nautilus_analysis/statistics/
expectancy.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.
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
16use std::fmt::{self, Display};
17
18use nautilus_model::position::Position;
19
20use super::{loser_avg::AvgLoser, winner_avg::AvgWinner};
21use crate::{Returns, statistic::PortfolioStatistic};
22
23/// Calculates the expectancy of a trading strategy based on realized PnLs.
24///
25/// Expectancy is defined as: `(Average Win × Win Rate) + (Average Loss × Loss Rate)`
26/// This metric provides insight into the expected profitability per trade and helps
27/// evaluate the overall edge of a trading strategy.
28///
29/// A positive expectancy indicates a profitable system over time, while a negative
30/// expectancy suggests losses.
31///
32/// # References
33///
34/// - Tharp, V. K. (1998). *Trade Your Way to Financial Freedom*. McGraw-Hill.
35/// - Elder, A. (1993). *Trading for a Living*. John Wiley & Sons.
36/// - Vince, R. (1992). *The Mathematics of Money Management*. John Wiley & Sons.
37#[repr(C)]
38#[derive(Debug, Clone)]
39#[cfg_attr(
40    feature = "python",
41    pyo3::pyclass(module = "nautilus_trader.core.nautilus_pyo3.analysis")
42)]
43pub struct Expectancy {}
44
45impl Display for Expectancy {
46    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
47        write!(f, "Expectancy")
48    }
49}
50
51impl PortfolioStatistic for Expectancy {
52    type Item = f64;
53
54    fn name(&self) -> String {
55        self.to_string()
56    }
57
58    fn calculate_from_realized_pnls(&self, realized_pnls: &[f64]) -> Option<Self::Item> {
59        if realized_pnls.is_empty() {
60            return Some(0.0);
61        }
62
63        let avg_winner = AvgWinner {}
64            .calculate_from_realized_pnls(realized_pnls)
65            .unwrap_or(0.0);
66        let avg_loser = AvgLoser {}
67            .calculate_from_realized_pnls(realized_pnls)
68            .unwrap_or(0.0);
69
70        let (winners, losers): (Vec<f64>, Vec<f64>) =
71            realized_pnls.iter().partition(|&&pnl| pnl > 0.0);
72
73        let total_trades = winners.len() + losers.len();
74        let win_rate = winners.len() as f64 / total_trades.max(1) as f64;
75        let loss_rate = 1.0 - win_rate;
76
77        Some(avg_winner.mul_add(win_rate, avg_loser * loss_rate))
78    }
79    fn calculate_from_returns(&self, _returns: &Returns) -> Option<Self::Item> {
80        None
81    }
82
83    fn calculate_from_positions(&self, _positions: &[Position]) -> Option<Self::Item> {
84        None
85    }
86}
87
88////////////////////////////////////////////////////////////////////////////////
89// Tests
90////////////////////////////////////////////////////////////////////////////////
91
92#[cfg(test)]
93mod tests {
94    use nautilus_core::approx_eq;
95    use rstest::rstest;
96
97    use super::*;
98
99    #[rstest]
100    fn test_empty_pnl_list() {
101        let expectancy = Expectancy {};
102        let result = expectancy.calculate_from_realized_pnls(&[]);
103        assert!(result.is_some());
104        assert!(approx_eq!(f64, result.unwrap(), 0.0, epsilon = 1e-9));
105    }
106
107    #[rstest]
108    fn test_all_winners() {
109        let expectancy = Expectancy {};
110        let pnls = vec![10.0, 20.0, 30.0];
111        let result = expectancy.calculate_from_realized_pnls(&pnls);
112
113        assert!(result.is_some());
114        // Expected: avg_winner = 20.0, win_rate = 1.0, loss_rate = 0.0
115        // Expectancy = (20.0 * 1.0) + (0.0 * 0.0) = 20.0
116        assert!(approx_eq!(f64, result.unwrap(), 20.0, epsilon = 1e-9));
117    }
118
119    #[rstest]
120    fn test_all_losers() {
121        let expectancy = Expectancy {};
122        let pnls = vec![-10.0, -20.0, -30.0];
123        let result = expectancy.calculate_from_realized_pnls(&pnls);
124
125        assert!(result.is_some());
126        // Expected: avg_loser = -20.0, win_rate = 0.0, loss_rate = 1.0
127        // Expectancy = (0.0 * 0.0) + (-20.0 * 1.0) = -20.0
128        assert!(approx_eq!(f64, result.unwrap(), -20.0, epsilon = 1e-9));
129    }
130
131    #[rstest]
132    fn test_mixed_pnls() {
133        let expectancy = Expectancy {};
134        let pnls = vec![10.0, -5.0, 15.0, -10.0];
135        let result = expectancy.calculate_from_realized_pnls(&pnls);
136
137        assert!(result.is_some());
138        // Expected:
139        // avg_winner = 12.5 (average of 10.0 and 15.0)
140        // avg_loser = -7.5 (average of -5.0 and -10.0)
141        // win_rate = 0.5 (2 winners out of 4 trades)
142        // loss_rate = 0.5
143        // Expectancy = (12.5 * 0.5) + (-7.5 * 0.5) = 2.5
144        assert!(approx_eq!(f64, result.unwrap(), 2.5, epsilon = 1e-9));
145    }
146
147    #[rstest]
148    fn test_single_trade() {
149        let expectancy = Expectancy {};
150        let pnls = vec![10.0];
151        let result = expectancy.calculate_from_realized_pnls(&pnls);
152
153        assert!(result.is_some());
154        // Expected: avg_winner = 10.0, win_rate = 1.0, loss_rate = 0.0
155        // Expectancy = (10.0 * 1.0) + (0.0 * 0.0) = 10.0
156        assert!(approx_eq!(f64, result.unwrap(), 10.0, epsilon = 1e-9));
157    }
158
159    #[rstest]
160    fn test_name() {
161        let expectancy = Expectancy {};
162        assert_eq!(expectancy.name(), "Expectancy");
163    }
164}
nautilus_analysis/statistics/expectancy.rs

nautilus_analysis/statistics/
expectancy.rs
