All forward estimates use copio's 2026 Q4 euro-denominated capital market assumptions, published on 19 October 2026, over a 10-15 year horizon. Historical stress examples use the explicitly dated windows below.
Where the assumptions come from
Copio combines reviewed institutional forecasts. Nine asset classes use a 50/50 average of comparable return and volatility estimates. The current edition combines September 2026 estimates with selected inputs from a second provider's 2026 Q2 edition. The source dates therefore differ across the model.
Euro area and broad European large caps use those averages. US large caps use one forecast because the two providers' benchmarks cover different stocks. Euro area small caps also use one forecast because a comparable second input is unavailable. These choices explain why copio's regional ranking can differ from an individual provider's.
Correlations come from the September 2026 euro-denominated matrix. Small adjustments keep the matrix mathematically valid for portfolio calculations while preserving every published correlation at two decimal places. All five articles use the same copio assumptions.
What the numbers mean
Estimated compound return describes an annualised long-term growth rate under the assumptions. Estimated annual volatility describes dispersion, not a maximum loss or a crash probability. The portfolios are illustrative constant-weight mixes, before product fees, transaction costs and personal taxes. They are not backtests, optimised recommendations or guarantees that an investment goal will be reached. The currency hedge is part of the US aggregate bond assumption. Actual products introduce costs, tracking differences and implementation constraints.
Portfolio weights
| Exposure | Regional equities | Strategic illustration |
|---|---|---|
| US large caps | 40% | 30% |
| Euro area large caps | 20% | 15% |
| Euro area small caps | 10% | 0% |
| Japanese equities, unhedged | 20% | 15% |
| Emerging market equities | 10% | 0% |
| US aggregate bonds, euro-hedged | 0% | 30% |
| Gold | 0% | 10% |
| Total | 100% | 100% |
The strategic illustration omits several markets and has material US bond exposure. It demonstrates a combination of assets, rather than a universal allocation. The other comparisons are 100% US equities, 100% world equities, 60% world equities with 40% euro aggregate bonds, and 50% world equities with 40% euro aggregate bonds and 10% gold.
Formula
Let gᵢ be each asset's assumed compound return, σᵢ its volatility, ρᵢⱼ the assumed correlation and wᵢ its portfolio weight. Use decimal values throughout the calculation.
- Covariance: Σᵢⱼ = ρᵢⱼ × σᵢ × σⱼ.
- Portfolio variance: V = ΣᵢΣⱼ wᵢwⱼΣᵢⱼ.
- Portfolio volatility: √V.
- Compound-return approximation: gₚ = Σᵢ wᵢ(gᵢ + σᵢ² / 2) - V / 2.
This approximation is also used by copio's CMA reference calculation. It assumes maintained weights and does not simulate a particular rebalancing schedule. A change in correlations affects both volatility and the diversification component of compound return.
Results
| Illustration | Compound return | Annual volatility |
|---|---|---|
| US equities | 7.00% | 16.96% |
| World equities | 7.00% | 15.52% |
| Regional equities | 7.67% | 15.07% |
| 60/40 | 6.18% | 10.03% |
| 50/40/10 | 6.13% | 8.60% |
| Strategic illustration | 7.00% | 9.48% |
Sensitivity
| Change to the strategic illustration | Compound return | Annual volatility |
|---|---|---|
| Base assumptions | 7.00% | 9.48% |
| Every cross-asset correlation moves halfway to 1 | 6.80% | 11.41% |
| Every asset's assumed return is two percentage points lower | 5.00% | 9.48% |
The correlation stress uses R′ = 0.5R + 0.5J, where J is an all-ones matrix. This preserves a valid correlation matrix rather than changing selected entries independently. It is a sensitivity exercise, not a forecast or calibrated crisis scenario. No loss probabilities are published because these inputs alone do not establish crash frequency or tail behaviour.
