Socrate II — Fund Market-State Review

The question

A fund delegates its capital to ten managers. Each mandate is monitored on its own; the risk committee sees the consolidated book. Two questions sit on its agenda. How diversified is the consolidated fund once the ten books are combined? And do the correlation stresses already in use still describe markets that can exist?

The conventional view

On the usual measures, nothing calls for attention. The regime is normal and every figure sits inside its recent range.

Measure	Value	How to read it
Volatility, annualised	9.4 %	typical yearly swing
VaR 95 % · 1 day / expected shortfall	0.83 % / 1.37 %	one bad day in twenty; average of those days
Worst fall, 2 years	‚àí8.8 %	bottomed 8 Apr 2025
Drawdown at risk, 3 months ¬∑ VaR at 1 month from today’s value	8.3 % ¬∑ ‚àí2.7 %	replays of the last two years, flat and history-only
First direction (PC1)	39 %	share of variance carried by the dominant direction

The geometric reading

54 positions ‚Üí 36 by weight ‚Üí 13 effective market directions.

The fund holds 54 securities. By weight they behave like 36 equally-sized positions. Measured on how they actually move together, the market currently gives this portfolio only 13 effective directions.

Consolidation. Consolidating the ten mandates reduces annualised volatility from about 10.0 % (mandates on average) to 9.4 %: that is the diversification the managers actually deliver once their books are combined.

Where the risk sits. The largest sources of risk are not the largest positions: Silver is 2.5 % of capital but 7.5 % of risk; MSCI Korea is 2.0 % of capital but 5.7 % of risk; MSCI Taiwan is 2.5 % of capital but 5.3 % of risk.

Where we are. The portfolio is in a normal regime; its structural concentration sits at the 13th percentile of its own history, and the dependence structure has been expanding over the last month.

The market-state journey

Question	Answer	Reading
Where are we?	normal regime ¬∑ concentration 13th pct ¬∑ 4.2 directions across 8 buckets (88th pct)	the state of the book’s dependence structure, ranked in its own history
Where did we come from?	1-month move 1.05 (47th pct of monthly moves) · 3-month move 2.58 (84th pct)	affine-invariant (geodesic) distance travelled between market states
Which way are we moving?	diversification expanding (trace +1.50, 11 % of the step in contraction) · first direction 59 % → 52 %	sign of the change of log-determinant: negative = diversification lost

The movement comes from declining coupling between emerging-market countries and government bonds (+0.52 ‚Üí +0.30), emerging-market countries and US sectors (+0.31 ‚Üí +0.12), and credit and emerging-market countries (+0.63 ‚Üí +0.45). Descriptive: the direction depends on the observation window and does not forecast the next move.

The Eratosthenes model-risk diagnostic

The same changes of market state are measured by a straight ruler and by the affine-invariant ruler. Over the whole history, the two rulers disagree by 48 % of the affine-invariant length: that is the geometry gap.

The Eratosthenes step Œ∫ ‚Äî by how much each affine-invariant step exceeds the straight one ‚Äî is 115 % in calm quarters and 179 % in stressed quarters; the last 21 sessions read 48 %, in the book’s calm range.

This is a property of the measurement geometry of a correlation-based risk engine, not a VaR correction: it identifies where a flat representation and an affine-invariant representation materially diverge when measuring changes between market states.

Do the stress scenarios remain possible market states?

Scenario (observed shock)	Admissible as specified	Ceases to be a market state beyond	Amplification headroom	Reading
COVID 2020	yes	1.01√ó	1 %	at the edge
Rate shock 2022	yes	1.13√ó	13 %	tight
Rotation 2024	yes	1.06√ó	6 %	at the edge
Synthetic ρ → 0.8	yes	1.10×	10 %	at the edge

Scaling an observed correlation shock in a straight line stops producing a possible market state at s* = 1 / (1 ‚àí Œª_min), the smallest generalised eigenvalue of (scenario, today’s state). We test whether an existing scenario remains admissible; we do not construct better scenarios.

What the risk committee takes away

	Conclusion
1. Diversification	The consolidated fund is currently more diversified than its own history, but 54 securities still collapse into only 13 effective market directions.
2. Structural change	Diversification has been expanding over the last month; the one-month move sits at the 47th percentile of the fund’s monthly moves, the three-month move at the 84th.
3. Model-risk action	Do not mechanically amplify the four existing correlation stresses: all four are within 50 % of the admissibility boundary (headroom 1 %, 13 %, 6 %, 10 %) and should be revalidated before use at larger severity. No action required on VaR.

Conclusions address the risk process, not the portfolio: the risk officer asks, the manager decides. No forecast is implied; no buy or sell.

Method and scope

States are correlation matrices of the portfolio’s 8 buckets over rolling windows. The Eratosthenes test uses a frozen protocol: 21-session window, three historical episodes and one synthetic scenario, thresholds fixed in advance. The market-state journey uses 63-session states one month apart. Forward-looking losses are block-bootstrap replays of the last two years.

Levels of κ and of the geometry gap depend on the universe and on the estimation window; the ordering — larger in stressed states than in calm ones — is the result that carries from one calibration to the next, including the 54-security calibration of the methodology note.

Shares and returns only, no amounts. The review is computed from weights expressed as shares of the book. Every document carries a SHA-256 fingerprint of what was analysed and of the results printed: the same book and the same results reproduce the same fingerprint.

The same review, on your universe

A review of this kind is what we call a tailored showcase. It follows a discovery session and takes about a week of work on our side.

• Universe-level review ‚Äî public market data only. No holdings, no weights, no data transfer.
• Portfolio-level review ‚Äî weights supplied as shares, under your control. Never amounts, never transactions.

Download the full Socrate II review (PDF, 5 pages) ‚Üí