Gold Steers Crypto Prices, but No Long-Term Link Offers Diversification

Cryptocurrencies and precious metals show a short-run connection but no long-run cointegration, according to an empirical study published in Financial Innovation that analyzed daily closing prices from August 2017 to November 2022. The finding matters for portfolio construction: because the two asset classes do not move together over long horizons, investors holding precious metals may be able to add cryptocurrencies to their baskets without inheriting their long-term swings. The study, conducted by Asanga Jayawardhana and Sisira Colombage, applied an autoregressive distributed lag (ARDL) framework alongside causality and comovement tests to global market data.

The researchers drew their data from the Bloomberg data terminal, using the Bloomberg Galaxy Crypto Index (BGCI) as the proxy for the broader cryptocurrency market. That index tracks ten major digital assets: Bitcoin, Ethereum, Ripple, Bitcoin Cash, EOS, Litecoin, Dash, Monero, Ethereum Classic, and Zcash. On the commodities side, the study examined gold, silver, copper, platinum, palladium, and nickel, with precious metal prices measured in US dollars per troy ounce. All series were converted to US dollars using August 2017 exchange rates to strip out currency fluctuations. The dataset comprised 1,766 daily observations, and descriptive statistics revealed high skewness and kurtosis across the variables, signaling asymmetrical distributions with heavy tails and an elevated probability of extreme values, particularly for the cryptocurrencies.

The analysis began with stationarity testing, a prerequisite for cointegration analysis. The authors ran the augmented Dickey-Fuller (ADF) test, whose null hypothesis is the presence of a unit root, alongside the Kwiatkowski-Phillips-Schmidt-Shin (KPSS) test, which assumes stationarity under the null. This dual approach showed that all variables were integrated of order one, meaning they became stationary only after first differencing. Because standard cointegration tests lose power when parameters shift over time, the researchers then applied the Gregory and Hansen residual-based structural break test within three model specifications. The test identified two breakpoints: December 2017 and May 2020. The first coincides with the dramatic cryptocurrency bubble in which Bitcoin surged from below 2,000 dollars toward 20,000 dollars; the second reflects post-COVID-19 investor behavior. Neither breakpoint produced evidence of cointegration, pointing instead to a short-run dynamic between the markets.

The ARDL bounds test then formalized that picture. Using maximum lags identified through the Akaike information criterion, the adjusted R-squared, and the Schwartz Bayesian criterion, the model produced an F-statistic of 3.08. That value falls below the lower bound of 3.14 and well short of the upper bound of 5.69, which means the test cannot reject the null hypothesis of no cointegration. In plain terms, cryptocurrency and precious metal prices do not share a long-run equilibrium relationship. Because no long-run relationship existed, the authors did not proceed to an error correction model, and CUSUM stability checks plus Durbin-Watson and Breusch-Godfrey serial correlation tests supported the robustness of the result.

The short-run coefficients told a more nuanced story. In the ARDL panel results, a one-unit increase in the price of gold was associated with a statistically significant decrease of 0.127728 units in the cryptocurrency price. Palladium also carried a negative and statistically significant coefficient, meaning increases in palladium prices tended to correspond with decreases in cryptocurrency prices. Silver and copper showed positive coefficients that were not statistically significant, so no consistent relationship could be claimed for either. Platinum’s negative coefficient was only marginally significant at p = 0.052, warranting caution, while nickel’s positive coefficient was marginally significant and flagged for further investigation.

Causality testing added a directional layer to these correlations. Using the Toda and Yamamoto (1995) approach within a bivariate vector autoregression, chosen because the standard Granger test ignores combined effects of other variables, cannot deliver pairwise causality, and risks spurious regression with nonstationary data, the study found a unidirectional causal linkage running from the gold market to the cryptocurrency market. No causal linkage emerged between the cryptocurrency market and the remaining precious metals. Among the metals themselves, Granger causality tests revealed bidirectional patterns between gold and silver, gold and copper, gold and platinum, and copper and silver, marking gold as the most active market in the system. The authors note that unidirectional or absent causal links, unlike bidirectional ones, leave room for portfolio diversification.

Comovement analysis reinforced the diversification case. Unconditional correlations between the cryptocurrency market and precious metals were weakly positive and negative, consistent with modern portfolio theory’s premise that holding imperfectly positively correlated instruments reduces portfolio risk. An R-squared comovement model showed the highest co-movement during the sample among gold and silver, with an R-squared of 0.7280, and gold and copper, at 0.6796. Pairs involving cryptocurrencies displayed lower comovement values, and lower comovement is precisely what signals diversification potential under the framework the authors cite.

The study then translated these statistical patterns into portfolio results using a mean-CVaR approach, with Conditional Value at Risk chosen over Value at Risk because VaR is not convex, violates subadditivity, and ignores loss severity beyond its quantile. Four optimization frameworks were tested: an unconstrained portfolio, a portfolio with weights bounded between minus 100 and plus 100 percent, a long-only portfolio, and an equally weighted portfolio. Each framework was run with and without cryptocurrencies, producing eight portfolios backtested monthly over 59 months with a 12-month rolling horizon for weight estimation. The mean monthly cryptocurrency weight stayed low across all frameworks, ranging from 0.47 percent in the long-only case to 4.14 percent in the equally weighted portfolios, and 1.01 percent in the minus 100 to plus 100 percent framework.

The portfolio backtesting results were consistent across frameworks. Mean monthly returns rose when cryptocurrencies were added: the unconstrained framework showed the largest gain, with crypto-inclusive portfolios yielding a 2.63 percent mean monthly return against 0.46 percent without, an increase of 2.17 percentage points. Risk rose in tandem, with mean monthly CVaR at the 95 percent confidence level increasing by 0.19, 0.73, and 0.08 percentage points in the equally weighted, unconstrained, and minus 100 to plus 100 percent frameworks respectively. Crucially, the mean monthly risk-return ratio improved consistently in every optimization framework when cryptocurrencies joined the precious metal basket, with unconstrained portfolios showing a 1.85 percentage point improvement between the with-crypto and without-crypto versions.

The authors frame these findings through Markowitz’s modern portfolio theory: the absence of long-run cointegration and the lack of bidirectional causality between most precious metals and cryptocurrencies suggest genuine diversification benefits, and the mean-CVaR backtests support holding both asset classes together. They also attach clear caveats. The diversification potential may shrink during periods of poor market sentiment, potentially dragging on portfolio performance, and the authors acknowledge that the evaluation window was inadequate for assessing long-term effects. They call for extended out-of-sample testing, replication in other regions, and a larger pool of investable assets, noting that institutional environments, legal frameworks, and economic characteristics differ across markets. For now, the evidence supports a modest allocation, not a heavy one, given the small optimal crypto weights and the elevated tail risk documented throughout the study.

Subject of Research: Portfolio diversification between precious metals and cryptocurrencies using ARDL cointegration, causality, and mean-CVaR portfolio analysis

Article Title: Exploring portfolio diversification possibilities in the precious metal market through cryptocurrencies: an empirical approach using global evidence

Article References: Jayawardhana, A., & Colombage, S. (2026). Exploring portfolio diversification possibilities in the precious metal market through cryptocurrencies: an empirical approach using global evidence. Financial Innovation, 12(1), Article 149. https://doi.org/10.1186/s40854-026-00966-1

Image Credits: AI Generated

DOI: 10.1186/s40854-026-00966-1

Keywords: cryptocurrencies, precious metals, portfolio diversification, ARDL, cointegration, gold, Bitcoin, modern portfolio theory, mean-CVaR, causality, comovement, Financial Innovation