v1.0.0 to v2.0.0

+ factor for objective strategy comparison. Computes per-period statistics from a returns

+ series; it does not read a trade log or judge whether a strategy is deployable.

+ version: "2.0.0"

+ "Standardized" only holds if the conventions are pinned down, because the same returns produce different Sharpe and Calmar values under different defensible choices. This implementation fixes them explicitly and `references/standards.md` records each one with its source.

+

+ ## When NOT to Use

+

+ - **Not a trade-level analysis.** The generator consumes a per-period returns array. `Hit Rate` is the fraction of *periods* that were positive, which is not the same number as a per-trade win rate — a strategy holding one winning trade across 20 flat days has a 100% trade win rate and a 5% daily hit rate. For per-trade statistics, aggregate the trade log first and feed per-trade returns with `periods_per_year` set accordingly.

+ - **Not a compliance-ready performance presentation.** Under the SEC Marketing Rule, 17 CFR § 275.206(4)-1(e)(8), backtested results are *hypothetical performance*: "performance results that were not actually achieved by any portfolio of the investment adviser". A US-registered investment adviser putting this tearsheet in an advertisement must satisfy the conditions in § 275.206(4)-1(d)(6). This is a US adviser-advertising rule; it does not govern internal research. Check the rule and your own jurisdiction before distributing.

+ - **Not a correction for selection bias.** These are descriptive statistics for one backtest. If the parameters were chosen by searching many configurations, the reported Sharpe is the maximum of many noisy estimates and overstates expectation. See `backtest-parameter-sensitivity-analysis` and `factor-research-multiple-testing-correction`.

+ - **Not a verdict.** Nothing here says a strategy is deployable. Pair it with out-of-sample and regime evidence.

+ - **Not for log returns.** Inputs must be simple per-period returns; the equity curve compounds them as $\prod(1+R_t)$.

+

+ - Daily portfolio returns series $R_t$ as **simple** decimal returns, chronologically ordered, with no gaps.

+ - Annual risk-free rate $r_f$ (e.g. 0.04) on the same annualization basis as `periods_per_year`.

+ - At least 2 observations; annualized figures from less than one year are flagged, not suppressed.

+ 1. **Set the Annualization Basis First**: `periods_per_year` must match the sampling frequency — 252 daily, 52 weekly, 12 monthly. Using 365 on a trading-day series overstates annualized volatility by roughly 20% and understates Sharpe by the same factor.

+ 2. **Calculate Risk-Adjusted Ratios**: Sharpe uses arithmetic annualized excess return over annualized sample standard deviation (`ddof=1`). Sortino replaces the denominator with target downside deviation, averaging the squared below-target shortfalls over **all** periods rather than only the losing ones. Calmar divides CAGR by the absolute maximum drawdown; the excess-return variant is available via `calmar_uses_excess_return` and the report labels which was used.

+ 3. **Compute Drawdown Statistics**: Maximum drawdown is measured on an equity curve **seeded at 1.0**, so a decline starting on the first period counts against starting capital. Also reported: periods from peak to trough, and periods from trough back to the prior peak (`None` if never recovered).

+ 4. **Compute Per-Period Trade Statistics**: Hit rate, profit factor (gross win / gross loss) and average win/loss, all on periods, not trades.

+ 5. **Read the Degenerate Values Literally**: A zero denominator returns $\pm\infty$ or `nan`, never `0.0`. An infinite Sharpe means zero variance, not a bad strategy; a `nan` profit factor means there were neither gains nor losses.

+ 6. **Format Tearsheet Summary**: Generate structured report dictionary for standardized presentation, carrying `Periods`, `Calmar Convention` and `Annualization Extrapolated` alongside the metrics so the numbers stay interpretable.

+ - **Unseeded Drawdown Curve**: Starting the running maximum at the first period's close instead of at starting capital. A series that opens $-50\%$ then recovers slightly reports a maximum drawdown of **zero**, and three consecutive $-10\%$ periods report $-19\%$ instead of the true $-27.1\%$.

+ - **Dividing Downside Deviation by the Losing Periods**: Averaging squared shortfalls over only the below-target observations instead of all of them inflates Sortino — by a factor of 2 in a series where a quarter of the periods are losses.

+ - **Silent NaN**: A NaN return leaves hit rate and profit factor looking perfectly normal while every risk statistic becomes `nan`, producing a report that is half plausible. Reject it at the boundary.

+ - **Annualizing a Handful of Periods**: One $+5\%$ day compounds to over $20{,}000{,}000\%$ per year. The figure is arithmetically correct and completely meaningless.

+ - **Reporting 0.0 for a Degenerate Denominator**: A flawless constant-return curve has infinite Sharpe and infinite Calmar. Collapsing those to `0.0` makes the best possible result look like one of the worst. Note also that `numpy.std` of a constant series returns rounding error near $10^{-18}$, not exact zero, so an unguarded division yields an absurd finite value like $8.7\times10^{16}$.

+ - **Comparing Calmar Across Sources**: Both $\text{CAGR}/|\text{maxDD}|$ and $(\text{CAGR}-r_f)/|\text{maxDD}|$ are in circulation. They differ whenever $r_f \neq 0$; always state which one produced the number.

+ - **Returns Below $-100\%$**: These drive the equity curve negative, where CAGR and drawdown are undefined. Before this was guarded, a $-150\%$ return produced a reported drawdown of $-151\%$.

+ - Assert the seeded-curve drawdown: returns $[-0.50, +0.10, +0.05]$ must report a maximum drawdown of exactly $-0.50$.

+ - Assert the Sharpe closed form: returns $[a, 0, a, 0]$ with `periods_per_year=4` and $r_f=0$ give exactly $\sqrt{3}$, independent of $a$.

+ - Assert the Sortino convention: returns $[0.02, 0, 0.02, -0.02]$ with `periods_per_year=4` and $r_f=0$ give exactly $1.0$; dividing by the losing-period count instead would give $0.5$.

+ - Cross-check maximum drawdown against a brute-force $O(n^2)$ peak-to-trough scan on real data.

+ - Run `python -m unittest discover -s skills/backtest-reporting-standardized-tearsheet/scripts` and confirm 100% pass rate.

+ - `backtest-parameter-sensitivity-analysis`

+ - `monte-carlo-strategy-robustness-testing`