Which strategies work in the silver and gold markets?


In the fourth part of the article, we show which strategy achieved a better return than a classic “buy and hold” approach. While the third article dealt with moving-average based strategies, the fourth part examines strategies based on momentum and valuation. It shows that the stationarity of the gold-silver ratio (GSR) cannot be proven in the period under consideration and therefore the foundations for valuation-based investment strategies are lacking. In other words, the GSR is not very suitable for investment decisions in the period under consideration. In contrast, very simple momentum-based strategies seem to work well. So when should one be invested in gold or silver? We venture the following answer: When the 12-month momentum is positive.


Statistical properties of the GSR ratio are crucial

We start by examining the properties of the GSR a little more closely. Only if the GSR has certain statistical properties does it make sense to use it for investment decisions. In doing so, we want to spare the reader technical details. Interested, econometrically savvy experts will find the information in the appendix.


The GSR is decomposed into a deterministic and random part

Every time series can theoretically be broken down into a deterministic and a random part. In order for time series to be forecast, it is important that the random part is not a summation of completely unpredictable shocks. If the latter were the case, there would be no adjustment tendency towards equilibrium in the case of jumps in the time series upwards or downwards, the random shocks would be permanent and add up. Then it is not possible to forecast where the time series will go, even in the long term. If a time series is stationary, it tends to return to its equilibrium. If there is then a deviation, one can use this deviation to make forecasts.


An equally weighted GSR cannot be found

We have tested the GSR to see if it is stationary. The experts can find the test results in the appendix. The result is sobering: Unfortunately, it cannot be proven that the GSC is stationary in the period under consideration. Thus, no equally weighted, fair GSR can be calculated. This means that systematically profitable investment strategies based on the GSR are also “theoretically impossible”. Of course, one could find randomly profitable strategies if one “tortured” the data enough. In real life, however, the patterns found in the past would in all likelihood break down, there would be a risk of systematically losing money.

Preliminary conclusion: the level of the GSC does not seem to be suitable for investment decisions


Momentum strategies often work surprisingly well

The financial literature is full of studies showing that so-called momentum strategies “work” for equities, currencies, but also commodities, i.e. that on average they can achieve risk-adjusted outperformance in the medium term.


Winners of the last 12 months often win the next month as well

In many studies, for example, all stocks are sorted according to the past 12-month return. Then it is calculated what return and what risk (standard deviation of returns) would have been achieved if an investor had always invested in the 20% best (20% second best, etc.) stocks. The simple strategy of investing in the best performing stocks often works amazingly well. Could this also work for gold and silver?


Investment strategy 1: Buy silver or gold, depending on which metal performed best

In the first strategy, investments are made in gold (silver) if the return in the last 12 months was better than that of silver (gold). So you are always invested either in silver or in gold, depending on which performed better.

As chart 1 shows, this strategy would have worked. However, it would not have been significantly better than simply always being invested in silver over the entire period. If one adds the transaction costs, investment strategy 1 is uninteresting, which is why we do not discuss it further.


Chart 1: Silver, gold price and momemtum strategies


Investment strategy 2: Buy if 12-month return was positive, otherwise buy nothing

In investment strategy 2, 50% of the funds are invested in gold if the price of gold has risen in the last 12 months. Likewise, 50% of the funds are invested in silver if the price of silver has risen in the last 12 months. If neither gold nor silver has risen, we assume for simplicity that the money was held without interest.


Chart 2 compares the performance of gold and investment strategy 2 on a logarithmic scale indexed to 100 in May 1955

As chart 2 shows, this strategy would have been quite successful, beating both the buy and hold strategy on silver and the buy and hold strategy on gold.

Only now is it worth taking a closer look.

We use the gold price as a reference because we want to set the bar as high as possible. It turns out (compare Table 1) that investment strategy 2 has desirable characteristics:

  1. A significant outperformance was achieved.
  2. The slumps are much smaller than with the “buy & hold” gold strategy, especially at the beginning of the 1980s.
  3. The annualised volatility of 17.9% is significantly lower than that of gold.
  4. The returns of strategy 2 show significantly less negative “skewness” than the return of gold.


Table 1: Investment strategy 2 and gold in comparison

Conclusion 1: For “absolute return” investors, strategy 2 is thus clearly better in the medium term than simply holding gold.


Table 2: Investment strategy 2 active returns versus gold


Table 2 shows some key figures of the active return, i.e. the returns of strategy 2 relative to the development of the gold price. It turns out that the relative returns have a high standard deviation of 17%, which is not surprising since we occasionally invest in the much more volatile silver, are not invested at all for some years and measure ourselves against gold as a “benchmark”. After all, the returns have a high positive skewness. This means that the strategy has some clear positive outliers (exceptionally higher returns than the gold price) and fewer negative outliers (exceptionally lower returns than the gold price). A histogram of monthly active returns for the interested reader can be found in Appendix 3.

Look again at chart 2. You will see that compared to a pure buy & hold strategy in gold, the strategy would have greatly cushioned the big falls, especially the dramatic fall at the beginning of the 1980s.

Conclusion: Compared to the buy & hold strategy, in the past it made more sense in the medium term to buy gold and silver only if they have already risen in the last 12 months. It is likely that this rule will also work in the medium term in the future.


Thomas Härter
Chief Investment Officer Aquila



Teil 1

Teil 2

Teil 3


Further information on the subject

Appendix 1: ADF test: Hypothesis that the GSR is not stationary cannot be rejected

Appendix 2: ADF test: hypothesis that the GSR is not trend stationary (linear trend) can be rejected with 5% significance level

If one had been able to reliably estimate the linear trend, one could have calculated an equilibrium GSR. However, we consider this almost impossible, which is why this result is not discussed further here.


Appendix 3: Distribution of monthly active returns of strategy 2 versus gold


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