chore: import upstream snapshot with attribution
This commit is contained in:
wehub-resource-sync
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/*
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* QUANTCONNECT.COM - Democratizing Finance, Empowering Individuals.
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* Lean Algorithmic Trading Engine v2.0. Copyright 2014 QuantConnect Corporation.
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*
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* Licensed under the Apache License, Version 2.0 (the "License");
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* you may not use this file except in compliance with the License.
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* You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an "AS IS" BASIS,
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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using System;
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using System.Collections.Generic;
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using System.Linq;
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using MathNet.Numerics.Distributions;
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using MathNet.Numerics.Statistics;
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using Newtonsoft.Json;
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using QuantConnect.Data;
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using QuantConnect.Util;
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namespace QuantConnect.Statistics
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{
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/// <summary>
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/// The <see cref="PortfolioStatistics"/> class represents a set of statistics calculated from equity and benchmark samples
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/// </summary>
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public class PortfolioStatistics
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{
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/// <summary>
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/// The average rate of return for trades with positive profit loss
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/// </summary>
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[JsonConverter(typeof(JsonRoundingConverter))]
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public decimal AverageWinRate { get; set; }
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/// <summary>
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/// The average rate of return for trades with zero or negative profit loss
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/// </summary>
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[JsonConverter(typeof(JsonRoundingConverter))]
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public decimal AverageLossRate { get; set; }
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/// <summary>
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/// The ratio of the average win rate to the average loss rate
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/// </summary>
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/// <remarks>If the average loss rate is zero, ProfitLossRatio is set to 0</remarks>
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[JsonConverter(typeof(JsonRoundingConverter))]
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public decimal ProfitLossRatio { get; set; }
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/// <summary>
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/// The ratio of the number of trades with positive profit loss to the total number of trades
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/// </summary>
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/// <remarks>If the total number of trades is zero, WinRate is set to zero</remarks>
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[JsonConverter(typeof(JsonRoundingConverter))]
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public decimal WinRate { get; set; }
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/// <summary>
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/// The ratio of the number of trades with zero or negative profit loss to the total number of trades
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/// </summary>
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/// <remarks>If the total number of trades is zero, LossRate is set to zero</remarks>
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[JsonConverter(typeof(JsonRoundingConverter))]
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public decimal LossRate { get; set; }
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/// <summary>
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/// The expected value of the rate of return
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/// </summary>
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[JsonConverter(typeof(JsonRoundingConverter))]
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public decimal Expectancy { get; set; }
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/// <summary>
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/// Initial Equity Total Value
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/// </summary>
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[JsonConverter(typeof(JsonRoundingConverter))]
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public decimal StartEquity { get; set; }
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/// <summary>
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/// Final Equity Total Value
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/// </summary>
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[JsonConverter(typeof(JsonRoundingConverter))]
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public decimal EndEquity { get; set; }
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/// <summary>
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/// Annual compounded returns statistic based on the final-starting capital and years.
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/// </summary>
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/// <remarks>Also known as Compound Annual Growth Rate (CAGR)</remarks>
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[JsonConverter(typeof(JsonRoundingConverter))]
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public decimal CompoundingAnnualReturn { get; set; }
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/// <summary>
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/// Drawdown maximum percentage.
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/// </summary>
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[JsonConverter(typeof(JsonRoundingConverter))]
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public decimal Drawdown { get; set; }
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/// <summary>
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/// The total net profit percentage.
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/// </summary>
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[JsonConverter(typeof(JsonRoundingConverter))]
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public decimal TotalNetProfit { get; set; }
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/// <summary>
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/// Sharpe ratio with respect to risk free rate: measures excess of return per unit of risk.
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/// </summary>
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/// <remarks>With risk defined as the algorithm's volatility</remarks>
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[JsonConverter(typeof(JsonRoundingConverter))]
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public decimal SharpeRatio { get; set; }
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/// <summary>
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/// Probabilistic Sharpe Ratio is a probability measure associated with the Sharpe ratio.
