nautilus_analysis/statistics/
cagr.rs

1// -------------------------------------------------------------------------------------------------
2//  Copyright (C) 2015-2025 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.
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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//! Compound Annual Growth Rate (CAGR) statistic.
17
18use std::collections::BTreeMap;
19
20use nautilus_core::UnixNanos;
21
22use crate::statistic::PortfolioStatistic;
23
24/// Calculates the Compound Annual Growth Rate (CAGR) for returns.
25///
26/// CAGR represents the mean annual growth rate of an investment over a specified period,
27/// assuming the profits were reinvested at the end of each period.
28///
29/// Formula: CAGR = (Ending Value / Beginning Value)^(Period/Days) - 1
30///
31/// For returns: CAGR = ((1 + Total Return)^(Period/Days)) - 1
32#[repr(C)]
33#[derive(Debug, Clone)]
34#[cfg_attr(
35    feature = "python",
36    pyo3::pyclass(module = "nautilus_trader.core.nautilus_pyo3.analysis")
37)]
38pub struct CAGR {
39    /// The number of periods per year for annualization (e.g., 252 for trading days).
40    pub period: usize,
41}
42
43impl CAGR {
44    /// Creates a new [`CAGR`] instance.
45    #[must_use]
46    pub fn new(period: Option<usize>) -> Self {
47        Self {
48            period: period.unwrap_or(252),
49        }
50    }
51}
52
53impl PortfolioStatistic for CAGR {
54    type Item = f64;
55
56    fn name(&self) -> String {
57        format!("CAGR ({} days)", self.period)
58    }
59
60    fn calculate_from_returns(&self, returns: &BTreeMap<UnixNanos, f64>) -> Option<Self::Item> {
61        if returns.is_empty() {
62            return Some(0.0);
63        }
64
65        // Downsample to daily bins to count actual trading days (not calendar days or trade count)
66        let daily_returns = self.downsample_to_daily_bins(returns);
67
68        // Calculate total return (cumulative)
69        let total_return: f64 = daily_returns.values().map(|&r| 1.0 + r).product::<f64>() - 1.0;
70
71        // Use the number of trading days (bins) for annualization
72        // Minimum of 1 day to handle intraday-only strategies
73        let days = daily_returns.len().max(1) as f64;
74
75        // CAGR = (1 + total_return)^(period/days) - 1
76        let cagr = (1.0 + total_return).powf(self.period as f64 / days) - 1.0;
77
78        if cagr.is_finite() {
79            Some(cagr)
80        } else {
81            Some(0.0)
82        }
83    }
84}
85
86#[cfg(test)]
87mod tests {
88    use rstest::rstest;
89
90    use super::*;
91
92    fn create_returns(values: Vec<f64>) -> BTreeMap<UnixNanos, f64> {
93        let mut returns = BTreeMap::new();
94        let nanos_per_day = 86_400_000_000_000;
95        let start_time = 1_600_000_000_000_000_000;
96
97        for (i, &value) in values.iter().enumerate() {
98            let timestamp = start_time + i as u64 * nanos_per_day;
99            returns.insert(UnixNanos::from(timestamp), value);
100        }
101
102        returns
103    }
104
105    #[rstest]
106    fn test_name() {
107        let cagr = CAGR::new(Some(252));
108        assert_eq!(cagr.name(), "CAGR (252 days)");
109    }
110
111    #[rstest]
112    fn test_empty_returns() {
113        let cagr = CAGR::new(Some(252));
114        let returns = BTreeMap::new();
115        let result = cagr.calculate_from_returns(&returns);
116        assert_eq!(result, Some(0.0));
117    }
118
119    #[rstest]
120    fn test_positive_cagr() {
121        let cagr = CAGR::new(Some(252));
122        // Simulate 252 days with 0.1% daily return
123        // Total return = (1.001)^252 - 1 ≈ 0.288 (28.8%)
124        // CAGR should be approximately same as total return for full year
125        let returns = create_returns(vec![0.001; 252]);
126        let result = cagr.calculate_from_returns(&returns).unwrap();
127
128        // For 252 days of 0.1% daily return
129        // CAGR = (1 + 0.288)^(252/252) - 1 = 0.288
130        assert!((result - 0.288).abs() < 0.01);
131    }
132
133    #[rstest]
134    fn test_cagr_half_year() {
135        let cagr = CAGR::new(Some(252));
136        // Simulate 126 days (half year) with total return of 10%
137        let daily_return = (1.10_f64.powf(1.0 / 126.0)) - 1.0;
138        let returns = create_returns(vec![daily_return; 126]);
139        let result = cagr.calculate_from_returns(&returns).unwrap();
140
141        // CAGR should annualize the 10% half-year return
142        // CAGR = (1.10)^(252/126) - 1 = (1.10)^2 - 1 ≈ 0.21 (21%)
143        assert!((result - 0.21).abs() < 0.01);
144    }
145
146    #[rstest]
147    fn test_negative_returns() {
148        let cagr = CAGR::new(Some(252));
149        // Simulate losses
150        let returns = create_returns(vec![-0.001; 252]);
151        let result = cagr.calculate_from_returns(&returns).unwrap();
152
153        // Should be negative
154        assert!(result < 0.0);
155    }
156
157    #[rstest]
158    fn test_multiple_trades_per_day() {
159        let cagr = CAGR::new(Some(252));
160
161        // Simulate 500 trades over 252 days
162        let mut returns = BTreeMap::new();
163        let nanos_per_day = 86_400_000_000_000;
164        let start_time = 1_600_000_000_000_000_000;
165
166        // Create 500 trades with small returns spread across 252 days (~2 trades per day)
167        for i in 0..500 {
168            let day = (i * 252) / 500; // Map trade index to day
169            let timestamp =
170                start_time + day as u64 * nanos_per_day + (i % 3) as u64 * 1_000_000_000;
171            returns.insert(UnixNanos::from(timestamp), 0.0005);
172        }
173
174        let result = cagr.calculate_from_returns(&returns).unwrap();
175
176        // With downsample_to_daily_bins, we get 252 bins (trading days)
177        // Daily returns are aggregated, then we compound and annualize
178        // The CAGR should reflect 252 trading days, NOT 500 trades
179        assert!((result - 0.285).abs() < 0.02);
180        assert!(result > 0.2); // Should be much higher than what trade-count formula would give
181    }
182
183    #[rstest]
184    fn test_intraday_trading() {
185        let cagr = CAGR::new(Some(252));
186
187        // Simulate multiple trades within a single day
188        let mut returns = BTreeMap::new();
189        let start_time = 1_600_000_000_000_000_000;
190
191        // 10 trades within the same day, each with 1% return
192        for i in 0..10 {
193            let timestamp = start_time + i as u64 * 3_600_000_000_000; // 1 hour apart
194            returns.insert(UnixNanos::from(timestamp), 0.01);
195        }
196
197        let result = cagr.calculate_from_returns(&returns).unwrap();
198
199        // Total return: (1.01)^10 - 1 ≈ 0.1046 (10.46%)
200        // This should be treated as 1 trading day
201        // Annualized: (1.1046)^(252/1) - 1 = very large number
202        // The key is it should NOT return 0.0
203        assert!(result > 0.0);
204        assert!(result.is_finite());
205    }
206}
nautilus_analysis/statistics/cagr.rs

nautilus_analysis/statistics/
cagr.rs
