ATFX Popular Science: Gold and Silver Price Arbitrage Analysis, Empirical Statistical Data

atfxPopular Science: Gold and silver are both safe-haven currencies, with long-term resonance. In the face of risk events, gold's volatility is smaller than that of silver, but gold can maintain a limited retracement after the risk event subsides, but silver often has a larger-than-expected decline. Due to the different supply and demand fundamentals of gold and silver, the quotation bases of the two are also different. According to the latest data, the price of gold is 1813, and the price of silver is 28. Since the latter base is smaller, the percentage of silver is larger for the same fluctuation.

The core formula of gold-silver price comparison arbitrage analysis is to divide the price of gold by the price of silver, and then observe the running law of the result curve. Due to the similarity of gold and silver in the hedging properties, we expect the price comparison between the two to be within a certain normal range. If for some reason, the gold-silver price comparison deviates from the normal range, it forms an arbitrage opportunity. The basic trading principle is: if the gold-silver price is higher than the normal value, it means that the gold price is too high or the silver price is too low, and the "convergence" strategy of buying silver and selling gold can be adopted at this time; if the gold-silver price is lower than the normal value, it means that the gold price is too low or the silver price is too high, and the "divergence" strategy of selling silver and buying gold can be adopted at this time.

Figure 1, Gold-Silver Comparison Curve - ATFX

The graph above shows the gold and silver price ratio curve. The reference period is from 2011 to early 2021, and the time interval of each data is one year. It can be seen that the maximum value of the gold and silver price ratio is 86.18, which occurred in 2019; the minimum value is 55.23, which occurred in 2012. If the divergent arbitrage strategy is adopted, the holding time is 7 years. The 7-year period is very long for ordinary traders and may not have practical significance. However, a long cycle means greater profits. In 2012, the gold price was $1675, and the silver price was $30; in 2019, the gold price was $1470, and the silver price was $17. The long gold lost 12.23% of the total funds per ounce, and the short silver lost 43.33% of the total profits per ounce. The net profit margin of the two is 31.1%. A total return of 31.1% over 7 years may not seem like much, but it is achieved without any leverage. With 50 times the basic leverage, the total return in 7 years will expand to 1555%, which is very amazing. Moreover, there is a hedging mechanism for carry trades. The decline of gold will be hedged by the rise of silver, and the decline of silver will be hedged by the rise of gold. Even with leverage above 50 times, the net risk is much lower than the risk of trend trading.

Since the curve in the graph is data obtained in annual terms, it can only describe the general trend of the gold-silver price ratio from 2011 to the present. If the time interval of the data points is adjusted to monthly, then the highest gold-silver price ratio and the lowest gold-silver price comparison in history will change to some extent. For example, the highest price ratio in 2019 is 86.18 in the data points in annual terms; but if it is placed in the data points in monthly terms, it will grow to around 100.

Figure 2: Gold and silver prices over the past 30 years - ATFX

Although the monthly data is more accurate than the annual data, it is inferior to the daily data. The daily line is compared to the hourly line, the hourly line to the minute line, and the minute line to each price point. It is the same principle. We cannot force traders to put all the data points into the EXCEL table to plot by themselves, which is too difficult and error-prone. For the convenience of traders, in the chart above we show the trend of gold and silver prices below all price points over the past 30 years. It can be seen that the exact time when the lowest point of the gold-silver ratio was formed was May 1, 2011, not 2012, and its lowest point was 31.78, not 55.23; similarly, the exact time when the highest point was formed was March 27, 2020, not 2019, and its highest point was 119.896, not a rough calculation of 86.18. After more accurate data is obtained, the high and low points are extended, and the arbitrage gains obtained are even greater.

Figure 3, Gold and Silver Prices from 1971 to the Present - ATFX

The chart above shows the comparison curve of all gold and silver prices in history. It can be seen that the normalized ratio range is around 60, which is the part of the red box in the picture. When the ratio curve is above this range and reaches around 100, a convergence arbitrage strategy is formed; when the ratio curve is below this range and reaches around 40, a diffusion arbitrage strategy is formed. Of course, if you are patient enough, you can wait until the high is above 100, or the low is below 40, but such greater arbitrage opportunities are rare.

The above is our basic research on the price of gold and silver, thank you for reading.

ATFX Disclaimer:

1. The above analysis only represents the views of analysts. The foreign exchange market is risky and investment requires caution.

2. ATFX will not be responsible for any profits or losses that may result from the direct or indirect use or reliance on this information.