Calculate all the statistics required from the backtest, based on the equity curve and the profit loss statement. More...

Static Public Member Functions
static decimal	DrawdownPercent (SortedDictionary< DateTime, decimal > equityOverTime, int rounding=2)
	Drawdown maximum percentage. More...

static decimal	CompoundingAnnualPerformance (decimal startingCapital, decimal finalCapital, decimal years)
	Annual compounded returns statistic based on the final-starting capital and years. More...

static double	AnnualPerformance (List< double > performance, double tradingDaysPerYear)
	Annualized return statistic calculated as an average of daily trading performance multiplied by the number of trading days per year. More...

static double	AnnualVariance (List< double > performance, double tradingDaysPerYear)
	Annualized variance statistic calculation using the daily performance variance and trading days per year. More...

static double	AnnualStandardDeviation (List< double > performance, double tradingDaysPerYear)
	Annualized standard deviation More...

static double	AnnualDownsideVariance (List< double > performance, double tradingDaysPerYear, double minimumAcceptableReturn=0)
	Annualized variance statistic calculation using the daily performance variance and trading days per year. More...

static double	AnnualDownsideStandardDeviation (List< double > performance, double tradingDaysPerYear, double minimumAcceptableReturn=0)
	Annualized downside standard deviation More...

static double	TrackingError (List< double > algoPerformance, List< double > benchmarkPerformance, double tradingDaysPerYear)
	Tracking error volatility (TEV) statistic - a measure of how closely a portfolio follows the index to which it is benchmarked More...

static double	SharpeRatio (double averagePerformance, double standardDeviation, double riskFreeRate)
	Sharpe ratio with respect to risk free rate: measures excess of return per unit of risk. More...

static decimal	SharpeRatio (decimal averagePerformance, decimal standardDeviation, decimal riskFreeRate)
	Sharpe ratio with respect to risk free rate: measures excess of return per unit of risk. More...

static double	SharpeRatio (List< double > algoPerformance, double riskFreeRate, double tradingDaysPerYear)
	Sharpe ratio with respect to risk free rate: measures excess of return per unit of risk. More...

static double	SortinoRatio (List< double > algoPerformance, double riskFreeRate, double tradingDaysPerYear, double minimumAcceptableReturn=0)
	Sortino ratio with respect to risk free rate: measures excess of return per unit of downside risk. More...

static double	ProbabilisticSharpeRatio (List< double > listPerformance, double benchmarkSharpeRatio)
	Helper method to calculate the probabilistic sharpe ratio More...

static double	ObservedSharpeRatio (List< double > listPerformance)
	Calculates the observed sharpe ratio More...

static decimal	DrawdownPercent (decimal current, decimal high, int roundingDecimals=2)
	Calculate the drawdown between a high and current value More...

Detailed Description

Calculate all the statistics required from the backtest, based on the equity curve and the profit loss statement.

This is a particularly ugly class and one of the first ones written. It should be thrown out and re-written.

Definition at line 31 of file Statistics.cs.

Member Function Documentation

◆ DrawdownPercent() [1/2]

static decimal QuantConnect.Statistics.Statistics.DrawdownPercent	(	SortedDictionary< DateTime, decimal >	equityOverTime,
		int	rounding = `2`
	)

static

Drawdown maximum percentage.

Parameters

equityOverTime
rounding

Returns

Definition at line 39 of file Statistics.cs.

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◆ CompoundingAnnualPerformance()

static decimal QuantConnect.Statistics.Statistics.CompoundingAnnualPerformance	(	decimal	startingCapital,
		decimal	finalCapital,
		decimal	years
	)

static

Annual compounded returns statistic based on the final-starting capital and years.

Parameters

startingCapital	Algorithm starting capital
finalCapital	Algorithm final capital
years	Years trading

Returns: Decimal fraction for annual compounding performance

Definition at line 68 of file Statistics.cs.

