Correcting Market Variance in Multi-Asset Equity Simulations
Summary
This study addresses a variance double-counting problem in synthetic multi-asset equity data. When full asset-return generators are combined with a market factor, the simulated returns can include market variance twice. The proposed correction centers and rescales each generator’s draws over a fixed horizon before adding the market component, avoiding the need to fit a separate generator to regression residuals.
Tests on a United States equity and exchange-traded-fund universe found that corrected paths retained heavy tails and recovered calibrated market loadings with low error. On held-out 2025 histories, the method improved the mean distributional pass rate over naive composition and brought median synthetic-to-observed variance close to one. The reported one-day left-tail Value-at-Risk exceedance rate remained above the nominal rate. A jump-duration extension improved volatility clustering for SPY in one setting, but transferring its settings worsened temporal fit in the holdout. Residual dependence is not modeled and may inflate simulated rebalancing returns; the zero-sum constraint also removes terminal residual uncertainty.
Key ideas
- Combining full-return generators with a market factor can count market variance twice.
- The correction centers and rescales generator draws over a fixed horizon before adding the market factor.
- Tests found heavy tails and calibrated market loadings were retained, with improved distributional fit on held-out histories.
- The reported tail-risk exceedance rate was above the nominal rate, and jump-setting transfer worsened holdout temporal fit.
- Unmodeled dependence among asset residuals may overstate simulated rebalancing returns.
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Full text
# Variance-Corrected Multi-Asset Equity Simulation with Hybrid Hidden Markov Marginals # Variance-Corrected Multi-Asset Equity Simulation with Hybrid Hidden Markov Marginals Synthetic multi-asset equity data must reproduce each asset's return distribution and its relationship with the market. Reusing a generator fitted to full asset returns creates a problem: adding its draws to a market factor counts market variance twice. We derived a correction that centers and rescales each draw over a fixed horizon before adding the market factor, allowing reuse without fitting a second generator to regression residuals. We tested the correction on 423 non-market assets in a 424-asset United States equity and exchange-traded-fund universe, using hidden Markov generators with heavy-tailed emissions. The corrected paths retained heavy tails and recovered the calibrated market loadings with low error. On 416 complete asset histories held out from 2025, the correction improved the mean Kolmogorov-Smirnov pass rate over naive composition and brought the median ratio of synthetic to observed variance close to one. Its one-day left-tail 99% Value-at-Risk exceedance rate, using thresholds pooled across separate simulated paths, was 1.12%, compared with 1.16% for the residual-fit hidden Markov comparator and a nominal rate of 1%. We also tested a jump-duration mechanism that extended visits to extreme-return states and improved volatility clustering for the broad-market exchange-traded fund with ticker SPY. The multi-asset correction remained effective with jumps enabled, but transferring the SPY jump settings improved temporal fit in training and worsened it in the 2025 holdout. The method provides a way to reuse fitted asset generators for daily-fit comparisons. Its zero-sum residual constraint removes terminal residual uncertainty, and unmodeled dependence among asset-specific residuals can lead to overstated rebalancing returns. Code, cached inputs, result summaries, and instructions for fitting the per-asset models accompany the paper.
Shown in full with attribution under the source's licence. Licence: abstract CC0
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