REF: Use geometric mean return in Sharpe/Sortino stats computation

See:
https://qoppac.blogspot.com/2017/02/can-you-eat-geometric-returns.html
https://www.investopedia.com/ask/answers/06/geometricmean.asp

Author: kernc

backtesting/backtesting.py

@@ -1285,7 +1285,7 @@ def _round_timedelta(value, _period=_data_period(index)):
         s.loc['Win Rate [%]'] = win_rate = np.nan if not n_trades else (pl > 0).sum() / n_trades * 100  # noqa: E501
         s.loc['Best Trade [%]'] = returns.max() * 100
         s.loc['Worst Trade [%]'] = returns.min() * 100
-        mean_return = returns.mean()
+        mean_return = np.exp(np.log(1 + returns).sum() / (len(returns) or np.nan)) - 1
         s.loc['Avg. Trade [%]'] = mean_return * 100
         s.loc['Max. Trade Duration'] = _round_timedelta(durations.max())
         s.loc['Avg. Trade Duration'] = _round_timedelta(durations.mean())

backtesting/test/_test.py

@@ -253,10 +253,10 @@ def test_compute_stats(self):
                 'Avg. Drawdown Duration': pd.Timedelta('41 days 00:00:00'),
                 'Avg. Drawdown [%]': -5.925851581948801,
                 'Avg. Trade Duration': pd.Timedelta('46 days 00:00:00'),
-                'Avg. Trade [%]': 3.097629974370268,
+                'Avg. Trade [%]': 2.3537113951143773,
                 'Best Trade [%]': 53.59595229490424,
                 'Buy & Hold Return [%]': 703.4582419772772,
-                'Calmar Ratio': 0.06456068720154355,
+                'Calmar Ratio': 0.049055964204885415,
                 'Duration': pd.Timedelta('3116 days 00:00:00'),
                 'End': pd.Timestamp('2013-03-01 00:00:00'),
                 'Equity Final [$]': 51959.94999999997,
@@ -269,8 +269,8 @@ def test_compute_stats(self):
                 'Profit Factor': 2.0880175388920286,
                 'Return [%]': 419.59949999999964,
                 'SQN': 0.916892986080858,
-                'Sharpe Ratio': 0.2357610034211845,
-                'Sortino Ratio': 0.7355072888872161,
+                'Sharpe Ratio': 0.17914126763602636,
+                'Sortino Ratio': 0.5588698138148217,
                 'Start': pd.Timestamp('2004-08-19 00:00:00'),
                 'Win Rate [%]': 46.15384615384615,
                 'Worst Trade [%]': -18.39887353835481,