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/// It informs us of the probability that the estimated Sharpe ratio is greater than a chosen benchmark
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/// </summary>
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/// <remarks>See https://www.quantconnect.com/forum/discussion/6483/probabilistic-sharpe-ratio/p1</remarks>
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[JsonConverter(typeof(JsonRoundingConverter))]
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public decimal ProbabilisticSharpeRatio { get; set; }
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/// <summary>
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/// Sortino ratio with respect to risk free rate: measures excess of return per unit of downside risk.
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/// </summary>
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/// <remarks>With risk defined as the algorithm's volatility</remarks>
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[JsonConverter(typeof(JsonRoundingConverter))]
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public decimal SortinoRatio { get; set; }
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/// <summary>
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/// Algorithm "Alpha" statistic - abnormal returns over the risk free rate and the relationshio (beta) with the benchmark returns.
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/// </summary>
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[JsonConverter(typeof(JsonRoundingConverter))]
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public decimal Alpha { get; set; }
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/// <summary>
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/// Algorithm "beta" statistic - the covariance between the algorithm and benchmark performance, divided by benchmark's variance
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/// </summary>
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[JsonConverter(typeof(JsonRoundingConverter))]
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public decimal Beta { get; set; }
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/// <summary>
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/// Annualized standard deviation
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/// </summary>
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[JsonConverter(typeof(JsonRoundingConverter))]
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public decimal AnnualStandardDeviation { get; set; }
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/// <summary>
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/// Annualized variance statistic calculation using the daily performance variance and trading days per year.
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/// </summary>
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[JsonConverter(typeof(JsonRoundingConverter))]
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public decimal AnnualVariance { get; set; }
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/// <summary>
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/// Information ratio - risk adjusted return
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/// </summary>
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/// <remarks>(risk = tracking error volatility, a volatility measures that considers the volatility of both algo and benchmark)</remarks>
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[JsonConverter(typeof(JsonRoundingConverter))]
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public decimal InformationRatio { get; set; }
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/// <summary>
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/// Tracking error volatility (TEV) statistic - a measure of how closely a portfolio follows the index to which it is benchmarked
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/// </summary>
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/// <remarks>If algo = benchmark, TEV = 0</remarks>
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[JsonConverter(typeof(JsonRoundingConverter))]
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public decimal TrackingError { get; set; }
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/// <summary>
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/// Treynor ratio statistic is a measurement of the returns earned in excess of that which could have been earned on an investment that has no diversifiable risk
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/// </summary>
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[JsonConverter(typeof(JsonRoundingConverter))]
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public decimal TreynorRatio { get; set; }
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/// <summary>
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/// The average Portfolio Turnover
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/// </summary>
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[JsonConverter(typeof(JsonRoundingConverter))]
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public decimal PortfolioTurnover { get; set; }
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/// <summary>
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/// The 1-day VaR for the portfolio, using the Variance-covariance approach.
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/// Assumes a 99% confidence level, 1 year lookback period, and that the returns are normally distributed.
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/// </summary>
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[JsonConverter(typeof(JsonRoundingConverter))]
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public decimal ValueAtRisk99 { get; set; }
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/// <summary>
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/// The 1-day VaR for the portfolio, using the Variance-covariance approach.
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/// Assumes a 95% confidence level, 1 year lookback period, and that the returns are normally distributed.
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/// </summary>
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[JsonConverter(typeof(JsonRoundingConverter))]
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public decimal ValueAtRisk95 { get; set; }
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/// <summary>
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/// The recovery time of the maximum drawdown.
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/// </summary>
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[JsonConverter(typeof(JsonRoundingConverter))]
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public int DrawdownRecovery { get; set; }
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/// <summary>
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/// Initializes a new instance of the <see cref="PortfolioStatistics"/> class
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/// </summary>
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/// <param name="profitLoss">Trade record of profits and losses</param>
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/// <param name="equity">The list of daily equity values</param>
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/// <param name="portfolioTurnover">The algorithm portfolio turnover</param>
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/// <param name="listPerformance">The list of algorithm performance values</param>
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/// <param name="listBenchmark">The list of benchmark values</param>
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/// <param name="startingCapital">The algorithm starting capital</param>
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/// <param name="riskFreeInterestRateModel">The risk free interest rate model to use</param>
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/// <param name="tradingDaysPerYear">The number of trading days per year</param>
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/// <param name="winCount">
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/// The number of wins, including ITM options with profitLoss less than 0.
