The paper supports a better model of annual gold volatility. Its tables never isolate the contribution of bank runs, even though the text says it reports out-of-sample results without them.

What goes into the models?

Liu, Pierdzioch, Gupta and Bouri begin with flight to safety. Bank runs make deposits look risky; gold carries no counterparty risk and should attract the money leaving banks. Policy responses, including rate cuts and liquidity injections, also reduce the opportunity cost of holding gold. The authors therefore expect runs to raise real gold returns and their volatility.

They use the annual gold price in British pounds from MeasuringWorth, deflate it by UK CPI and calculate log returns. The resulting sample contains 329 observations. Most of the paper gives 1696 as the starting date; the introduction gives 1694. Normality is a poor description of these returns: the mean is 0.31, standard deviation 9.90, skewness 1.02 and kurtosis 6.71. The Jarque-Bera p-value is below 0.01.

The predictor measures worldwide bank-run frequency: runs divided by the number of countries in the sample that year. Its source is the Jamilov et al. (2025) chronology, with 405 episodes across 192 countries. The paper gives its coverage as 1800 to 2024. Frequency reaches roughly 0.20 in the early 20th century.

Each of the four models includes this covariate in the mean equation, through phi1, and the variance equation, through phi2. GARCH-X and the asymmetric GJR-X are the standard versions. GARCHSK-X and GJRSK-X follow León, Rubio and Serna (2005), allowing conditional skewness and kurtosis to follow their own autoregressions. They use a Gram-Charlier expansion to adjust the normal density.

Forecasting begins after a 100-year burn-in. The estimation window expands annually, with one-step forecasts assessed using RMSE, MAE, Diebold-Mariano tests and a Sharpe ratio. Log-likelihood rises from -1155.577 for GARCH-X to -195.900 for GJRSK-X. The latter delivers the lowest out-of-sample volatility RMSE at 279.731. GARCHSK-X leads the Sharpe column with 0.141.

We could not reproduce the exercise. We do not hold the hand-assembled cross-country panel of bank runs. Reconstructing returns would also require three centuries of sterling gold prices and UK CPI. Our gold history begins around 2010, leaving us short of even the paper's 100-year burn-in.

The missing comparison

The abstract credits bank runs with improving the GARCH models' in-sample performance and significantly improving their out-of-sample performance. Table 1 divides the models into columns headed "Without SK" and "With SK". Every model retains the -X covariate. Table 3 presents five rows, comprising the same four -X models and a linear regression. Although the text says it also reports out-of-sample results for models without bank runs, we could not locate those rows. The tabulated comparisons consequently show the contribution of skewness and kurtosis dynamics while keeping bank runs in every model.

The conclusion starts by asserting the importance of bank runs. Two sentences later, it offers a narrower finding: out of sample, SK models outperform GARCH models without time-varying skewness and kurtosis. The tables allow us to test only the latter claim. Their volatility columns give it partial support. GJRSK-X records the lowest volatility RMSE, 279.731, while GARCHSK-X records the lowest MAE, 125.313. Neither comparison supports the headline claim about bank runs.

The coefficient estimates leave the issue unresolved. GARCHSK-X estimates phi1 at 4.391 (SE 1.007), and GJRSK-X at 4.893 (SE 1.388). The corresponding estimates are 8.194 (SE 19.000) in GARCH-X and 7.862 (SE 13.163) in GJR-X. Standard errors fall about 19-fold across the GARCH pair and about 9.5-fold across the GJR pair. But the inference method changes too. According to the table note, bootstrap standard errors apply only to the SK models.

The appendix specifies a moving block bootstrap with B = 1000, resampling the return series. We found no block length. Nor could we establish whether the bank-run series is resampled in matching blocks.

The estimated economic effect is small.

At a peak frequency around 0.20, phi1 of 4.391 contributes roughly 0.9 points to expected annual real returns. The return standard deviation is 9.90.

Some estimates land on conspicuously round values. In GARCH-X, phi2 is 99.998; in GJRSK-X, it is 5.000. Both SK models have gamma0 = 1.000 and gamma2 = 0.950. These resemble optimizer bounds or initial values, though we found no reported bounds. GARCHSK-X also has kurtosis-equation standard errors of 94.895 for the intercept and 32.409 for persistence. Those are consistent with weak identification.

Adding two autoregressions to 329 observations produces a log-likelihood gain of about 950 points. That is difficult to interpret as a like-for-like improvement. Different density scales across the model families offer a better explanation. If that explains the gap, comparing AIC of 1.306 for GARCHSK-X with 7.083 for GARCH-X amounts to ranking measurement units.

Another claim lacks a test. The paper says gold's distribution during runs "becomes more skewed and leptokurtic." Yet the bank-run variable enters neither the skewness equation nor the kurtosis equation in equation 2.

Gold volatility gains reach only the 10% level

The authors are explicit about returns: "As for returns, we do not find significant test results." Across all five models, return RMSE ranges from 11.454 to 11.686.

The volatility improvement is genuine, though thin. GJRSK-X achieves RMSE of 279.731, versus 295.998 for GJR-X and 313.349 for the linear regression. Significance reaches only 10%. By MAE, the models effectively tie: GARCHSK-X scores 125.313 and GJRSK-X scores 125.392. The authors describe that margin as small.

The significance marks also need explanation. A single star appears beside the lowest RMSE, 279.731. For MAE, the minimum of 125.313 receives a single star, while the runner-up at 125.392 receives a double star despite being 0.079 higher. The note does not account for this placement. It also calls these out-of-sample results "in-sample".

Higher returns during bank runs are the paper's first prediction. Its return forecasts deliver no significant out-of-sample improvement, with RMSE ranging from 11.454 to 11.686 across five models.

Spending GARCHSK-X's 0.141 Sharpe ratio

The complete Sharpe column is:

These figures assume a real risk-free rate of 0.5%. We found neither a rule for converting forecasts into positions nor transaction costs. GJRSK-X, the volatility winner, earns almost nothing. The economic and statistical rankings disagree.

After the burn-in, about 229 annual forecasts remain. Interpreting 0.141 as a per-year Sharpe gives a t of about 2.1. The strategy takes one decision at year-end each year for about 229 years.

Two results would make this investable. First, re-estimate the same four models without the covariate and report them alongside the existing estimates. Second, begin a run in 1800, the starting date the paper assigns to the Jamilov dataset. The source of its 1696-1799 bank-run values remains unexplained. A no-run GJRSK-X with volatility RMSE well above 279.731 would make us take the bank-run channel seriously. Pending that comparison, the usable result remains narrower: time-varying higher moments improve the modeling of annual gold volatility.