for the given level are returned, by default None

Returns

Partial autocorrelations, nlags elements, including lag zero, of type np.ndarray and

Confidence intervals for the PACF if alpha is not None, of type np.ndarray

Return type

Union[np.ndarray,tuple]

quant_risk.statistics.tests.granger_causality(series: pandas.core.frame.DataFrame, maxLags: Union[int, list], addConst: bool = True, verbose: bool = True, testToUse: str = 'ssr_ftest') → dict

Performs the Granger Causality Test for the given series Note: pd.DataFrame should contain two columns Note: series data must be stationary, difference before passing if needed

Parameters

• series (pd.DataFrame) – data for testing whether the time series in the second column Granger causes the time series in the first column (missing values not supported)

• maxLags (int) – If an integer, computes the test for all lags up to maxlag. If a list, computes the tests only for the lags in maxlag

• addConst (bool) – Add a constant to the model, by default True

• verbose (bool, optional) – True if debugging information is to be printed, by default True

Returns

All test results, dictionary keys are the number of lags. For each lag the values are a tuple,

First element: a dictionary with test statistic, p-values, degrees of freedom, keys: ‘lrtest’, ‘params_ftest’, ‘ssr_chi2test’, ‘ssr_ftest’ Second element: the OLS estimation results for the restricted model, the unrestricted model and the restriction (contrast) matrix for the parameter f_test For example: to get p-value for ssr_ftest for ith lag: res[i][0][‘ssr_ftest’][1]

Return type

dict

quant_risk.statistics.tests.granger_causality_matrix(data: pandas.core.frame.DataFrame, testToUse: str = 'ssr_ftest', verbose: bool = False, maxlag: int = 10)

The function returns a NxN matrix where N is the number of columns in our time series dataframe(should be the same as the number of variables in variables). The matrix is just the minimum p-value of the Johansen Cointegration test that is performed for each lag till maxlag for each series pair. The function also returns a dataframe that contains the lag value where the minimum pvalue was found. The variables in the columns are the predictors and the variables in the rows are reponses. The value in each cell of the matrix can be interpreted as the whether we can assume(<0.05) if our column causes our row variable.

Parameters

• data (pd.DataFrame) –

• of Multivariate time series (Dataframe) –

• testToUse (str, optional) – Which test statistic to use for our Granger Causality test, by default ‘ssr_ftest’

• verbose (boolean, optional) – Should the computation be shown for each lag value for each pair computed, by default False

• maxlag (int, optional) – The maximum lag that the test checks causality for, by default 6

Returns

Returns two dataframes that contain the pvalues and the value of the lag at which the minimum pvalue was found.

Return type

[pd.DataFrame, pd.DataFrame]

quant_risk.statistics.tests.hurst_exponent(series: pandas.core.series.Series, maxlag: int) → float

Returns the Hurst Exponent value for a given time series Source: https://towardsdatascience.com/introduction-to-the-hurst-exponent-with-code-in-python-4da0414ca52e

Parameters

• series (pd.Series) – time series

• maxLags (int) – maximum number of lags

Returns

Hurst Exponent

Return type

float

quant_risk.statistics.tests.stationary_test_adf(series: pandas.core.series.Series, verbose: bool = True, stationaritySignifiance: float = 0.05) → tuple

Runs the Augmented Dickey-Fuller test on the series, with the Null Hypothesis of non-stationarity i.e data has a unit root

Parameters

• series (pd.Series) – Time series data that we want to test for stationarity

• verbose (bool, optional) – True if the ADF statistic, p-value and critical values are to be printed, by default True

• stationaritySignificance (float, optional) – The level of signifiance at which stationarity is checked, by default 0.05 (5%)

Returns

Returns the relevant values in the format (p-value, ADF statistic, stationaryBool)

Return type

tuple

Module contents