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/// If this and <paramref name="lossCount"/> are null, they will be calculated from <paramref name="profitLoss"/>
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/// </param>
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/// <param name="lossCount">The number of losses</param>
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public PortfolioStatistics(
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SortedDictionary<DateTime, decimal> profitLoss,
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SortedDictionary<DateTime, decimal> equity,
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SortedDictionary<DateTime, decimal> portfolioTurnover,
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List<double> listPerformance,
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List<double> listBenchmark,
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decimal startingCapital,
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IRiskFreeInterestRateModel riskFreeInterestRateModel,
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int tradingDaysPerYear,
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int? winCount = null,
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int? lossCount = null)
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{
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StartEquity = startingCapital;
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EndEquity = equity.LastOrDefault().Value;
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if (portfolioTurnover.Count > 0)
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{
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PortfolioTurnover = portfolioTurnover.Select(kvp => kvp.Value).Average();
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}
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if (startingCapital == 0
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// minimum amount of samples to calculate variance
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|| listBenchmark.Count < 2
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|| listPerformance.Count < 2)
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{
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return;
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}
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var runningCapital = startingCapital;
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var totalProfit = 0m;
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var totalLoss = 0m;
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var totalWins = 0;
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var totalLosses = 0;
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foreach (var pair in profitLoss)
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{
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var tradeProfitLoss = pair.Value;
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if (tradeProfitLoss > 0)
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{
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totalProfit += tradeProfitLoss / runningCapital;
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totalWins++;
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}
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else
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{
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totalLoss += tradeProfitLoss / runningCapital;
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totalLosses++;
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}
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runningCapital += tradeProfitLoss;
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}
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AverageWinRate = totalWins == 0 ? 0 : totalProfit / totalWins;
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AverageLossRate = totalLosses == 0 ? 0 : totalLoss / totalLosses;
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ProfitLossRatio = AverageLossRate == 0 ? 0 : AverageWinRate / Math.Abs(AverageLossRate);
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// Set the actual total wins and losses count.
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// Some options assignments (ITM) count as wins even though they are losses.
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if (winCount.HasValue && lossCount.HasValue)
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{
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totalWins = winCount.Value;
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totalLosses = lossCount.Value;
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}
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var totalTrades = totalWins + totalLosses;
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WinRate = totalTrades == 0 ? 0 : (decimal)totalWins / totalTrades;
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LossRate = totalTrades == 0 ? 0 : (decimal)totalLosses / totalTrades;
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Expectancy = WinRate * ProfitLossRatio - LossRate;
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if (startingCapital != 0)
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{
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TotalNetProfit = equity.Values.LastOrDefault() / startingCapital - 1;
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}
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var fractionOfYears = (decimal)(equity.Keys.LastOrDefault() - equity.Keys.FirstOrDefault()).TotalDays / 365;
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CompoundingAnnualReturn = Statistics.CompoundingAnnualPerformance(startingCapital, equity.Values.LastOrDefault(), fractionOfYears);
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AnnualVariance = Statistics.AnnualVariance(listPerformance, tradingDaysPerYear).SafeDecimalCast();
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AnnualStandardDeviation = (decimal)Math.Sqrt((double)AnnualVariance);
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var benchmarkAnnualPerformance = GetAnnualPerformance(listBenchmark, tradingDaysPerYear);
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var annualPerformance = GetAnnualPerformance(listPerformance, tradingDaysPerYear);
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var riskFreeRate = riskFreeInterestRateModel.GetAverageRiskFreeRate(equity.Select(x => x.Key));
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SharpeRatio = AnnualStandardDeviation == 0 ? 0 : Statistics.SharpeRatio(annualPerformance, AnnualStandardDeviation, riskFreeRate);
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var annualDownsideDeviation = Statistics.AnnualDownsideStandardDeviation(listPerformance, tradingDaysPerYear).SafeDecimalCast();
