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Technical report 07Risk & mandates

Hold the ceiling, not the number

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Abstract

We rebuild Orpheus (TR06) around the mandate as the Group stated it: the most yield the limits allow at no more volatility than the Bloomberg US Aggregate. Three findings. First, a fixed 4.64% ceiling cannot be held out of sample. Re-solved monthly from July 2016 on prior data only, the TR06 construction at 4.64% realised 6.14% volatility, because the risk model was estimated on the calm years and the Aggregate itself then ran 5.12%. Solving at 0.85 × 4.64% still breached. The Aggregate’s volatility is 3.0% over 2013–2019, 4.69% over the full record, 5.61% trailing 36 months and 8.4% in 2022; 4.64% is a regime average, not a current reading. The ceiling must be the Aggregate’s volatility measured the same way as the book’s risk, re-estimated at every solve. Under that definition the ceiling held in every variant tested (0.95–1.00 × the Aggregate’s realised volatility). Second, Orpheus+ adds five components, each drawn from the literature reviewed in the companion note and each kept only after it survived an out-of-sample test: the relative ceiling; a worst-of-three risk memory; yields haircut for expected loss (high yield −2.0% a year, bank loans −1.7%, emerging markets −0.75%, TIPS −8.5% of yield); a worst-case floor, the linearised corner of Luxenberg, Schiele and Boyd’s robust construction, requiring the first-order return over the next year to be no worse than −10% with rates +150 bp and spreads +150 bp; and a requirement to be at least 25 bp ahead of the current Core Plus, first order, in every scenario a book at the Aggregate’s volatility can win. That is eight of the eleven: the three rallies of 50 bp or more need Core Plus’s 6.9 years of duration, which breaks the ceiling, and we prove no compliant book at the Aggregate’s volatility wins all eleven (the best uniform margin is −0.29 points). The duration guard of TR06 is unchanged. Today’s book has a distribution yield of 5.18% (4.95% after the expected-loss haircuts) against the Aggregate’s 4.16% and Core Plus’s 4.85%, at 5.7 years of duration. Out of sample, July 2016 to August 2026, Orpheus+ with the guard earned 3.23% a year at a realised volatility of 3.30%, 0.64 × the Aggregate’s 5.12%, with a worst drawdown of −4.8%, ahead of the Aggregate in 69% of twelve-month windows (77 of 111) and of Core Plus in 60% (67 of 111); without the guard 1.93% at 1.00 ×. The Aggregate earned 1.41% and Core Plus 1.68%. Third, thirteen further ideas from the literature were tested and rejected on this data, including every refinement of the duration guard (excess-return signal, 3- and 12-month ensemble, per-sleeve application, re-entry bands), a high-yield credit guard, cushion and breach overlays, Ledoit–Wolf shrinkage, and Kelly objectives. Full long-only Kelly under the Group’s limits produces the Orpheus+ book exactly; fractional Kelly slides down the same frontier. Every figure is a hypothetical backtest on public data.

Keywords volatility ceiling · benchmark-relative risk · expected-loss haircut · worst-case floor · duration guard · walk-forward evaluation

1Introduction

TR06 [23] answered the Group’s July review: the optimiser’s preference for leveraged loans over agency MBS was an artefact of a three-year estimation window, and on the UMA menu the construction method mattered little while a one-signal duration guard lifted the Orpheus book’s out-of-sample Sharpe ratio from 0.01 to 0.29 (the Aggregate’s was −0.14; TR06’s abstract set the Aggregate’s −0.14 against a different book’s 0.40). It recommended the Orpheus book at a 3.80% ex-ante volatility ceiling (the risk model’s forecast), 84 bp under the Aggregate’s 4.64%, on the grounds that those 84 bp of volatility bought only 13 bp of yield (5.20% against 5.07%). Out of sample the same book realised 4.63% volatility without the guard and 3.08% with it. The first figure is above the book’s own 3.80% ceiling, which is where this report starts; the second is lower because the guard holds the rate-sensitive sleeves in T-bills in some months.

The Group’s response was that 3.80% leaves yield on the table. The mandate is the most yield possible at no more volatility than the Aggregate, and the Group gave 4.64% as the Aggregate’s number in the current environment while noting that it moves. This report takes that instruction literally and finds that the number is the wrong object. A ceiling stated as a constant is met in the risk model and missed in the market, because the two are estimated on different histories. A ceiling stated as the benchmark’s volatility under the book’s own risk model is met in both.

The report makes three contributions. (i) It measures how far a fixed ceiling drifts out of sample and shows that no safety margin short of 15% closes the gap, while the relative definition closes it exactly (Section 4.1). (ii) It specifies Orpheus+: the relative ceiling, a worst-of-three risk memory, an expected-loss haircut on yields, and a worst-case floor, with the TR06 guard unchanged, and reports the book, its out-of-sample record and its standing against the Aggregate and the current Core Plus (Section 3, Section 4.2 to Section 4.6). (iii) It records every idea from the literature that was tested and failed on this menu, so the Group does not pay to retest them (Section 4.4). The literature review that produced the candidate list is a companion note, Haircut the Yield, Margin the Ceiling (13 October 2026) [23]. The further works the note draws on are in the reference list [2, 7, 9, 11, 14, 16, 17, 18, 22].

One result of TR06 is overturned and one is strengthened. Overturned: TR06 stated that no feasible book exists below about 3.6% volatility; the floors admit a book at 2.98%, which the earlier solver could not find. Strengthened: every refinement of the duration guard proposed in the trend-following literature loses to the rule as TR06 wrote it.

Restricted from here

The rest of this paper opens with an access code.

This paper was written for one portfolio team and its firm’s risk reviewers. The abstract and the introduction are public and may be cited. The rest of the paper, with its references and appendices, opens with the access code and the confidential materials terms the team was given.

Held 2. Data · 3. Method · 4. Results · 5. Discussion · 6. Recommended policy · References · Appendices

Cite as

ARCANE Research (2026). Hold the ceiling, not the number. ARCANE Research Technical Report 07, v2, 19 October 2026. https://arcane.markets/research/orpheus-plus

@techreport{arcane2026orpheusplus,
  title       = {Hold the ceiling, not the number},
  author      = {{ARCANE Research}},
  institution = {ARCANE},
  type        = {Technical Report},
  number      = {07},
  year        = {2026},
  month       = oct,
  note        = {Version 2},
  url         = {https://arcane.markets/research/orpheus-plus}
}
Hold the ceiling, not the number — Research · ARCANE