Scorecard omits tail risk — no CVaR, tail ratio, skew/kurtosis, or drawdown recovery time

[algotester123]

Problem

summarize() reports CAGR, Sharpe, Sortino, max drawdown, Calmar, annualised vol, and worst month. Every one of those is either a mean-variance summary or a single worst-point statistic.

Nothing describes the shape of the loss tail: no CVaR/expected shortfall, no tail ratio, no skew or kurtosis, no time-to-recover.

Why it matters

Two strategies can share a Sharpe and a max drawdown while having completely different risk of ruin. The classic failure mode — small steady gains punctuated by rare severe losses — is invisible to every metric currently reported, and it is exactly the profile a naive backtest makes look attractive.

There's a concrete internal reason too: deflated_sharpe.py already computes skewness and kurtosis (_moments()), because the PSR/DSR formulas need them — negative skew and fat tails make a given Sharpe less trustworthy. Those moments are calculated and then discarded rather than surfaced to the user. The framework is already telling itself the distribution is non-normal but not telling the reader.

Max drawdown also says nothing about duration: a −20% drawdown recovered in two months and one that takes four years are not the same risk.

Proposed fix

Add to metrics.py and include in summarize():

• cvar(returns, alpha=0.05) — mean of the worst alpha tail (expected shortfall)
• tail_ratio(returns) — |95th percentile| / |5th percentile|; below ~1 means losses outweigh gains at the extremes
• skewness / kurtosis — reuse the moment code already in deflated_sharpe._moments
• max_drawdown_duration(returns) — longest peak-to-recovery span in days
• avg_recovery_time(returns)

Acceptance criteria

• Hand-computed values verified on small fixtures
• A symmetric-normal synthetic yields skew ≈ 0, tail ratio ≈ 1
• A negatively-skewed synthetic is correctly flagged
• Duration metrics handle a series that never recovers (return inf or the censored length, documented)
• Moment code shared with deflated_sharpe, not duplicated