Math

Derived series

Dollar stocks never vote a colour. They sit on the lookback, or they become a ratio, a spread, or a rate of change. FRED units first: Fed assets and the Treasury account in millions, reverse repo in billions, Bank of Japan assets in hundreds of millions of yen.

Net liquidity

WALCL(bn) − TGA(bn) − ON RRP(bn) WALCL and TGA ÷ 1,000 from millions. GDP share votes; the stock does not.

Reserves ÷ GDP

(WRESBAL millions ÷ 1,000) ÷ nominal GDP × 100 Trailing five-year, not a fixed band.

Net liquidity ÷ GDP

net liquidity (bn) ÷ nominal GDP × 100 Trailing five-year.

Funding vs target top

(overnight funding − fed funds target top) × 100 bp. SOFR from 2018-04-02, EFFR before. Trailing five-year. High is tight.

G4 central bank assets

Fed + ECB×USD/EUR + BoJ×(100 / yen per dollar) + China FX reserves Each leg at that day’s rate, summed in $tn. Level does not vote.

Global CB assets, 12m

(G4 today − G4 ~1y ago) / |G4 ~1y ago| × 100 The G4 voter. Neutral at +5%, not zero.

Dollar, 12m change

(broad dollar today − ~1y ago) / |~1y ago| × 100 DTWEXBGS. Rising is tight for Liquidity.

Global long rates (G3)

(Bund 10y + gilt 10y + JGB 10y) / 3 Last observation carried across holidays.

Credit impulse (US)

Δ over ~1y of (TOTLL YoY %) Lookback only. Does not vote a colour.

China credit impulse

China credit/GDP today − China credit/GDP four quarters ago Lookback only. The stock votes Liquidity at half weight.

Equity risk premium

S&P earnings yield − 10-year real yield Wide = equities cheap versus duration.

Nominal − real GDP

nominal GDP YoY − real GDP YoY Story, not a ballot.

Stock–bond correlation

60-day Pearson of SPX returns vs −Δ 10-year yield Confirm / falsify, not a component vote.

Gold positioning

156-week min–max of CFTC non-commercial net % of open interest 0 least crowded, 100 most. Taxes Gold when longs are crowded.

2-year real (Rates vote)

2-year yield − core PCE YoY Built at score time. TIPS 5y and 10y vote as published.

How a print becomes a score

Each voter maps to −1…+1. Positive is the reflationary side of that component. If high is the contractionary end, the sign flips once, in the band.

band: ≤ low → −1 · mid → 0 · ≥ high → +1 · linear between

Trailing five-year (reserves ÷ GDP, net liquidity ÷ GDP, funding spread). Needs about two years or it abstains:

clip( (print − 5y mean) / sd / 2 , −1, +1 )

How scores become a component

Related prints share a ballot, then ballots average. Inside a ballot, members can be weighted.

• Liquidity — Fed GDP shares · funding cost · commercial paper · global CBs and the dollar. Four ballots, all counted: the trim needs six.
• Rates — real yields · nominal yields · the curve · bond vol
• Growth — coincident × 0.5 · leading × 1.5 · surveys × 1. Coincident is halved because jobs and GDP describe the quarter that ended. When the surveys are past ±0.45 while coincident is still inside it, coincident has followed them within a quarter about two thirds of the time since 2003, against 50% on all other days — so the surveys may take the word.
• Inflation — realized × 2 · persistence · expectations
• Risk — credit spreads · volatility

Five or more ballots: drop the high and the low, then average. Liquidity is the one that trims. MOVE can turn Rates red, never green. If funding cost or commercial paper is ≤ −0.5, Liquidity is held at least that tight.

Then recenter and stretch so all five share one spread:

score = clip( ((raw − mean) / sd) × shared spread × scale, −1.5, +1.5 )

Green and red at ±0.45. The middle is the word. Today’s fit:

Lookback, and when a series stops voting

1w = 7 calendar days, 2w = 14, 1m = 30, 3m = 91, 6m = 182. A series too slow to fill the window steps back whole prints instead. Monthly: one step back on 1w / 2w / 1m, three on 3m, six on 6m. Quarterly: one step back on 1w / 2w / 1m / 3m, two on 6m — so a weekly lookback on a quarterly series is still the last quarter-on-quarter change, not a flat line. Stale (does not vote): 14d daily, 21d weekly, 85d monthly, 190d quarterly.

