nautilus_analysis/statistics/
returns_kurtosis.rs

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14// -------------------------------------------------------------------------------------------------
15
16//! Returns Kurtosis statistic.
17
18use nautilus_model::position::Position;
19
20use crate::{Returns, statistic::PortfolioStatistic};
21
22/// Calculates the excess kurtosis of portfolio returns.
23///
24/// Kurtosis measures the heaviness of the tails of the return distribution
25/// relative to a normal distribution. A positive value indicates fatter tails
26/// (more outliers); a negative value indicates thinner tails.
27///
28/// Uses the bias-corrected sample excess kurtosis (adjusted Fisher-Pearson),
29/// matching `pandas.Series.kurt` and Excel `KURT`. A normal distribution yields 0:
30///
31/// `G2 = n(n + 1) / ((n - 1)(n - 2)(n - 3)) * sum(((x - mean) / s)^4)
32///       - 3(n - 1)^2 / ((n - 2)(n - 3))`
33///
34/// where `s` is the sample standard deviation (Bessel's correction, ddof=1).
35/// Returns `NaN` for fewer than four returns or zero dispersion.
36///
37/// # References
38///
39/// - Joanes, D. N., & Gill, C. A. (1998). Comparing measures of sample skewness
40///   and kurtosis. *Journal of the Royal Statistical Society: Series D*, 47(1), 183-189.
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 ReturnsKurtosis {}
52
53impl ReturnsKurtosis {
54    /// Creates a new [`ReturnsKurtosis`] instance.
55    #[must_use]
56    pub fn new() -> Self {
57        Self {}
58    }
59}
60
61impl PortfolioStatistic for ReturnsKurtosis {
62    type Item = f64;
63
64    fn name(&self) -> String {
65        "Returns Kurtosis".to_string()
66    }
67
68    fn calculate_from_returns(&self, raw_returns: &Returns) -> Option<Self::Item> {
69        if !self.check_valid_returns(raw_returns) {
70            return Some(f64::NAN);
71        }
72
73        let returns = self.downsample_to_daily_bins(raw_returns);
74        let n = returns.len();
75        if n < 4 {
76            return Some(f64::NAN);
77        }
78
79        let n_f = n as f64;
80        let mean = returns.values().sum::<f64>() / n_f;
81        let std = self.calculate_std(&returns);
82        if std == 0.0 || !std.is_finite() {
83            return Some(f64::NAN);
84        }
85
86        let sum_quartic = returns
87            .values()
88            .map(|x| ((x - mean) / std).powi(4))
89            .sum::<f64>();
90        let kurtosis = (n_f * (n_f + 1.0)) / ((n_f - 1.0) * (n_f - 2.0) * (n_f - 3.0))
91            * sum_quartic
92            - 3.0 * (n_f - 1.0).powi(2) / ((n_f - 2.0) * (n_f - 3.0));
93
94        Some(kurtosis)
95    }
96
97    fn calculate_from_realized_pnls(&self, _realized_pnls: &[f64]) -> Option<Self::Item> {
98        None
99    }
100
101    fn calculate_from_positions(&self, _positions: &[Position]) -> Option<Self::Item> {
102        None
103    }
104}
105
106#[cfg(test)]
107mod tests {
108    use std::collections::BTreeMap;
109
110    use nautilus_core::{UnixNanos, approx_eq};
111    use rstest::rstest;
112
113    use super::*;
114
115    fn create_returns(values: &[f64]) -> BTreeMap<UnixNanos, f64> {
116        let mut new_return = BTreeMap::new();
117        let one_day_in_nanos = 86_400_000_000_000;
118        let start_time = 1_600_000_000_000_000_000;
119
120        for (i, &value) in values.iter().enumerate() {
121            let timestamp = start_time + i as u64 * one_day_in_nanos;
122            new_return.insert(UnixNanos::from(timestamp), value);
123        }
124
125        new_return
126    }
127
128    #[rstest]
129    fn test_name() {
130        let kurtosis = ReturnsKurtosis::new();
131        assert_eq!(kurtosis.name(), "Returns Kurtosis");
132    }
133
134    #[rstest]
135    fn test_empty_returns() {
136        let kurtosis = ReturnsKurtosis::new();
137        let returns = create_returns(&[]);
138        let result = kurtosis.calculate_from_returns(&returns);
139        assert!(result.is_some());
140        assert!(result.unwrap().is_nan());
141    }
142
143    #[rstest]
144    fn test_insufficient_data() {
145        let kurtosis = ReturnsKurtosis::new();
146        let returns = create_returns(&[0.01, -0.02, 0.03]);
147        let result = kurtosis.calculate_from_returns(&returns);
148        assert!(result.is_some());
149        assert!(result.unwrap().is_nan());
150    }
151
152    #[rstest]
153    fn test_zero_dispersion() {
154        let kurtosis = ReturnsKurtosis::new();
155        let returns = create_returns(&[0.01, 0.01, 0.01, 0.01]);
156        let result = kurtosis.calculate_from_returns(&returns);
157        assert!(result.is_some());
158        assert!(result.unwrap().is_nan());
159    }
160
161    #[rstest]
162    fn test_kurtosis_calculation() {
163        // Reference value from pandas Series.kurt() (excess, adjusted Fisher-Pearson).
164        let kurtosis = ReturnsKurtosis::new();
165        let returns = create_returns(&[
166            0.01, -0.02, 0.03, -0.01, 0.02, 0.04, -0.03, 0.05, -0.04, 0.02,
167        ]);
168        let result = kurtosis.calculate_from_returns(&returns);
169        assert!(result.is_some());
170        assert!(approx_eq!(
171            f64,
172            result.unwrap(),
173            -1.2622443251995028,
174            epsilon = 1e-12
175        ));
176    }
177}
nautilus_analysis/statistics/returns_kurtosis.rs

nautilus_analysis/statistics/
returns_kurtosis.rs
