diff --git a/Algorithm/QCAlgorithm.Indicators.cs b/Algorithm/QCAlgorithm.Indicators.cs index e399deb7ed30..63c85c8d8e70 100644 --- a/Algorithm/QCAlgorithm.Indicators.cs +++ b/Algorithm/QCAlgorithm.Indicators.cs @@ -1872,6 +1872,27 @@ public ParabolicStopAndReverse PSAR(Symbol symbol, decimal afStart = 0.02m, deci return parabolicStopAndReverse; } + /// + /// Creates a new RachevRatio indicator. + /// + /// The symbol whose Rachev ratio we want + /// Number of returns in the lookback period + /// Tail probability of the best returns, the numerator of the ratio + /// Tail probability of the worst returns, the denominator of the ratio + /// Risk-free rate per period, subtracted from each return + /// The resolution + /// Selects a value from the BaseData to send into the indicator, if null defaults to the Value property of BaseData (x => x.Value) + /// The RachevRatio indicator for the requested symbol over the specified period + [DocumentationAttribute(Indicators)] + public RachevRatio RACHEV(Symbol symbol, int period, double alpha = 0.05, double beta = 0.05, double riskFreeRate = 0.0, Resolution? resolution = null, Func selector = null) + { + var name = CreateIndicatorName(symbol, $"RACHEV({period},{alpha},{beta},{riskFreeRate})", resolution); + var rachevRatio = new RachevRatio(name, period, alpha, beta, riskFreeRate); + InitializeIndicator(rachevRatio, resolution, selector, symbol); + + return rachevRatio; + } + /// /// Creates a new RegressionChannel indicator which will compute the LinearRegression, UpperChannel and LowerChannel lines, the intercept and slope /// diff --git a/Indicators/RachevRatio.cs b/Indicators/RachevRatio.cs new file mode 100644 index 000000000000..8f7424049ce8 --- /dev/null +++ b/Indicators/RachevRatio.cs @@ -0,0 +1,185 @@ +/* + * QUANTCONNECT.COM - Democratizing Finance, Empowering Individuals. + * Lean Algorithmic Trading Engine v2.0. Copyright 2014 QuantConnect Corporation. + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. +*/ + +using System; +using System.Linq; + +namespace QuantConnect.Indicators +{ + /// + /// Calculation of the Rachev Ratio, the expected tail return of the best outcomes + /// divided by the expected tail loss of the worst outcomes of the return distribution. + /// + /// Reference: Biglova, Ortobelli, Rachev and Stoyanov (2004), "Different Approaches to Risk Estimation + /// in Portfolio Theory", The Journal of Portfolio Management 31(1), 103-112. + /// https://en.wikipedia.org/wiki/Rachev_ratio + /// Formula: RR(x) = ETL_alpha(Rf - Rx) / ETL_beta(Rx - Rf) + /// Where: + /// RR(x) - Rachev ratio of x + /// Rx - one period returns of x over the lookback period + /// Rf - risk-free rate per period + /// ETL_q(X) - expected tail loss (CVaR) of X in the worst q fraction of the observations + /// + /// The historical expected tail loss weights the observation at the tail boundary by its fraction, + /// as in Acerbi and Tasche (2002), "On the coherence of expected shortfall". + /// + public class RachevRatio : IndicatorBase, IIndicatorWarmUpPeriodProvider + { + /// + /// Tail probability of the best returns, used in the numerator + /// + private readonly double _alpha; + + /// + /// Tail probability of the worst returns, used in the denominator + /// + private readonly double _beta; + + /// + /// Risk-free rate per period + /// + private readonly double _riskFreeRate; + + /// + /// RateOfChange indicator to calculate the returns + /// + private readonly RateOfChange _rateOfChange; + + /// + /// Rolling window to store the excess returns of the input data + /// + private readonly RollingWindow _returns; + + /// + /// Required period, in data points, for the indicator to be ready and fully initialized. + /// + public int WarmUpPeriod { get; } + + /// + /// Gets a flag indicating when the indicator is ready and fully initialized + /// + public override bool IsReady => _returns.IsReady; + + /// + /// Creates a new RachevRatio indicator using the specified periods + /// + /// The name of this indicator + /// Number of returns in the lookback period + /// Tail probability of the best returns, the numerator of the ratio + /// Tail probability of the