The table lookback only colors rows and sets spark length. Chevrons, duration, credit, and in / mixed / out use the 1m turn.

Duration risk and credit risk

Soft weight 0…1, fully on at the colour line ±0.45. The six asset nets use these weights on the score, not only the word — so Neutral Risk at +0.40 is almost fully Risk-on for every net. Positive net = that risk is falling. Call at ±0.35.

The two weights are not mirrors: easeW ramps over 0.65 from −0.2, tightW over 0.25 from −0.2. A score of exactly 0.00 therefore returns easeW 0.31 and tightW 0.00. Deliberate — fear and drain must be clearly present before they price, while ample conditions are the resting state — and it tilts every net slightly toward reflation.

easeW = clip((score + 0.2) / 0.65, 0, 1) tightW = clip((−0.2 − score) / 0.25, 0, 1)

Duration (positive = duration risk falling):

−0.70 × hot inflation that is not cooling +0.65 × cold inflation +0.45 × hot-but-cooling on the 1m turn −0.55 × tight Rates +0.35 × easy Rates +0.70 × term-premium z +0.55 × 10-year real-yield z −0.25 × strong Growth × (1 − cold inflation)

Credit (positive = credit risk falling):

+0.35 × strong Growth −0.35 × soft Growth +0.35 × Risk-on −0.35 × Risk-off −0.30 if activity is rolling over on the 1m turn, +0.20 if it is firming −0.30 if high-yield spreads are widening, +0.20 if they are tightening −0.35 if US bank-credit impulse is slowing, +0.35 if it is speeding up −0.15 if China credit impulse is slowing, +0.15 if it is speeding up +0.25 × credit-spread z (wide = you are paid)

Valuation: clip((print − median) / scale, −1, +1). High-yield OAS is pinned at 4.0%. Today’s centres:

How a class gets in / mixed / out

Each class has its own net of conditions. Most map in at +0.35 and out at −0.35. Equities 0.10 / −0.18; Crypto 0.14 / −0.24; Gold ±0.18. Credit parent 0.24 / −0.26; HY ±0.26; oil, copper, and the commodity parent 0.12 / −0.22. 5 (cash) is on the Treasuries strip and out of the parent net and the parent needle — the long end is the Treasuries call.

These cuts are not one shared scale. Each net is fitted against its own spread, and the spreads differ: the 10s and 30s nets can run to about ±3.3, the equity net to about ±1.1, the 5s net to exactly ±1. So ±0.35 is roughly a tenth of the range on the long end and about a third of it on the front end. Read a threshold against its own class, never across two.

needle = 0.72 × checklist + 0.28 × 1m turn

The 1m turn may slide the needle. It cannot flip the call. The table lookback does not enter this mix.

The archive, and how a comparable day is found

The archive is a replay: today’s rules run over 2003 to now, rebuilt from scratch each morning. It is not a record of what the app said. Scores in it are calibrated on an expanding window — each day is scored against only the days before it, so 2004 never sees 2015’s distribution. The live score uses the full-sample fit instead, which is why the two are built by different paths on purpose.

A comparable day is straight-line distance across the five component scores:

d = √( Σ (pasti − todayi)² ) over the five components

Nearest first, but no two picked days may sit within 21 days of each other, and at most 40 are kept. Without the gap rule a single quiet stretch would supply all forty and one episode would be reported as forty precedents. The set’s median distance names the match: < 0.35 close · < 0.70 loose · beyond that distant. For scale, a typical day in the archive sits about 0.57 from its own forty nearest, so “loose” is the ordinary result and not by itself a warning.

Forward returns are simple percent changes measured in trading days — 1w = 5, 2w = 10, 1m = 21, 3m = 63, 6m = 126, 12m = 252 — and equal-weighted where a class has more than one asset: Treasuries from 5s, 10s and 30s; credit from HY and IG; commodity from oil and copper. Bond and equity ETFs use adjusted close, since a coupon is most of a bond’s return. Treasury forwards are synthetic total returns built from yields (daily ≈ y/252 − D·Δy), so the grade matches the 5s / 10s / 30s the strip actually names.

Grading counts independent windows, not days. A call held for 58 straight days and graded on a one-month forward return is roughly two separate bets on one episode, not 58, because every window overlaps its neighbours. The count is greedy: take a window, skip everything it covers, take the next.