nautilus_analysis/statistics/
returns_skewness.rs

1// -------------------------------------------------------------------------------------------------
2//  Copyright (C) 2015-2026 Nautech Systems Pty Ltd. All rights reserved.
3//  https://nautechsystems.io
4//
5//  Licensed under the GNU Lesser General Public License Version 3.0 (the "License");
6//  You may not use this file except in compliance with the License.
7//  You may obtain a copy of the License at https://www.gnu.org/licenses/lgpl-3.0.en.html
8//
9//  Unless required by applicable law or agreed to in writing, software
10//  distributed under the License is distributed on an "AS IS" BASIS,
11//  WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
12//  See the License for the specific language governing permissions and
13//  limitations under the License.
14// -------------------------------------------------------------------------------------------------
15
16//! Returns Skewness statistic.
17
18use nautilus_model::position::Position;
19
20use crate::{Returns, statistic::PortfolioStatistic};
21
22/// Calculates the skewness of portfolio returns.
23///
24/// Skewness measures the asymmetry of the return distribution about its mean. A
25/// negative value indicates a longer left tail (downside outliers); a positive
26/// value indicates a longer right tail.
27///
28/// Uses the bias-corrected sample skewness (adjusted Fisher-Pearson), matching
29/// `pandas.Series.skew` and Excel `SKEW`:
30///
31/// `G1 = n / ((n - 1)(n - 2)) * sum(((x - mean) / s)^3)`
32///
33/// where `s` is the sample standard deviation (Bessel's correction, ddof=1).
34/// Returns `NaN` for fewer than three returns or zero dispersion.
35///
36/// # References
37///
38/// - Joanes, D. N., & Gill, C. A. (1998). Comparing measures of sample skewness
39///   and kurtosis. *Journal of the Royal Statistical Society: Series D*, 47(1), 183-189.
40#[repr(C)]
41#[derive(Debug, Clone, Default)]
42#[cfg_attr(
43    feature = "python",
44    pyo3::pyclass(module = "nautilus_trader.analysis", from_py_object)
45)]
46#[cfg_attr(
47    feature = "python",
48    pyo3_stub_gen::derive::gen_stub_pyclass(module = "nautilus_trader.analysis")
49)]
50pub struct ReturnsSkewness {}
51
52impl ReturnsSkewness {
53    /// Creates a new [`ReturnsSkewness`] instance.
54    #[must_use]
55    pub fn new() -> Self {
56        Self {}
57    }
58}
59
60impl PortfolioStatistic for ReturnsSkewness {
61    type Item = f64;
62
63    fn name(&self) -> String {
64        "Returns Skewness".to_string()
65    }
66
67    fn calculate_from_returns(&self, raw_returns: &Returns) -> Option<Self::Item> {
68        if !self.check_valid_returns(raw_returns) {
69            return Some(f64::NAN);
70        }
71
72        let returns = self.downsample_to_daily_bins(raw_returns);
73        let n = returns.len();
74        if n < 3 {
75            return Some(f64::NAN);
76        }
77
78        let n_f = n as f64;
79        let mean = returns.values().sum::<f64>() / n_f;
80        let std = self.calculate_std(&returns);
81        if std == 0.0 || !std.is_finite() {
82            return Some(f64::NAN);
83        }
84
85        let sum_cubed = returns
86            .values()
87            .map(|x| ((x - mean) / std).powi(3))
88            .sum::<f64>();
89        let skewness = n_f / ((n_f - 1.0) * (n_f - 2.0)) * sum_cubed;
90
91        Some(skewness)
92    }
93
94    fn calculate_from_realized_pnls(&self, _realized_pnls: &[f64]) -> Option<Self::Item> {
95        None
96    }
97
98    fn calculate_from_positions(&self, _positions: &[Position]) -> Option<Self::Item> {
99        None
100    }
101}
102
103#[cfg(test)]
104mod tests {
105    use std::collections::BTreeMap;
106
107    use nautilus_core::{UnixNanos, approx_eq};
108    use rstest::rstest;
109
110    use super::*;
111
112    fn create_returns(values: &[f64]) -> BTreeMap<UnixNanos, f64> {
113        let mut new_return = BTreeMap::new();
114        let one_day_in_nanos = 86_400_000_000_000;
115        let start_time = 1_600_000_000_000_000_000;
116
117        for (i, &value) in values.iter().enumerate() {
118            let timestamp = start_time + i as u64 * one_day_in_nanos;
119            new_return.insert(UnixNanos::from(timestamp), value);
120        }
121
122        new_return
123    }
124
125    #[rstest]
126    fn test_name() {
127        let skewness = ReturnsSkewness::new();
128        assert_eq!(skewness.name(), "Returns Skewness");
129    }
130
131    #[rstest]
132    fn test_empty_returns() {
133        let skewness = ReturnsSkewness::new();
134        let returns = create_returns(&[]);
135        let result = skewness.calculate_from_returns(&returns);
136        assert!(result.is_some());
137        assert!(result.unwrap().is_nan());
138    }
139
140    #[rstest]
141    fn test_insufficient_data() {
142        let skewness = ReturnsSkewness::new();
143        let returns = create_returns(&[0.01, -0.02]);
144        let result = skewness.calculate_from_returns(&returns);
145        assert!(result.is_some());
146        assert!(result.unwrap().is_nan());
147    }
148
149    #[rstest]
150    fn test_zero_dispersion() {
151        let skewness = ReturnsSkewness::new();
152        let returns = create_returns(&[0.01, 0.01, 0.01, 0.01]);
153        let result = skewness.calculate_from_returns(&returns);
154        assert!(result.is_some());
155        assert!(result.unwrap().is_nan());
156    }
157
158    #[rstest]
159    fn test_skewness_calculation() {
160        // Reference value from pandas Series.skew() (adjusted Fisher-Pearson).
161        let skewness = ReturnsSkewness::new();
162        let returns = create_returns(&[
163            0.01, -0.02, 0.03, -0.01, 0.02, 0.04, -0.03, 0.05, -0.04, 0.02,
164        ]);
165        let result = skewness.calculate_from_returns(&returns);
166        assert!(result.is_some());
167        assert!(approx_eq!(
168            f64,
169            result.unwrap(),
170            -0.22872023422596313,
171            epsilon = 1e-12
172        ));
173    }
174}
nautilus_analysis/statistics/returns_skewness.rs

nautilus_analysis/statistics/
returns_skewness.rs