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◆ AnnualPerformance()

static double QuantConnect.Statistics.Statistics.AnnualPerformance	(	List< double >	performance,
		double	tradingDaysPerYear
	)

static

Annualized return statistic calculated as an average of daily trading performance multiplied by the number of trading days per year.

Parameters

performance	Dictionary collection of double performance values
tradingDaysPerYear	Trading days per year for the assets in portfolio

May be unaccurate for forex algorithms with more trading days in a year

Returns: Double annual performance percentage

Definition at line 87 of file Statistics.cs.

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◆ AnnualVariance()

static double QuantConnect.Statistics.Statistics.AnnualVariance	(	List< double >	performance,
		double	tradingDaysPerYear
	)

static

Annualized variance statistic calculation using the daily performance variance and trading days per year.

Parameters

performance
tradingDaysPerYear

Invokes the variance extension in the MathNet Statistics class

Returns: Annual variance value

Definition at line 99 of file Statistics.cs.

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◆ AnnualStandardDeviation()

static double QuantConnect.Statistics.Statistics.AnnualStandardDeviation	(	List< double >	performance,
		double	tradingDaysPerYear
	)

static

Annualized standard deviation

Parameters

performance	Collection of double values for daily performance
tradingDaysPerYear	Number of trading days for the assets in portfolio to get annualize standard deviation.

Invokes the variance extension in the MathNet Statistics class. Feasibly the trading days per year can be fetched from the dictionary of performance which includes the date-times to get the range; if is more than 1 year data.

Returns: Value for annual standard deviation

Definition at line 115 of file Statistics.cs.

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◆ AnnualDownsideVariance()

static double QuantConnect.Statistics.Statistics.AnnualDownsideVariance	(	List< double >	performance,
		double	tradingDaysPerYear,
		double	minimumAcceptableReturn = `0`
	)

static

Annualized variance statistic calculation using the daily performance variance and trading days per year.

Parameters

performance
tradingDaysPerYear
minimumAcceptableReturn	Minimum acceptable return

Invokes the variance extension in the MathNet Statistics class

Returns: Annual variance value

Definition at line 128 of file Statistics.cs.

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◆ AnnualDownsideStandardDeviation()

static double QuantConnect.Statistics.Statistics.AnnualDownsideStandardDeviation	(	List< double >	performance,
		double	tradingDaysPerYear,
		double	minimumAcceptableReturn = `0`
	)

static

Annualized downside standard deviation

Parameters

performance	Collection of double values for daily performance
tradingDaysPerYear	Number of trading days for the assets in portfolio to get annualize standard deviation.
minimumAcceptableReturn	Minimum acceptable return

Returns: Value for annual downside standard deviation

Definition at line 140 of file Statistics.cs.

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◆ TrackingError()

static double QuantConnect.Statistics.Statistics.TrackingError	(	List< double >	algoPerformance,
		List< double >	benchmarkPerformance,
		double	tradingDaysPerYear
	)

static

Tracking error volatility (TEV) statistic - a measure of how closely a portfolio follows the index to which it is benchmarked

If algo = benchmark, TEV = 0

Parameters

algoPerformance	Double collection of algorithm daily performance values
benchmarkPerformance	Double collection of benchmark daily performance values
tradingDaysPerYear	Number of trading days per year

Returns: Value for tracking error

Definition at line 153 of file Statistics.cs.

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◆ SharpeRatio() [1/3]

static double QuantConnect.Statistics.Statistics.SharpeRatio	(	double	averagePerformance,
		double	standardDeviation,
		double	riskFreeRate
	)

static

Sharpe ratio with respect to risk free rate: measures excess of return per unit of risk.

With risk defined as the algorithm's volatility

Parameters

averagePerformance	Average daily performance
standardDeviation	Standard deviation of the daily performance
riskFreeRate	The risk free rate

Returns: Value for sharpe ratio

Definition at line 178 of file Statistics.cs.

