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::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 std::fmt::Formatter<'_>) -> std::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(f64::NAN);
61        }
62
63        // Treat NaN as 0.0 for expectancy calculation (no winners/losers = no contribution)
64        let avg_winner = AvgWinner {}
65            .calculate_from_realized_pnls(realized_pnls)
66            .map_or(0.0, |v| if v.is_nan() { 0.0 } else { v });
67        let avg_loser = AvgLoser {}
68            .calculate_from_realized_pnls(realized_pnls)
69            .map_or(0.0, |v| if v.is_nan() { 0.0 } else { v });
70
71        // Count only non-zero trades (zeros are breakeven, neither winners nor losers)
72        let winners: Vec<f64> = realized_pnls
73            .iter()
74            .filter(|&&pnl| pnl > 0.0)
75            .copied()
76            .collect();
77        let losers: Vec<f64> = realized_pnls
78            .iter()
79            .filter(|&&pnl| pnl < 0.0)
80            .copied()
81            .collect();
82
83        let total_trades = winners.len() + losers.len();
84        if total_trades == 0 {
85            return Some(0.0);
86        }
87
88        let win_rate = winners.len() as f64 / total_trades as f64;
89        let loss_rate = losers.len() as f64 / total_trades as f64;
90
91        Some(avg_winner.mul_add(win_rate, avg_loser * loss_rate))
92    }
93    fn calculate_from_returns(&self, _returns: &Returns) -> Option<Self::Item> {
94        None
95    }
96
97    fn calculate_from_positions(&self, _positions: &[Position]) -> Option<Self::Item> {
98        None
99    }
100}
101
102#[cfg(test)]
103mod tests {
104    use nautilus_core::approx_eq;
105    use rstest::rstest;
106
107    use super::*;
108
109    #[rstest]
110    fn test_empty_pnl_list() {
111        let expectancy = Expectancy {};
112        let result = expectancy.calculate_from_realized_pnls(&[]);
113        assert!(result.is_some());
114        assert!(result.unwrap().is_nan());
115    }
116
117    #[rstest]
118    fn test_all_winners() {
119        let expectancy = Expectancy {};
120        let pnls = vec![10.0, 20.0, 30.0];
121        let result = expectancy.calculate_from_realized_pnls(&pnls);
122
123        assert!(result.is_some());
124        // Expected: avg_winner = 20.0, win_rate = 1.0, loss_rate = 0.0
125        // Expectancy = (20.0 * 1.0) + (0.0 * 0.0) = 20.0
126        assert!(approx_eq!(f64, result.unwrap(), 20.0, epsilon = 1e-9));
127    }
128
129    #[rstest]
130    fn test_all_losers() {
131        let expectancy = Expectancy {};
132        let pnls = vec![-10.0, -20.0, -30.0];
133        let result = expectancy.calculate_from_realized_pnls(&pnls);
134
135        assert!(result.is_some());
136        // Expected: avg_loser = -20.0, win_rate = 0.0, loss_rate = 1.0
137        // Expectancy = (0.0 * 0.0) + (-20.0 * 1.0) = -20.0
138        assert!(approx_eq!(f64, result.unwrap(), -20.0, epsilon = 1e-9));
139    }
140
141    #[rstest]
142    fn test_mixed_pnls() {
143        let expectancy = Expectancy {};
144        let pnls = vec![10.0, -5.0, 15.0, -10.0];
145        let result = expectancy.calculate_from_realized_pnls(&pnls);
146
147        assert!(result.is_some());
148        // Expected:
149        // avg_winner = 12.5 (average of 10.0 and 15.0)
150        // avg_loser = -7.5 (average of -5.0 and -10.0)
151        // win_rate = 0.5 (2 winners out of 4 trades)
152        // loss_rate = 0.5
153        // Expectancy = (12.5 * 0.5) + (-7.5 * 0.5) = 2.5
154        assert!(approx_eq!(f64, result.unwrap(), 2.5, epsilon = 1e-9));
155    }
156
157    #[rstest]
158    fn test_single_trade() {
159        let expectancy = Expectancy {};
160        let pnls = vec![10.0];
161        let result = expectancy.calculate_from_realized_pnls(&pnls);
162
163        assert!(result.is_some());
164        // Expected: avg_winner = 10.0, win_rate = 1.0, loss_rate = 0.0
165        // Expectancy = (10.0 * 1.0) + (0.0 * 0.0) = 10.0
166        assert!(approx_eq!(f64, result.unwrap(), 10.0, epsilon = 1e-9));
167    }
168
169    #[rstest]
170    fn test_zeros_excluded_from_win_loss_rates() {
171        let expectancy = Expectancy {};
172        let pnls = vec![10.0, 0.0, -10.0];
173        let result = expectancy.calculate_from_realized_pnls(&pnls);
174
175        assert!(result.is_some());
176        // Zeros excluded: only [10.0, -10.0] counted
177        // avg_winner = 10.0, win_rate = 0.5
178        // avg_loser = -10.0, loss_rate = 0.5
179        // Expectancy = (10.0 * 0.5) + (-10.0 * 0.5) = 0.0
180        assert!(approx_eq!(f64, result.unwrap(), 0.0, epsilon = 1e-9));
181    }
182
183    #[rstest]
184    fn test_only_zeros() {
185        let expectancy = Expectancy {};
186        let pnls = vec![0.0, 0.0, 0.0];
187        let result = expectancy.calculate_from_realized_pnls(&pnls);
188
189        assert!(result.is_some());
190        // No winners or losers, expectancy = 0.0
191        assert!(approx_eq!(f64, result.unwrap(), 0.0, epsilon = 1e-9));
192    }
193
194    #[rstest]
195    fn test_name() {
196        let expectancy = Expectancy {};
197        assert_eq!(expectancy.name(), "Expectancy");
198    }
199}
nautilus_analysis/statistics/expectancy.rs

nautilus_analysis/statistics/
expectancy.rs
