alpha-101: add bias config for long-biased / long-only mandates

[gangtao]

Background

The alpha-101 demo currently produces a strictly mean-zero Alpha #1 signal: (rank − 1) / (N − 1) − 0.5, summing to 0 across the N ranked stocks per bucket. That's the right default for evaluating the pure alpha — it isolates relative-value skill from market drift.

In practice, real books often want a non-zero mean (long-tilted):

• Long-only mandates — can't short, so the portfolio is structurally biased
• 130/30 or other tilts — the bias is a deliberate, sized component
• Stacked sleeves — a mean-zero alpha plus an explicit beta exposure

These should be expressible by the demo without abandoning the mean-zero foundation.

Proposal

Add a bias config knob to apps/alpha-101/manifest.yaml:

- key: bias
  type: string  # accept a float as string, parsed downstream
  required: false
  default: "0.0"
  description: >
    Constant added to alpha_1 *after* mean-zero centering. 0 = pure
    mean-zero (default). +0.5 ≈ 100% long-only tilt (every position
    is long; the rank still determines relative sizing). Negative
    values produce a net-short tilt. The tilt is reported separately
    from the alpha so P&L attribution can decompose alpha-skill
    from beta-exposure.

Plumb it into v_alpha_1:

cast(idx - 1, 'float64') / null_if(n - 1, 0) - 0.5 + {{ .Config.bias }}  AS alpha_1

Reporting / attribution

To keep the bias visible (not just absorbed into a single PnL number), v_backtest should also emit the decomposition:

SELECT
  ...,
  (alpha_prev - bias_value) * returns  AS pnl_alpha,   -- pure mean-zero contribution
  bias_value * returns                  AS pnl_bias,    -- tilt contribution
  alpha_prev * returns                  AS pnl_total
FROM ...

Then the backtest dashboard's "Backtest Summary" gets two extra columns (alpha-only Sharpe vs total Sharpe), and the "PnL over time" line chart can render both series so users see how much of the cum-PnL is "skill" vs "beta drift".

Acceptance criteria

• bias config in manifest (string, default "0.0", validated as a float)
• v_alpha_1 adds the bias constant after mean-zero centering
• v_backtest decomposes pnl into pnl_alpha and pnl_bias
• Backtest dashboard panels show both decomposed Sharpes / cum-PnLs
• README documents the trade-off (pure alpha vs tilted) and references the factorization principle: alpha (mean-zero) + beta sizing (macro view) + gross sizing (capital at risk), tracked separately
• End-to-end install verified with at least bias=0.0 (default), bias=0.5 (long-only tilt), and bias=-0.5 (short tilt)

Out of scope

• A continuous (non-rank) version of the alpha (would discard rank's outlier-robustness — different design discussion).
• Risk-based bias sizing (Kelly, target-vol, etc.) — that belongs at a portfolio-construction layer above the per-alpha view, not here.

References

Discussion thread that motivated this: PR for #24, conversation about mean-zero conventions in research vs production. Summary:

Research / signal evaluation → always mean-zero (otherwise Sharpe measures market drift, not skill).
Production / portfolio construction → factorized: alpha (mean-zero) + beta sizing (separate scalar) + gross sizing (separate scalar). Mixing bias into the alpha makes P&L attribution opaque.

This issue's bias config preserves that factorization by keeping the pure mean-zero alpha intact and exposing the tilt as a separately-reported component.