A Commodity Price Volatility Calculation

On Megan McArdle Trolls the Gold Standard, an Anonymous reader questioned my claim:

The price of gold/silver is stable. The price of oil/gold is stable. If you look at the price of one commodity relative to another, the prices are usually stable. The price of commodities, quoted in dollars, is unstable.

In this post, I illustrate the calculation that backs up my claim. I had not performed it when I made that post, but I intuitively guessed the result. The disparity is not as extreme as I predicted, but the price of gold/silver REALLY IS more stable than the price of gold/$ or silver/$.

I use the GLD ETF as my historic price of gold and the SLV ETF as my historic price of silver. These aren't exactly accurate, but they're the best resource available. I don't know how good those ETFs are at tracking the actual gold or silver price. I downloaded the historic daily ETF closing prices into a .csv file and then into Excel.

I now performed a historic volatility calculation. If P_i and P_(i+1) are two adjacent daily stock prices, then let Y_i = ln(P_i / P_(i+1)). I then calculate the standard deviation of Y_i, which is sqrt(E(Y^2) - E(Y)^2)). This is the historic daily volatility. I used daily price points, so I must convert to an annual volatility. I multiply by sqrt(252), because there are 252 trading days in a year. The justification for multiplying by sqrt(252) is the "Central Limit Theorem".

Do I need to give further details for "how to perform a historic volatility calculation"? It's just the standard deviation of ln(P_i / P_(i+1)), converted to an annual scale. I take the logarithm because, when investing, you only care about the % gain or loss and not the absolute $ gain or loss.

For GLD, I calculated that the 1 year historic volatility was 17.7%. In 1 year, a "1 standard deviation" increase or decrease in the gold price is 17.7%. Professional traders always quote volatility as a %. Professional traders always quote the "1 year standard deviation" movement, which is the reason I multiplied by sqrt(252).

For SLV, I calculated that the 1 year historic volatility was 26.1%.

Then, I looked at GLD/SLV. This is the price of gold divided by the price of silver. This should remove the effect of dollar volatility from the price. The 1 year historic volatility of GLD/SLV was 13.8%. (The fact that I was using the ETF instead of the physical price is irrelevant at this step, assuming the ETF closely tracks the physical price.)

For comparison, the VIX is the CBOE's S&P 500 volatility index. The VIX is calculated from the prices of S&P 500 index options. The current value of the VIX is 22.5%. Its 52 week range was 9.7%-37.5%.

I found the conclusions to be surprising.

The volatility of silver is A LOT HIGHER than the volatility of gold. I expected them to be nearly equal. There are two possible explanations. One conclusion is that someone is manipulating the gold price, dampening the volatility. Another explanation is that silver has much greater industrial demand than gold. This would cause the price of silver to have greater volatility than gold, because more silver is consumed by industrial processes than gold. I'm more inclined to believe the "someone is manipulating gold" explanation.

The price of gold/silver was only half as volatile as the price of silver/$, and 22% less volatile than the price of gold/$. My original claim is verified, but not to the degree I originally expected.

The most surprising conclusion I draw from this calculation is "Someone *MUST* be manipulating the gold price. There's no other reason for the volatility of gold/$ to be so much lower than the volatility of silver/$." If someone were manipulating gold by selling whenever the price rose, that would show up as decreased volatility.

I could repeat the calculation for oil/gold, oil/silver, or other commodities. I'll only do that if someone asks.

Let me know if you don't understand my calculation and want to see more details. Does Blogger support including an HTML table so I can illustrate my calculation?