nautilus_analysis/statistics/
tail_ratio.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
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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//! Tail Ratio statistic.
17
18use nautilus_model::position::Position;
19
20use crate::{Returns, statistic::PortfolioStatistic};
21
22/// Calculates the tail ratio of portfolio returns.
23///
24/// The tail ratio compares the magnitude of the right (gain) tail to the left
25/// (loss) tail of the return distribution. It is the absolute ratio of the 95th
26/// to the 5th percentile of returns:
27///
28/// `TailRatio = | percentile(r, 95) / percentile(r, 5) |`
29///
30/// Percentiles use linear interpolation between closest ranks, matching
31/// `numpy.percentile` and `pandas.Series.quantile` with the default `linear`
32/// method (the convention used by the `quantstats` tail-ratio definition).
33///
34/// A value greater than `1` indicates a heavier upside tail (gains larger in
35/// magnitude than losses); a value below `1` indicates a heavier downside tail.
36/// Returns `NaN` for fewer than two returns or when the 5th percentile is zero.
37///
38/// # References
39///
40/// - empyrical `tail_ratio` (<https://github.com/quantopian/empyrical>).
41#[repr(C)]
42#[derive(Debug, Clone, Default)]
43#[cfg_attr(
44    feature = "python",
45    pyo3::pyclass(module = "nautilus_trader.analysis", from_py_object)
46)]
47#[cfg_attr(
48    feature = "python",
49    pyo3_stub_gen::derive::gen_stub_pyclass(module = "nautilus_trader.analysis")
50)]
51pub struct TailRatio {}
52
53impl TailRatio {
54    /// Creates a new [`TailRatio`] instance.
55    #[must_use]
56    pub fn new() -> Self {
57        Self {}
58    }
59}
60
61/// Returns the `q`-th percentile (`q` in `[0, 100]`) of `sorted_values` using
62/// linear interpolation between closest ranks, matching `numpy.percentile` with
63/// the default `linear` method.
64///
65/// `sorted_values` must be sorted ascending and non-empty.
66fn percentile_linear(sorted_values: &[f64], q: f64) -> f64 {
67    debug_assert!(
68        !sorted_values.is_empty(),
69        "percentile requires a non-empty slice"
70    );
71    let n = sorted_values.len();
72    if n == 1 {
73        return sorted_values[0];
74    }
75
76    let rank = (q / 100.0) * (n - 1) as f64;
77    let lower = rank.floor() as usize;
78    let upper = rank.ceil() as usize;
79    if lower == upper {
80        return sorted_values[lower];
81    }
82
83    let weight = rank - lower as f64;
84    // lower + (upper - lower) * weight, fused to match numpy's linear interpolation.
85    (sorted_values[upper] - sorted_values[lower]).mul_add(weight, sorted_values[lower])
86}
87
88impl PortfolioStatistic for TailRatio {
89    type Item = f64;
90
91    fn name(&self) -> String {
92        "Tail Ratio".to_string()
93    }
94
95    fn calculate_from_returns(&self, raw_returns: &Returns) -> Option<Self::Item> {
96        if !self.check_valid_returns(raw_returns) {
97            return Some(f64::NAN);
98        }
99
100        let returns = self.downsample_to_daily_bins(raw_returns);
101        let n = returns.len();
102        if n < 2 {
103            return Some(f64::NAN);
104        }
105
106        let mut values: Vec<f64> = returns.values().copied().collect();
107        values.sort_by(f64::total_cmp);
108
109        let p95 = percentile_linear(&values, 95.0);
110        let p5 = percentile_linear(&values, 5.0);
111        if p5 == 0.0 || !p5.is_finite() {
112            return Some(f64::NAN);
113        }
114
115        Some((p95 / p5).abs())
116    }
117
118    fn calculate_from_realized_pnls(&self, _realized_pnls: &[f64]) -> Option<Self::Item> {
119        None
120    }
121
122    fn calculate_from_positions(&self, _positions: &[Position]) -> Option<Self::Item> {
123        None
124    }
125}
126
127#[cfg(test)]
128mod tests {
129    use std::collections::BTreeMap;
130
131    use nautilus_core::{UnixNanos, approx_eq};
132    use rstest::rstest;
133
134    use super::*;
135
136    fn create_returns(values: &[f64]) -> BTreeMap<UnixNanos, f64> {
137        let mut new_return = BTreeMap::new();
138        let one_day_in_nanos = 86_400_000_000_000;
139        let start_time = 1_600_000_000_000_000_000;
140
141        for (i, &value) in values.iter().enumerate() {
142            let timestamp = start_time + i as u64 * one_day_in_nanos;
143            new_return.insert(UnixNanos::from(timestamp), value);
144        }
145
146        new_return
147    }
148
149    #[rstest]
150    fn test_name() {
151        let tail_ratio = TailRatio::new();
152        assert_eq!(tail_ratio.name(), "Tail Ratio");
153    }
154
155    #[rstest]
156    fn test_empty_returns() {
157        let tail_ratio = TailRatio::new();
158        let returns = create_returns(&[]);
159        let result = tail_ratio.calculate_from_returns(&returns);
160        assert!(result.is_some());
161        assert!(result.unwrap().is_nan());
162    }
163
164    #[rstest]
165    fn test_insufficient_data() {
166        let tail_ratio = TailRatio::new();
167        let returns = create_returns(&[0.01]);
168        let result = tail_ratio.calculate_from_returns(&returns);
169        assert!(result.is_some());
170        assert!(result.unwrap().is_nan());
171    }
172
173    #[rstest]
174    fn test_tail_ratio_calculation() {
175        // Reference value from numpy.percentile (linear) / pandas.Series.quantile:
176        //   |percentile(r, 95)| / |percentile(r, 5)| = 0.0455 / 0.0355 = 91 / 71.
177        let tail_ratio = TailRatio::new();
178        let returns = create_returns(&[
179            0.01, -0.02, 0.03, -0.01, 0.02, 0.04, -0.03, 0.05, -0.04, 0.02,
180        ]);
181        let result = tail_ratio.calculate_from_returns(&returns);
182        assert!(result.is_some());
183        assert!(approx_eq!(
184            f64,
185            result.unwrap(),
186            1.2816901408450704,
187            epsilon = 1e-12
188        ));
189    }
190
191    #[rstest]
192    fn test_symmetric_returns_ratio_near_one() {
193        // A symmetric distribution has matching tails, so the ratio is ~1.
194        let tail_ratio = TailRatio::new();
195        let returns = create_returns(&[-0.03, -0.02, -0.01, 0.0, 0.01, 0.02, 0.03]);
196        let result = tail_ratio.calculate_from_returns(&returns);
197        assert!(result.is_some());
198        assert!(approx_eq!(f64, result.unwrap(), 1.0, epsilon = 1e-12));
199    }
200}
nautilus_analysis/statistics/tail_ratio.rs

nautilus_analysis/statistics/
tail_ratio.rs
