Skewness in gold and silver

by Bron Suchecki, Perth Mint hat tip/

Blogger John Koning recently posted on the negative skewness (or as he says: bulls walk up the stairs, bears jump out the window) of the stock market. He notes that “there are plenty of famous meltdowns in stocks, including 1914, 1929, 1987, and 2008, but almost no famous melt ups”. To demonstrate this, he produces a chart of 22,013 trading days since 1928 grouped by the daily return and showing the percentage of days that were negative.

The chart below replicates Koning’s figures but I have also included gold and silver London Fixes since 1968 for comparison, which is the longest data set I have.


In a rising market we should see percentages below 50 reflecting more up than down days. For the S&P Koning notes that 51.9% of daily changes over 2% were negative, that is, “there are more extreme negative results than extreme positive results”. He lists some of the academic theories to explain this but the only one the could apply to precious metals is volatility feedback:

“When important news arrives, this signals that market volatility has increased. If the news is good, investor jubilation will be partially offset by an increase in wariness over volatility, the final change in share price being smaller than it would otherwise have been. When the news is bad, disappointment will be reinforced by this wariness, amplifying the decline.”

It is interesting that gold doesn’t exhibit negative skewness like the S&P but silver demonstrates an unusual skew negative on small returns but no so much for the extremes, a case of bears walking down stairs.

However, because the groups in Koning’s chart compress the data quite and bit and there wasn’t a globally free market in gold until 1975, I think it is better to look at a time period starting from the 1976 bottom (after the excitement of gold becoming legal again had washed out). To get a better handle on the skewness, I have broken up the daily returns into 0.25% increments, and the chart below shows the distribution for gold.


Note that gold has a long tail with a lot of concentration in the sub 1% returns. Converting that data into Koning’s “percentage which are negative” results in the chart below.


Generally this shows little skewing, keeping in mind that the larger percentages for the groups over 3% are based on a very small number of days (less than 30) so a difference of a few days can result in large percentage variances. For silver, below, the distribution is a lot more fatter.


This reflect silver’s higher volatility and while not a statistically normal distribution it doesn’t to my eye show excessive tail skewness. When plotted as percentage negative we again see the skew negative on the small returns but with some big positive skews for daily returns above 2.5%.


Looking at these results I don’t think they support the volatility feedback theory. The best explanation I can come up with is that gold and silver react strongly to positive news (ie everyone is pretty clear what is bad economic news and good for gold and silver), hence we see more 55-60% skew to positive large daily returns. However, in general prices grind down as people slowly get out of the fear trade, due to everyone having a different assessment of when the bad news/event that triggers the price spike is no longer a risk.

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