added beta & alpha

[jensnesten]

Add Alpha and Beta Metrics to Performance Analysis

This PR introduces two key risk-adjusted performance metrics:

• Alpha: Measures strategy's excess return relative to buy & hold benchmark
• Beta: Measures strategy's systematic risk (correlation with market returns)

[kernc]

This is looking great!

You'll need to amend a few tests to get the lights green ...

[jensnesten]

When looking at the expected stats results, mine are quite off. Running the smacross strat as defined in _test.py i get the following output:

Start                     2004-08-19 00:00:00
End                       2013-03-01 00:00:00
Duration                   3116 days 00:00:00
Exposure Time [%]                    93.99441
Equity Final [$]                  39770.03122
Equity Peak [$]                     61303.036
Commissions [$]                    8584.81878
Return [%]                          297.70031
Buy & Hold Return [%]               522.06019
Return (Ann.) [%]                    17.58149
Volatility (Ann.) [%]                35.35528
CAGR [%]                             11.81185
Sharpe Ratio                          0.49728
Sortino Ratio                         0.89695
Calmar Ratio                          0.34926
Alpha [%]                           277.50897
Beta                                  0.03868
Max. Drawdown [%]                   -50.33958
Avg. Drawdown [%]                    -6.25468
Max. Drawdown Duration      963 days 00:00:00
Avg. Drawdown Duration       47 days 00:00:00
# Trades                                   65
Win Rate [%]                         46.15385
Best Trade [%]                       53.59595
Worst Trade [%]                     -18.39887
Avg. Trade [%]                        2.35371
Max. Trade Duration         183 days 00:00:00
Avg. Trade Duration          46 days 00:00:00
Profit Factor                         2.08802
Expectancy [%]                        3.09763
SQN                                   1.01383
Kelly Criterion                       0.14365

These do not line up with the expected output from the dataframe defined in test_compute_stats(). Seems like the last trade isn't closed properly, it should be 66 trades in total. Ran a simple strat that buys on first close and sells at the last, and it failed to close the trade as well (which works fine on my older version of this repo). Also the test results i get from this newer version differ from my older version when running the same strat, can't seem to tell why though - just thought I'd mention.

[kernc]

These do not line up with the expected output from the dataframe defined in test_compute_stats().

Your stats contain 'Commissions [$]' but no test_compute_stats specifies them ... 💡

backtesting.py/backtesting/test/_test.py

Lines 282 to 283 in ad6d6e0

	def test_compute_stats(self):
	stats = Backtest(GOOG, SmaCross, finalize_trades=True).run()

backtesting.py/backtesting/test/_test.py

Lines 902 to 903 in ad6d6e0

	def test_compute_stats(self):
	stats = Backtest(GOOG, SmaCross).run()

There were a few changes recently that might change results obtained with prior versions, notably:

ae3d69f*
d4ec0ba
8fbb902
8b88e81
58de404

The current tests are considered accurate as long as they are passing on CI.

[jensnesten]

Ahhh I see now, thank you! Have added some expected values of alpha and beta to the dataframe. Is that all that is needed?

[kernc]

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?

[kernc]

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 ... 🤔

[jensnesten]

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:

$\alpha=(R-r) - \beta(R_{b}-r)$
when $\beta \rightarrow 0$:
$\alpha=(R-r)$

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.