worst returns, the denominator of the ratio + /// Risk-free rate per period, subtracted from each return + public RachevRatio(string name, int period, double alpha = 0.05, double beta = 0.05, double riskFreeRate = 0) + : base(name) + { + if (period < 2) + { + throw new ArgumentException($"Period parameter for RachevRatio indicator must be greater than 1 but was {period}"); + } + if (alpha <= 0 || alpha >= 1) + { + throw new ArgumentException($"Alpha parameter for RachevRatio indicator must be between 0 and 1 but was {alpha}"); + } + if (beta <= 0 || beta >= 1) + { + throw new ArgumentException($"Beta parameter for RachevRatio indicator must be between 0 and 1 but was {beta}"); + } + + _alpha = alpha; + _beta = beta; + _riskFreeRate = riskFreeRate; + _rateOfChange = new RateOfChange(1); + _returns = new RollingWindow(period); + WarmUpPeriod = period + 1; + } + + /// + /// Creates a new RachevRatio indicator using the specified periods + /// + /// Number of returns in the lookback period + /// Tail probability of the best returns, the numerator of the ratio + /// Tail probability of the worst returns, the denominator of the ratio + /// Risk-free rate per period, subtracted from each return + public RachevRatio(int period, double alpha = 0.05, double beta = 0.05, double riskFreeRate = 0) + : this($"RACHEV({period},{alpha},{beta},{riskFreeRate})", period, alpha, beta, riskFreeRate) + { + } + + /// + /// Computes the next value for this indicator from the given state. + /// + /// The input given to the indicator + /// A new value for this indicator + protected override decimal ComputeNextValue(IndicatorDataPoint input) + { + _rateOfChange.Update(input); + if (!_rateOfChange.IsReady) + { + return 0m; + } + + _returns.Add((double)_rateOfChange.Current.Value - _riskFreeRate); + if (!_returns.IsReady) + { + return 0m; + } + + var sorted = _returns.OrderBy(x => x).ToArray(); + var expectedTailLoss = -TailMean(sorted, _beta); + if (expectedTailLoss == 0) + { + return 0m; + } + + Array.Reverse(sorted); + var expectedTailReturn = TailMean(sorted, _alpha); + return (expectedTailReturn / expectedTailLoss).SafeDecimalCast(); + } + + /// + /// Resets this indicator to its initial state + /// + public override void Reset() + { + _rateOfChange.Reset(); + _returns.Reset(); + base.Reset(); + } + + /// + /// Average of the first fraction of the given values. + /// When the tail size is not a whole number of observations, the last observation + /// in the tail is weighted by its fractional part. + /// + /// The sorted values, starting with the tail + /// The fraction of the values in the tail + /// The average of the tail + private static double TailMean(double[] values, double probability) + { + var tailSize = probability * values.Length; + var wholeObservations = (int)Math.Floor(tailSize); + + var sum = 0d; + for (var i = 0; i < wholeObservations; i++) + { + sum += values[i]; + } + if (wholeObservations < values.Length) + { + sum += (tailSize - wholeObservations) * values[wholeObservations]; + } + return sum / tailSize; + } + } +} diff --git a/Tests/Indicators/RachevRatioTests.cs b/Tests/Indicators/RachevRatioTests.cs new file mode 100644 index 000000000000..911f2129880e --- /dev/null +++ b/Tests/Indicators/RachevRatioTests.cs @@ -0,0 +1,102 @@ +/* + * QUANTCONNECT.COM - Democratizing Finance, Empowering Individuals. + * Lean Algorithmic Trading Engine v2.0. Copyright 2014 QuantConnect Corporation. + * + * Licensed under the Apache License, Version 2.0 (the "License"); + * you may not use this file except in compliance with the License. + * You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0 + * + * Unless required by applicable law or agreed to in writing, software + * distributed under the License is distributed on an "AS IS" BASIS, + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. + * See the License for the specific language governing permissions and + * limitations under the License. +*/ + +using NUnit.Framework; +using QuantConnect.Indicators; +using System; + +namespace QuantConnect.Tests.Indicators +{ + [TestFixture, Parallelizable(ParallelScope.Fixtures)] + public class RachevRatioTests : CommonIndicatorTests + { + private const int _tradingDays = 252; + + protected override string TestFileName => "spy_rachev_ratio.csv"; + + protected override string TestColumnName => "rachev_ratio"; + + protected override IndicatorBase CreateIndicator() + { + return new RachevRatio(_tradingDays); + } + + protected override Action, double> Assertion + { + get { return (indicator, expected) => Assert.AreEqual(expected, (double)indicator.Current.Value, 1e-6); } + } + + [Test] + public void ComparesAgainstExternalDataWithDifferentTailProbabilities() + { + var indicator = new RachevRatio(_tradingDays, alpha: 0.1, beta: 0.05); + + TestHelper.TestIndicator(indicator, TestFileName, "rachev_ratio_alpha_0.1_beta_0.05", Assertion); + } + + [Test] + public void ComparesAgainstExternalDataWithRiskFreeRate() + { + var indicator = new RachevRatio(_tradingDays, riskFreeRate: 0.0001); + + TestHelper.TestIndicator(indicator, TestFileName, "rachev_ratio_rf_0.0001", Assertion); + } + + [Test] + public void ComputesTailAveragesOfKnownReturns() + { + // Returns: -2%, +1%, +3%, -1%, +2% + // With alpha = beta = 0.2 each tail holds one observation: 3% / 2% = 1.5 + var prices = new[] { 100m, 98m, 98.98m, 101.9494m, 100.929906m, 102.94850412m }; + var indicator = new RachevRatio(5, alpha: 0.2, beta: 0.2); + + var time = new DateTime(2024, 1, 1); + for (var i = 0; i < prices.Length; i++) + { + Assert.IsFalse(indicator.IsReady); + indicator.Update(new IndicatorDataPoint(time.AddDays(i), prices[i])); + } + + Assert.IsTrue(indicator.IsReady); + Assert.AreEqual(1.5, (double)indicator.Current.Value, 1e-10); + } + + [Test] + public void ConstantValuesReturnZero() + { + // With the value not changing there is no tail loss, so the indicator should return 0m + var indicator = new RachevRatio(_tradingDays); + + var time = new DateTime(2024, 1, 1); + for (var i = 0; i < indicator.WarmUpPeriod; i++) + { + indicator.Update(new IndicatorDataPoint(time.AddDays(i), 100m)); + } + + Assert.IsTrue(indicator.IsReady); + Assert.AreEqual(0m, indicator.Current.Value); + } + + [TestCase(1, 0.05, 0.05)] + [TestCase(10, 0, 0.05)] + [TestCase(10, 1, 0.05)] + [TestCase(10, 0.05, 0)] + [TestCase(10, 0.05, 1)] + public void InvalidParametersThrow(int period, double alpha, double beta) + { + Assert.Throws(() => new RachevRatio(period, alpha, beta)); + } + } +} diff --git a/Tests/QuantConnect.Tests.csproj b/Tests/QuantConnect.Tests.csproj index 30dab6a1cacc..f7ef77be819c 100644 --- a/Tests/QuantConnect.Tests.csproj +++ b/Tests/QuantConnect.Tests.csproj @@ -367,6 +367,9 @@ PreserveNewest + + PreserveNewest + PreserveNewest diff --git a/Tests/TestData/spy_rachev_ratio.csv b/Tests/TestData/spy_rachev_ratio.csv new file mode 100644 index 000000000000..7c8a5014f176 --- /dev/null +++ b/Tests/TestData/spy_rachev_ratio.csv @@ -0,0 +1,5850 @@ +date,open,high,low,close,volume,returns,rachev_ratio,rachev_ratio_alpha_0.1_beta_0.05,rachev_ratio_rf_0.0001 +19980102 00:00,973100,975300,965300,973600,2150000,,,, +19980105 00:00,978400,984400,967800,977500,4030800,0.004005751849,,, +19980106 00:00,972500,972800,961900,966300,2821800,-0.01145780051,,, +19980107 00:00,960900,965000,952200,964700,5225400,-0.001655800476,,, +19980108 00:00,963100,963100,955000,957800,3249100,-0.007152482637,,, +19980109 00:00,952500,955000,919100,924700,10000200,-0.03455836292,,, +19980112 00:00,911300,941900,909100,940600,11953200,0.01719476587,,, +19980113 00:00,946300,956300,942200,952200,5006400,0.01233255369,,, +19980114 00:00,956900,959700,947200,958100,3738000,0.006196177274,,, +19980115 00:00,955000,957500,948100,949400,2726400,-0.009080471767,,, +19980116 00:00,962500,966900,956600,962300,4185400,0.01358752897,,, +19980120 00:00,966900,980000,965000,980000,4373400,0.0183934324,,, +19980121 00:00,972200,976900,961600,971600,4526300,-0.008571428571,,, +19980122 00:00,961600,968800,958800,963000,4484300,-0.008851379168,,, +19980123 00:00,965000,967800,950000,956600,6231300,-0.006645898235,,, +19980126 00:00,963800,967300,937500,957500,4280800,0.0009408321137,,, +19980127 00:00,958100,980000,956600,970000,6639000,0.01305483029,,, +19980128 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