Historical stress comparisons
Returns below are in US dollars, using distribution-adjusted fund prices as research proxies except for the front-month gold futures series. VFIAX represents US equities, IEF 7-10 year Treasuries, DBC commodities and DBMF a managed-futures replicator. A replicator is not the whole trend-following industry. Gold futures differ from spot gold and from a euro-denominated gold holding. Article 5's euro gold example converts the 2022 gold futures return with the EUR/USD change over the same window: (1 - 0.13%) / (1 - 5.87%) - 1, or about +6.1%.
| Window | US equity proxy | Treasury proxy | Gold futures | Commodity proxy | Managed-futures proxy |
|---|---|---|---|---|---|
| Calendar 2008 | -37.0% | +17.9% | +5.8% | -31.8% | No history |
| 19 Feb-23 Mar 2020 | -33.8% | +6.4% | -2.5% | -25.7% | -6.6% |
| Calendar 2022 | -18.2% | -15.2% | -0.1% | +19.3% | +21.6% |
| 19 Feb-8 Apr 2025 | -18.8% | +2.7% | +1.8% | -12.2% | -7.2% |
| 27 Feb-30 Mar 2026 | -7.7% | -2.5% | -13.8% | +16.6% | -3.6% |
The purpose of these selected episodes is to show different mechanisms, not to estimate how often each hedge will work. The euro-listed world-equity fund's 2025 peak-to-trough loss was 21.6% from 19 February to 9 April, so its endpoint differs from the 8 April US equity trough.
The stock-bond comparison in article 5 averages overlapping rolling 36-month correlations of monthly VFIAX and IEF returns: -0.372 in 2011-2021 and +0.426 from January 2022 through September 2026. Article 4 uses annual ten-year US Treasury returns and US inflation from Damodaran's historical dataset, a different source and frequency. Compounded after inflation, those returns were about -2.0% a year in 1941-1981 and +5.0% a year in 1982-2020. The correlation and the real-return comparison should not be treated as the same statistic.
Japan and the internet build-out
The Japan chart uses the Nikkei 225 monthly closing price in yen, rebased to December 1989 = 100. It excludes dividends and is a price-weighted 225-stock index, rather than the entire Japanese equity market. Monthly timestamps are converted to Tokyo calendar months before selecting completed observations from January 1989 through September 2026. The first subsequent month-end above the December 1989 level is February 2024.
Ten-year Japanese government yields are OECD monthly observations for the same 453 months. Inflation is the annual-average change in consumer prices from the World Bank's IMF-sourced series FP.CPI.TOTL.ZG, covering 1989-2025. Annual inflation observations are placed at the middle of each year; the line joins observed annual values. No missing monthly inflation data are filled or estimated, and no 2026 annual inflation forecast is included. The chart aligns the time axes without implying that equity prices depend only on these two macroeconomic series.
Intel gross margins are gross profit divided by revenue from its 2003 and 2005 annual reports. The selected observations are 51.8% in 1995, 62.5% in 2000, 49.2% in 2001 and 59.4% in 2005. Cisco's 2005 gross margin is 67.2% on the same calculation. Gross margin is measured before operating expenses and differs from the operating margin reported for SK hynix.
Share-price comparisons use split-adjusted monthly closing prices from Yahoo Finance, in dollars and excluding dividends. Intel's December 2005 price is 66.7% below its August 2000 monthly high; Cisco's is 77.9% below its March 2000 monthly high. These are selected historical cases and do not establish the timing or size of a future AI-chip cycle.
Japan market data · Japan inflation
Growth and inflation framework
The four-quadrant matrix is a qualitative copio framework, not a fitted model or a performance ranking. Growth and inflation refer to surprises relative to what asset prices already reflect. The same observed inflation rate can have different market effects depending on expectations and policy.
Stronger growth can support equity earnings and commodity demand. Lower inflation can support nominal bond values by reducing expected rates, while a demand slowdown can increase demand for high-quality government bonds. A supply-driven inflation increase can support scarce commodities while hurting equities and nominal bonds. Inflation-linked bonds provide contractual inflation adjustment, but remain exposed to real yields and duration. Gold depends on real yields, currency and confidence; options depend on their contract and the price path. The matrix makes no claim about a fixed winning asset in every episode.
Calculation data
Portfolio results · Historical results · Portfolio calculation
The portfolio calculation reads the return, volatility and correlation inputs embedded in the results file. These are the inputs used for the article comparisons. The historical results identify the selected windows and research proxies; the sections above explain their return basis and limitations.
Scope
The CMA has broad European and Asian asset classes, but no standalone French fiscal-risk, Korean-equity or Taiwanese-equity forecast. The broad macro hedge-fund category is not a pure trend-following index or a retail product. Descriptions of these exposures in the articles therefore distinguish the underlying economic evidence from what the model can quantify.
