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added beta & alpha #1221

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merged 14 commits into from
Mar 11, 2025
Merged

added beta & alpha #1221

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effda1a
added beta & alpha / resolved merge conflict
jensnesten Feb 16, 2025
763e2dc
simplified beta calculation
jensnesten Feb 23, 2025
150845f
Merge branch 'master' into master
jensnesten Feb 23, 2025
8f7c51f
remove DS_store
jensnesten Feb 23, 2025
62a2983
move beta & alpha / use log return
jensnesten Feb 25, 2025
871464e
Update backtesting/_stats.py
jensnesten Feb 26, 2025
65adda0
Update backtesting/_stats.py
jensnesten Feb 26, 2025
6be63bb
alpha & beta test
jensnesten Feb 27, 2025
a213d74
#noqa: E501
jensnesten Feb 27, 2025
5abc3d8
add space
jensnesten Feb 27, 2025
52ab559
update docs
jensnesten Feb 27, 2025
b03f333
Revert unrelated change
kernc Mar 11, 2025
fc6ffc6
Add comment
kernc Mar 11, 2025
d486c53
Merge branch 'master' into master
kernc Mar 11, 2025
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2 changes: 2 additions & 0 deletions README.md
View file
Original file line number Diff line number Diff line change
@@ -68,6 +68,8 @@ CAGR [%] 16.80
Sharpe Ratio 0.66
Sortino Ratio 1.30
Calmar Ratio 0.77
Alpha [%] 450.62
Beta 0.02
Comment on lines +71 to +72
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For given values of s.loc['Return [%]'] and s.loc['Buy & Hold Return [%]'], the previous computation of

s.loc['Alpha [%]'] = s.loc['Return [%]'] - s.loc['Buy & Hold Return [%]']  # == -144

seemed much more reasonable! Can you explain the discrepancy?

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LLM suggests, among the less applicable options, that the values are not computed on the same time scale—beta is computed on daily returns and alpha on the whole duration ... 🤔

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@jensnesten jensnesten Mar 4, 2025 •
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So the 'simple' alpha we first had is absolute alpha, where we simply calculate the absolute difference of our strategy relative to the underlying benchmark. The new calc is risk-adjusted alpha, which is the official definition of alpha, but here we might end up in situations where alpha is positive, despite underperforming the benchmark in terms of return. Especially in beta neutral strategies where beta approaches 0, you'd have situations where the right-most term will go to 0 - essentially signaling very little risk:

α = ( R − r ) − β ( R b − r )
when β → 0 :
α = ( R − r )

I personally like the simple alpha calc in this context, because its simple and intuitive. But the alpha we have now is the correct alpha definition.

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Thanks. I added a source code comment so that we remain aware of this counter-intuitive issue. Hope not too many users get confused by it, or that we eventually get to improve on it.

Max. Drawdown [%] -33.08
Avg. Drawdown [%] -5.58
Max. Drawdown Duration 688 days 00:00:00
7 changes: 7 additions & 0 deletions backtesting/_stats.py
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Original file line number Diff line number Diff line change
@@ -152,6 +152,13 @@ def _round_timedelta(value, _period=_data_period(index)):
s.loc['Sortino Ratio'] = (annualized_return - risk_free_rate) / (np.sqrt(np.mean(day_returns.clip(-np.inf, 0)**2)) * np.sqrt(annual_trading_days)) # noqa: E501
max_dd = -np.nan_to_num(dd.max())
s.loc['Calmar Ratio'] = annualized_return / (-max_dd or np.nan)
equity_log_returns = np.log(equity[1:] / equity[:-1])
market_log_returns = np.log(c[1:] / c[:-1])
cov_matrix = np.cov(equity_log_returns, market_log_returns)
beta = cov_matrix[0, 1] / cov_matrix[1, 1]
# Jensen CAPM Alpha: can be strongly positive when beta is negative and B&H Return is large
s.loc['Alpha [%]'] = s.loc['Return [%]'] - risk_free_rate * 100 - beta * (s.loc['Buy & Hold Return [%]'] - risk_free_rate * 100) # noqa: E501
s.loc['Beta'] = beta
s.loc['Max. Drawdown [%]'] = max_dd * 100
s.loc['Avg. Drawdown [%]'] = -dd_peaks.mean() * 100
s.loc['Max. Drawdown Duration'] = _round_timedelta(dd_dur.max())
2 changes: 2 additions & 0 deletions backtesting/backtesting.py
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Original file line number Diff line number Diff line change
@@ -1262,6 +1262,8 @@ def run(self, **kwargs) -> pd.Series:
Sharpe Ratio 0.58038
Sortino Ratio 1.08479
Calmar Ratio 0.44144
Alpha [%] 394.37391
Beta 0.03803
Max. Drawdown [%] -47.98013
Avg. Drawdown [%] -5.92585
Max. Drawdown Duration 584 days 00:00:00
2 changes: 2 additions & 0 deletions backtesting/test/_test.py
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Original file line number Diff line number Diff line change
@@ -317,6 +317,8 @@ def test_compute_stats(self):
'Start': pd.Timestamp('2004-08-19 00:00:00'),
'Win Rate [%]': 46.96969696969697,
'Worst Trade [%]': -18.39887353835481,
'Alpha [%]': 394.37391142027462,
'Beta': 0.03803390709192,
})

def almost_equal(a, b):