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SortinoRatio = annualDownsideDeviation == 0 ? 0 : Statistics.SharpeRatio(annualPerformance, annualDownsideDeviation, riskFreeRate);
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var benchmarkVariance = listBenchmark.Variance();
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Beta = benchmarkVariance.IsNaNOrZero() ? 0 : (decimal)(listPerformance.Covariance(listBenchmark) / benchmarkVariance);
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Alpha = Beta == 0 ? 0 : annualPerformance - (riskFreeRate + Beta * (benchmarkAnnualPerformance - riskFreeRate));
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TrackingError = (decimal)Statistics.TrackingError(listPerformance, listBenchmark, (double)tradingDaysPerYear);
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InformationRatio = TrackingError == 0 ? 0 : Extensions.SafeDecimalCast((double)annualPerformance - (double)benchmarkAnnualPerformance).SafeDivision(TrackingError);
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TreynorRatio = Beta == 0 ? 0 : Extensions.SafeDecimalCast((double)annualPerformance - (double)riskFreeRate).SafeDivision(Beta);
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// deannualize a 1 sharpe ratio
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var benchmarkSharpeRatio = 1.0d / Math.Sqrt(tradingDaysPerYear);
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ProbabilisticSharpeRatio = Statistics.ProbabilisticSharpeRatio(listPerformance, benchmarkSharpeRatio, (double)riskFreeRate / tradingDaysPerYear).SafeDecimalCast();
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ValueAtRisk99 = GetValueAtRisk(listPerformance, tradingDaysPerYear, 0.99d);
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ValueAtRisk95 = GetValueAtRisk(listPerformance, tradingDaysPerYear, 0.95d);
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var drawdownMetrics = Statistics.CalculateDrawdownMetrics(equity, 3);
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Drawdown = drawdownMetrics.Drawdown;
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DrawdownRecovery = drawdownMetrics.DrawdownRecovery;
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}
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/// <summary>
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/// Initializes a new instance of the <see cref="PortfolioStatistics"/> class
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/// </summary>
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public PortfolioStatistics()
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{
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}
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/// <summary>
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/// Annualized return statistic calculated as an average of daily trading performance multiplied by the number of trading days per year.
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/// </summary>
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/// <param name="performance">Dictionary collection of double performance values</param>
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/// <param name="tradingDaysPerYear">Trading days per year for the assets in portfolio</param>
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/// <remarks>May be inaccurate for forex algorithms with more trading days in a year</remarks>
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/// <returns>Double annual performance percentage</returns>
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private static decimal GetAnnualPerformance(List<double> performance, int tradingDaysPerYear)
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{
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try
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{
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return Statistics.AnnualPerformance(performance, tradingDaysPerYear).SafeDecimalCast();
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}
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catch (ArgumentException ex)
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{
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var partialSums = 0.0;
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var points = 0;
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double troublePoint = default;
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foreach (var point in performance)
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{
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points++;
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partialSums += point;
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if (Math.Pow(partialSums / points, tradingDaysPerYear).IsNaNOrInfinity())
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{
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troublePoint = point;
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break;
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}
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}
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throw new ArgumentException($"PortfolioStatistics.GetAnnualPerformance(): An exception was thrown when trying to cast the annual performance value due to the following performance point: {troublePoint}. " +
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$"The exception thrown was the following: {ex.Message}.");
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}
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}
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private static decimal GetValueAtRisk(
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List<double> performance,
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int lookbackPeriodDays,
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double confidenceLevel,
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int rounding = 3)
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{
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var periodPerformance = performance.TakeLast(lookbackPeriodDays);
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var mean = periodPerformance.Mean();
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var standardDeviation = periodPerformance.StandardDeviation();
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var valueAtRisk = (decimal)Normal.InvCDF(mean, standardDeviation, 1 - confidenceLevel);
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return Math.Round(valueAtRisk, rounding);
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}
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}
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}
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Reference in New Issue
Block a user