nautilus_analysis/statistics/
cagr.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//! Compound Annual Growth Rate (CAGR) statistic.
17
18use std::collections::BTreeMap;
19
20use nautilus_core::UnixNanos;
21use nautilus_model::position::Position;
22
23use crate::statistic::PortfolioStatistic;
24
25/// Calculates the Compound Annual Growth Rate (CAGR) for returns.
26///
27/// CAGR represents the mean annual growth rate of an investment over a specified period,
28/// assuming the profits were reinvested at the end of each period.
29///
30/// Formula: CAGR = (Ending Value / Beginning Value)^(Period/Days) - 1
31///
32/// For returns: CAGR = ((1 + Total Return)^(Period/Days)) - 1
33#[repr(C)]
34#[derive(Debug, Clone)]
35#[cfg_attr(
36    feature = "python",
37    pyo3::pyclass(module = "nautilus_trader.core.nautilus_pyo3.analysis", from_py_object)
38)]
39#[cfg_attr(
40    feature = "python",
41    pyo3_stub_gen::derive::gen_stub_pyclass(module = "nautilus_trader.analysis")
42)]
43pub struct CAGR {
44    /// The number of periods per year for annualization (e.g., 252 for trading days).
45    pub period: usize,
46}
47
48impl CAGR {
49    /// Creates a new [`CAGR`] instance.
50    #[must_use]
51    pub fn new(period: Option<usize>) -> Self {
52        Self {
53            period: period.unwrap_or(252),
54        }
55    }
56}
57
58impl PortfolioStatistic for CAGR {
59    type Item = f64;
60
61    fn name(&self) -> String {
62        format!("CAGR ({} days)", self.period)
63    }
64
65    fn calculate_from_returns(&self, returns: &BTreeMap<UnixNanos, f64>) -> Option<Self::Item> {
66        if returns.is_empty() {
67            return Some(0.0);
68        }
69
70        // Downsample to daily bins to count actual trading days (not calendar days or trade count)
71        let daily_returns = self.downsample_to_daily_bins(returns);
72
73        // Calculate total return (cumulative)
74        let total_return: f64 = daily_returns.values().map(|&r| 1.0 + r).product::<f64>() - 1.0;
75
76        // Use the number of trading days (bins) for annualization
77        // Minimum of 1 day to handle intraday-only strategies
78        let days = daily_returns.len().max(1) as f64;
79
80        // CAGR = (1 + total_return)^(period/days) - 1
81        let cagr = (1.0 + total_return).powf(self.period as f64 / days) - 1.0;
82
83        if cagr.is_finite() {
84            Some(cagr)
85        } else {
86            Some(0.0)
87        }
88    }
89    fn calculate_from_realized_pnls(&self, _realized_pnls: &[f64]) -> Option<Self::Item> {
90        None
91    }
92
93    fn calculate_from_positions(&self, _positions: &[Position]) -> Option<Self::Item> {
94        None
95    }
96}
97
98#[cfg(test)]
99mod tests {
100    use rstest::rstest;
101
102    use super::*;
103
104    fn create_returns(values: &[f64]) -> BTreeMap<UnixNanos, f64> {
105        let mut returns = BTreeMap::new();
106        let nanos_per_day = 86_400_000_000_000;
107        let start_time = 1_600_000_000_000_000_000;
108
109        for (i, &value) in values.iter().enumerate() {
110            let timestamp = start_time + i as u64 * nanos_per_day;
111            returns.insert(UnixNanos::from(timestamp), value);
112        }
113
114        returns
115    }
116
117    #[rstest]
118    fn test_name() {
119        let cagr = CAGR::new(Some(252));
120        assert_eq!(cagr.name(), "CAGR (252 days)");
121    }
122
123    #[rstest]
124    fn test_empty_returns() {
125        let cagr = CAGR::new(Some(252));
126        let returns = BTreeMap::new();
127        let result = cagr.calculate_from_returns(&returns);
128        assert_eq!(result, Some(0.0));
129    }
130
