/*
 * 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.Collections.Generic;
using NUnit.Framework;

namespace QuantConnect.Tests.Common.Statistics
{
    [TestFixture]
    public class ProbabilisticSharpeRatioTests
    {
        [Test]
        public void SameAsBenchmark()
        {
            var performance = new List<double> { 0.01, 0.02, 0.01, 0, 0, 3 };
            var benchmark = new List<double> { 0.01, 0.02, 0.01, 0, 0, 3 };

            var benchmarkSharpeRatio = QuantConnect.Statistics.Statistics.ObservedSharpeRatio(benchmark);

            var result = QuantConnect.Statistics.Statistics.ProbabilisticSharpeRatio(performance,
                benchmarkSharpeRatio);

            // they zero each other out
            Assert.AreEqual(0.5d, result, 0.001);
        }

        [Test]
        public void BeatBenchmark()
        {
            var performance = new List<double> { 0.01, 0.02, 0.01, 0, 0,3 };
            var benchmark = new List<double> { 0, 0, 0, -0.1, 0, 0.01, 0 };

            var benchmarkSharpeRatio = QuantConnect.Statistics.Statistics.ObservedSharpeRatio(benchmark);

            var result = QuantConnect.Statistics.Statistics.ProbabilisticSharpeRatio(performance,
                benchmarkSharpeRatio);

            Assert.AreEqual(1d, result, 0.001);
        }

        [Test]
        public void LoseAgainstBenchmark()
        {
            var benchmark = new List<double> { 0.01, 0.02, 0.01, 0, 0, 3 };
            var performance = new List<double> { 0, 0, 0, -0.1, 0, 0.01, 0 };

            var benchmarkSharpeRatio = QuantConnect.Statistics.Statistics.ObservedSharpeRatio(benchmark);

            var result = QuantConnect.Statistics.Statistics.ProbabilisticSharpeRatio(performance,
                benchmarkSharpeRatio);

            Assert.AreEqual(0d, result, 0.001);
        }

        [Test]
        public void ZeroValues()
        {
            var benchmark = new List<double> { 0, 0, 0 };
            var performance = new List<double> { 0, 0, 0 };

            var benchmarkSharpeRatio = QuantConnect.Statistics.Statistics.ObservedSharpeRatio(benchmark);

            var result = QuantConnect.Statistics.Statistics.ProbabilisticSharpeRatio(performance,
                benchmarkSharpeRatio);

            Assert.AreEqual(0d, result, 0.001);
        }

        [Test]
        public void UsesRiskFreeRateForObservedSharpeRatio()
        {
            // Gross returns clear the benchmark, so on a gross basis the PSR is high
            var performance = new List<double> { 0.01, 0.02, 0.01, 0, 0, 3 };
            var benchmarkSharpeRatio = 1.0d / System.Math.Sqrt(252);

            var grossResult = QuantConnect.Statistics.Statistics.ProbabilisticSharpeRatio(performance, benchmarkSharpeRatio);
            // A per-sample risk free rate above the average return makes the excess return negative,
            // so the PSR must collapse below the gross one
            var excessReturnResult = QuantConnect.Statistics.Statistics.ProbabilisticSharpeRatio(performance, benchmarkSharpeRatio, 0.6);

            Assert.Greater(grossResult, 0.5d);
            Assert.Less(excessReturnResult, 0.5d);
            Assert.Greater(grossResult, excessReturnResult);
        }

        [Test]
        public void ObservedSharpeRatioSubtractsRiskFreeRate()
        {
            var performance = new List<double> { 0.02, 0.04 };

            // A risk free rate equal to the average return zeroes the excess observed sharpe ratio
            Assert.AreEqual(0d, QuantConnect.Statistics.Statistics.ObservedSharpeRatio(performance, 0.03d), 1e-12);
            // and it is strictly lower than the gross observed sharpe ratio
            Assert.Greater(QuantConnect.Statistics.Statistics.ObservedSharpeRatio(performance),
                QuantConnect.Statistics.Statistics.ObservedSharpeRatio(performance, 0.03d));
        }
    }
}