// <copyright file="AbsoluteRiskStatistics.cs" company="Math.NET">
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// Math.NET Numerics, part of the Math.NET Project
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// http://numerics.mathdotnet.com
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// http://github.com/mathnet/mathnet-numerics
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//
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// Copyright (c) 2009-2013 Math.NET
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//
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// Permission is hereby granted, free of charge, to any person
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// obtaining a copy of this software and associated documentation
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// files (the "Software"), to deal in the Software without
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// copy, modify, merge, publish, distribute, sublicense, and/or sell
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// copies of the Software, and to permit persons to whom the
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// Software is furnished to do so, subject to the following
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// conditions:
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// included in all copies or substantial portions of the Software.
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// OTHER DEALINGS IN THE SOFTWARE.
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// </copyright>
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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 IStation.Numerics.Statistics;
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namespace IStation.Numerics.Financial
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{
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public static class AbsoluteRiskMeasures
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{
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// Note: The following statistics would be considered an absolute risk statistic in the finance realm as well.
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// Standard Deviation
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// Annualized Standard Deviation = Math.Sqrt(Monthly Standard Deviation x ( 12 ))
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// Skewness
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// Kurtosis
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/// <summary>
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/// Calculation is similar to Standard Deviation , except it calculates an average (mean) return only for periods with a gain
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/// and measures the variation of only the gain periods around the gain mean. Measures the volatility of upside performance.
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/// © Copyright 1996, 1999 Gary L.Gastineau. First Edition. © 1992 Swiss Bank Corporation.
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/// </summary>
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public static double GainStandardDeviation(this IEnumerable<double> data)
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{
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if (data == null)
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{
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throw new ArgumentNullException(nameof(data));
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}
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return data.Where(x => x >= 0).StandardDeviation();
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}
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/// <summary>
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/// Similar to standard deviation, except this statistic calculates an average (mean) return for only the periods with a loss and then
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/// measures the variation of only the losing periods around this loss mean. This statistic measures the volatility of downside performance.
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/// </summary>
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/// <remarks>http://www.offshore-library.com/kb/statistics.php</remarks>
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public static double LossStandardDeviation(this IEnumerable<double> data)
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{
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if (data == null)
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{
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throw new ArgumentNullException(nameof(data));
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}
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return data.Where(x => x < 0).StandardDeviation();
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}
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/// <summary>
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/// This measure is similar to the loss standard deviation except the downside deviation
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/// considers only returns that fall below a defined minimum acceptable return (MAR) rather than the arithmetic mean.
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/// For example, if the MAR is 7%, the downside deviation would measure the variation of each period that falls below
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/// 7%. (The loss standard deviation, on the other hand, would take only losing periods, calculate an average return for
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/// the losing periods, and then measure the variation between each losing return and the losing return average).
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/// </summary>
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public static double DownsideDeviation(this IEnumerable<double> data, double minimalAcceptableReturn)
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{
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if (data == null)
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{
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throw new ArgumentNullException(nameof(data));
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}
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return data.Where(x => x < minimalAcceptableReturn).StandardDeviation();
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}
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/// <summary>
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/// A measure of volatility in returns below the mean. It's similar to standard deviation, but it only
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/// looks at periods where the investment return was less than average return.
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/// </summary>
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public static double SemiDeviation(this IEnumerable<double> data)
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{
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if (data == null)
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{
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throw new ArgumentNullException(nameof(data));
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}
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var mean = data.Mean();
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var belowMeanData = data.Where(x => x < mean);
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return belowMeanData.StandardDeviation();
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}
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/// <summary>
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/// Measures a fund’s average gain in a gain period divided by the fund’s average loss in a losing
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/// period. Periods can be monthly or quarterly depending on the data frequency.
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/// </summary>
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public static double GainLossRatio(this IEnumerable<double> data)
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{
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if (data == null)
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{
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throw new ArgumentNullException(nameof(data));
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}
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var gains = data.Where(x => x >= 0);
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var losses = data.Where(x => x < 0);
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return Math.Abs(gains.Mean() / losses.Mean());
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}
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}
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}
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