Orthogonality prior

By prior

LIKELY CORRELATED SHARES A FACTOR WITH A LIVE SLEEVE

• analyst_revision_drift
• carbon_allowance_carry
• catastrophe_bond_event_risk
• inflation_breakeven_relative_value
• securities_lending_supply

STRONGLY ORTHOGONAL DRIVEN BY SOMETHING OTHER THAN PRICE

• index_reconstitution_flow

UNCERTAIN SHARES THE CRISIS DIRECTION OF A LIVE SLEEVE

• active_ownership_escalation
• credit_equity_relative_value
• cross_currency_basis
• crypto_liquidation_pressure
• dealer_gamma_pressure
• fallen_angel_flow
• freight_derivative_dislocation
• fx_option_risk_reversal
• merger_arbitrage
• mortgage_convexity_pressure
• municipal_taxable_basis
• sovereign_cds_fx_dislocation
• swap_spread_dislocation
• tender_offer_spread

Live sleeves

Measured structure

N days

1061

Resolved pairs

2

Rho bar

0.026037

Standard error per pair

0.030700

Unresolved pairs

4

Pairs

Nested beyond what this page renders. Read it in the artifact.

The axis with no local evidence. Crisis direction. This book holds one SHORT_LIQUIDITY sleeve, so no pair isolates it and nothing here tests it. It decides fourteen of the twenty rankings below, and that is the single weakest joint in this artifact.

What it cannot support. One informative pair per structural cell. That is a direction, not a coefficient, and any weighting fitted to it would be fitted to a single observation. The prior is published UNCALIBRATED.

What it supports. Of six pairs, two resolve against sampling error. The pair sharing a factor family is the largest correlation in the book; the pair sharing an asset class is negative. The four sharing neither are indistinguishable from zero.

What would calibrate it. A book of eight sleeves gives twenty-eight pairs instead of six. Calibration is a consequence of breadth, not a route to it — which is the uncomfortable ordering: the prior is least testable exactly while it is most needed.

Prior meanings

LIKELY CORRELATED SHARES A FACTOR WITH A LIVE SLEEVE. Trades the same idea as a live sleeve in different clothes. This is the one structural feature that produced a large measured correlation in this book.

LIKELY ORTHOGONAL NO SHARED FACTOR OR CRISIS DIRECTION. Shares no factor family and no crisis direction, but is price-driven, so it inherits whatever the market inherits when everything moves together.

STRONGLY ORTHOGONAL DRIVEN BY SOMETHING OTHER THAN PRICE. Shares no factor family and no crisis direction with any live sleeve, and what moves it is not a price. The strongest prior this rule can express, and still a prior.

UNCERTAIN SHARES THE CRISIS DIRECTION OF A LIVE SLEEVE. No shared factor, but it loses money in the same event as a live sleeve. Correlation measured over a calm window will understate it, and the window that would show it is the window nobody has enough of.

Rho bar under stress

Note. Published for the crisis axis it bears on and NOT used to score anything: the stress windows are predeclared but the book still holds one SHORT_LIQUIDITY sleeve, so these numbers describe the existing four rather than testing the axis.

The rule

1 shares a factor family with a live sleeve

LIKELY_CORRELATED_SHARES_A_FACTOR_WITH_A_LIVE_SLEEVE

2 else shares a crisis direction with a live sleeve

UNCERTAIN_SHARES_THE_CRISIS_DIRECTION_OF_A_LIVE_SLEEVE

3 else driven by something other than price

STRONGLY_ORTHOGONAL_DRIVEN_BY_SOMETHING_OTHER_THAN_PRICE

4 else

LIKELY_ORTHOGONAL_NO_SHARED_FACTOR_OR_CRISIS_DIRECTION

Stated before scoring

yes

Asset class is deliberately absent. The one measured pair sharing an asset class is NEGATIVE (-0.062) and the one sharing a factor family is the largest in the book (+0.210). Scoring asset class would encode the intuition the evidence contradicts. This is the most attackable choice here and it is stated first rather than buried.

What the ordering is for

Contract correlation gate

0

Forward sharpe at that rho bar optimistic haircut

1.157000

Forward sharpe at the objective optimistic haircut

1.498000

In sample sharpe at that rho bar

1.736000

In sample sharpe at the objective

2.247000

Objective rho bar

-0.030000

Pairs new

85

Pairs now

6

Required average over the new pairs

-0.033960

Rho bar if every new pair sits exactly at the gate

0.001717

Rho bar now

0.026037

Sleeves now

4

Sleeves target

14

Extends. artifacts/analysis/breadth_acquisition/result.json, which reached the same conclusion against the superseded 0.15 gate.

The gap. Every new pair landing exactly on the +0.00 gate gives a book average of +0.0017 and a forward Sharpe of 1.16 on this book's own optimistic haircut. The gate is necessary and it is not sufficient, and the shortfall is 0.34 of forward Sharpe. Ordering by expected orthogonality is the only lever that acts on the difference, because the gate cannot.