131    #[rstest]
132    fn test_positive_cagr() {
133        let cagr = CAGR::new(Some(252));
134        // Simulate 252 days with 0.1% daily return
135        // Total return = (1.001)^252 - 1 ≈ 0.288 (28.8%)
136        // CAGR should be approximately same as total return for full year
137        let returns = create_returns(&vec![0.001; 252]);
138        let result = cagr.calculate_from_returns(&returns).unwrap();
139
140        // For 252 days of 0.1% daily return
141        // CAGR = (1 + 0.288)^(252/252) - 1 = 0.288
142        assert!((result - 0.288).abs() < 0.01);
143    }
144
145    #[rstest]
146    fn test_cagr_half_year() {
147        let cagr = CAGR::new(Some(252));
148        // Simulate 126 days (half year) with total return of 10%
149        let daily_return = (1.10_f64.powf(1.0 / 126.0)) - 1.0;
150        let returns = create_returns(&vec![daily_return; 126]);
151        let result = cagr.calculate_from_returns(&returns).unwrap();
152
153        // CAGR should annualize the 10% half-year return
154        // CAGR = (1.10)^(252/126) - 1 = (1.10)^2 - 1 ≈ 0.21 (21%)
155        assert!((result - 0.21).abs() < 0.01);
156    }
157
158    #[rstest]
159    fn test_negative_returns() {
160        let cagr = CAGR::new(Some(252));
161        // Simulate losses
162        let returns = create_returns(&vec![-0.001; 252]);
163        let result = cagr.calculate_from_returns(&returns).unwrap();
164
165        // Should be negative
166        assert!(result < 0.0);
167    }
168
169    #[rstest]
170    fn test_multiple_trades_per_day() {
171        let cagr = CAGR::new(Some(252));
172
173        // Simulate 500 trades over 252 days
174        let mut returns = BTreeMap::new();
175        let nanos_per_day = 86_400_000_000_000;
176        let start_time = 1_600_000_000_000_000_000;
177
178        // Create 500 trades with small returns spread across 252 days (~2 trades per day)
179        for i in 0..500 {
180            let day = (i * 252) / 500; // Map trade index to day
181            let timestamp =
182                start_time + day as u64 * nanos_per_day + (i % 3) as u64 * 1_000_000_000;
183            returns.insert(UnixNanos::from(timestamp), 0.0005);
184        }
185
186        let result = cagr.calculate_from_returns(&returns).unwrap();
187
188        // With downsample_to_daily_bins, we get 252 bins (trading days)
189        // Daily returns are aggregated, then we compound and annualize
190        // The CAGR should reflect 252 trading days, NOT 500 trades
191        assert!((result - 0.285).abs() < 0.02);
192        assert!(result > 0.2); // Should be much higher than what trade-count formula would give
193    }
194
195    #[rstest]
196    fn test_intraday_trading() {
197        let cagr = CAGR::new(Some(252));
198
199        // Simulate multiple trades within a single day
200        let mut returns = BTreeMap::new();
201        let start_time = 1_600_000_000_000_000_000;
202
203        // 10 trades within the same day, each with 1% return
204        for i in 0..10 {
205            let timestamp = start_time + i as u64 * 3_600_000_000_000; // 1 hour apart
206            returns.insert(UnixNanos::from(timestamp), 0.01);
207        }
208
209        let result = cagr.calculate_from_returns(&returns).unwrap();
210
211        // Total return: (1.01)^10 - 1 ≈ 0.1046 (10.46%)
212        // This should be treated as 1 trading day
213        // Annualized: (1.1046)^(252/1) - 1 = very large number
214        // The key is it should NOT return 0.0
215        assert!(result > 0.0);
216        assert!(result.is_finite());
217    }
218}
nautilus_analysis/statistics/cagr.rs

nautilus_analysis/statistics/
cagr.rs