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◆ SharpeRatio() [2/3]

static decimal QuantConnect.Statistics.Statistics.SharpeRatio	(	decimal	averagePerformance,
		decimal	standardDeviation,
		decimal	riskFreeRate
	)

static

Sharpe ratio with respect to risk free rate: measures excess of return per unit of risk.

With risk defined as the algorithm's volatility

Parameters

averagePerformance	Average daily performance
standardDeviation	Standard deviation of the daily performance
riskFreeRate	The risk free rate

Returns: Value for sharpe ratio

Definition at line 191 of file Statistics.cs.

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◆ SharpeRatio() [3/3]

static double QuantConnect.Statistics.Statistics.SharpeRatio	(	List< double >	algoPerformance,
		double	riskFreeRate,
		double	tradingDaysPerYear
	)

static

Sharpe ratio with respect to risk free rate: measures excess of return per unit of risk.

With risk defined as the algorithm's volatility

Parameters

algoPerformance	Collection of double values for the algorithm daily performance
riskFreeRate	The risk free rate
tradingDaysPerYear	Trading days per year for the assets in portfolio

Returns: Value for sharpe ratio

Definition at line 204 of file Statistics.cs.

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◆ SortinoRatio()

static double QuantConnect.Statistics.Statistics.SortinoRatio	(	List< double >	algoPerformance,
		double	riskFreeRate,
		double	tradingDaysPerYear,
		double	minimumAcceptableReturn = `0`
	)

static

Sortino ratio with respect to risk free rate: measures excess of return per unit of downside risk.

With risk defined as the algorithm's volatility

Parameters

algoPerformance	Collection of double values for the algorithm daily performance
riskFreeRate	The risk free rate
tradingDaysPerYear	Trading days per year for the assets in portfolio
minimumAcceptableReturn	Minimum acceptable return for Sortino ratio calculation

Returns: Value for Sortino ratio

Definition at line 218 of file Statistics.cs.

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◆ ProbabilisticSharpeRatio()

static double QuantConnect.Statistics.Statistics.ProbabilisticSharpeRatio	(	List< double >	listPerformance,
		double	benchmarkSharpeRatio
	)

static

Helper method to calculate the probabilistic sharpe ratio

Parameters

listPerformance	The list of algorithm performance values
benchmarkSharpeRatio	The benchmark sharpe ratio to use

Returns: Probabilistic Sharpe Ratio

Definition at line 229 of file Statistics.cs.

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◆ ObservedSharpeRatio()

static double QuantConnect.Statistics.Statistics.ObservedSharpeRatio ( List< double > listPerformance )

static

Calculates the observed sharpe ratio

Parameters

listPerformance The performance samples to use

Returns: The observed sharpe ratio

Definition at line 258 of file Statistics.cs.

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◆ DrawdownPercent() [2/2]

static decimal QuantConnect.Statistics.Statistics.DrawdownPercent	(	decimal	current,
		decimal	high,
		int	roundingDecimals = `2`
	)

static

Calculate the drawdown between a high and current value

Parameters

current	Current value
high	Latest maximum
roundingDecimals	Digits to round the result too

Returns: Drawdown percentage

Definition at line 273 of file Statistics.cs.

The documentation for this class was generated from the following file:

Common/Statistics/Statistics.cs

Static Public Member Functions

Detailed Description

Member Function Documentation

◆ DrawdownPercent() [1/2]

◆ CompoundingAnnualPerformance()

◆ AnnualPerformance()

◆ AnnualVariance()

◆ AnnualStandardDeviation()

◆ AnnualDownsideVariance()

◆ AnnualDownsideStandardDeviation()

◆ TrackingError()

◆ SharpeRatio() [1/3]

◆ SharpeRatio() [2/3]

◆ SharpeRatio() [3/3]

◆ SortinoRatio()

◆ ProbabilisticSharpeRatio()

◆ ObservedSharpeRatio()

◆ DrawdownPercent() [2/2]