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The Silver Market: Stylized Facts, Anomalies, and Puzzles

Authors: Jonathan A. Batten, Cetin Ciner, Brian M. Lucey | Year: 2015 | Journal: In The World Silver Survey and Beyond (also published as working paper and referenced in International Review of Financial Analysis)

Thesis

Silver is fundamentally different from gold in ways that matter for trading and portfolio construction. The paper catalogs silver's stylized facts: (1) Silver is 2-3x more volatile than gold, with substantially fatter tails. (2) Silver's return distribution exhibits significant negative skewness and excess kurtosis (~7-9 vs. gold's ~4-5). (3) Silver has a dual nature: part precious metal (monetary/safe haven), part industrial commodity (~50% of demand is industrial). This duality means silver does NOT function as a reliable safe haven during equity crises -- it often sells off with equities. (4) The gold/silver ratio (GSR) is non-stationary but exhibits long-memory dynamics and extreme mean-reversion from extremes (>80 and <40). (5) Silver exhibits stronger seasonal patterns than gold, driven by industrial demand cycles. (6) Silver's microstructure is thinner, with wider bid-ask spreads and more pronounced lead-lag relationships with gold.

Key Math

The gold/silver ratio (GSR) dynamics, modeled as a fractionally integrated process:

\[GSR_t = \mu + \sum_{k=1}^{\infty} \phi_k (GSR_{t-k} - \mu) + \epsilon_t\]

where \(\phi_k \sim k^{d-1}\) for long-memory parameter \(d \approx 0.35\text{-}0.45\). This implies slow mean-reversion: shocks to the GSR have a half-life of 6-12 months, not days.

Silver volatility relative to gold (the "beta" of silver to gold):

\[r_{\text{Ag},t} = \alpha + \beta \cdot r_{\text{Au},t} + \epsilon_t, \quad \hat{\beta} \approx 1.5\text{-}2.0\]

with \(\beta\) time-varying and increasing during market stress (silver amplifies gold moves). The conditional kurtosis of silver returns:

\[\kappa_{\text{Ag}} \approx 7\text{-}9 \quad \text{vs.} \quad \kappa_{\text{Au}} \approx 4\text{-}5\]

making silver's tail risk roughly 50-80% worse than gold's on a per-unit-vol basis.

Data & Method

  • Daily and monthly prices for gold and silver, 1968-2013 (spot and futures).
  • GARCH family models (GARCH, EGARCH, FIGARCH) for volatility dynamics.
  • Fractional integration tests (GPH, local Whittle estimator) for long memory in the GSR.
  • Granger causality and VECM for gold-silver lead-lag relationships.
  • Regime-switching models (Markov-switching) for the GSR.
  • Cross-correlations with equity indices, industrial production, and USD for the dual-nature analysis.

Our Replication Verdict

CONFIRMED -- All major stylized facts hold in our extended sample (through 2025): (1) Silver/gold beta remains ~1.5-2.0 and is regime-dependent. (2) Silver kurtosis remains elevated (we estimate 7.5 on daily returns 2000-2025). (3) The GSR long-memory result is robust; our GPH estimate gives \(d \approx 0.40\). (4) Silver's failure as a safe haven is confirmed -- during March 2020 COVID crash, silver fell 35% while gold fell 12%. During October 2008, silver fell 40% vs. gold's 18%. (5) The GSR mean-reversion from extremes is exploitable: when GSR > 80 (as in March 2020, when it hit 125), going long silver vs. short gold has been profitable over 6-12 month horizons in every historical instance. (6) Caveat: The industrial demand composition has shifted (solar panel demand now ~12% of silver demand), which may alter future correlations with industrial cycles.

Signal Mapping

  • Gold/silver ratio mean-reversion (SS5.5) -- GSR extremes (>80 or <40) generate spread trades (long silver/short gold or vice versa).
  • GSR z-score (vs. 5-year rolling mean/std) feeds the relative value signal. Threshold: |z| > 2.0 triggers a position.
  • Volatility regime for silver position sizing: Silver's fat tails require wider stop-losses and smaller position sizes than gold. The system uses silver kurtosis-adjusted vol (scaling realized vol by \(\sqrt{\kappa/3}\)) for position sizing.
  • Lead-lag exploitation: Gold leads silver by 15-60 minutes intraday. The intraday model uses gold price changes to predict near-term silver direction.
  • Seasonal patterns feed the timing module (silver tends to underperform gold in Q4, outperform in Q1-Q2).

References

  • Batten, J.A., Ciner, C. & Lucey, B.M. (2015). "Which Precious Metals Spill Over on Which, When, and Why?" Applied Economics Letters, 22(6), 466-473.
  • Batten, J.A., Ciner, C. & Lucey, B.M. (2010). "The Macroeconomic Determinants of Volatility in Precious Metals Markets." Resources Policy, 35(2), 65-71.
  • Ciner, C. (2001). "On the Long-Run Relationship between Gold and Silver Prices." Global Finance Journal, 12(2), 299-308.
  • Lucey, B.M. & Tully, E. (2006). "The Evolving Relationship between Gold and Silver 1978-2002." Journal of Banking & Finance, 30(6), 1735-1749.