Gold volatility

Summarizing the class discussion.

Exploratory analysis suggested that monthly returns on gold have been in at least two different stages in the last 30 years.

Conceptually you could imagine a spreadsheet with two columns, the first with Pre 1980 monthly returns, and the second with Post 80 returns. Both sets of returns have approximate normal distributions with similar means but very different variances.

Our first analysis was akin to ignoring the fact that there should have been two columns, and treating the gold returns as a single column, in other words ignoring the two volatility regimes. The fact is that if you mix up two normal distributions with the same means but different variances then you get a new distribution which has heavy tails compared to the normal. The normal quantile plot picked up this heavy tailed distribution.

Hindsight is 20-20, but you can use this example in the following way: say someone comes to you with a single column of data. If the normal quantile plot comes out as heavy tailed, then you have reason to consider if this single column should really be broken out into two. There's no guarantee that breaking into two is the RIGHT thing to do, but it is certainly a sensible idea to think about.

In the gold example there's a reasonably intuitive breakout variable; Pre 1980 vs Post 1980. In a new situation it could be much harder to identify a breakout variable, but if you can then you have arrived at a valuable insight to the data, one that's been motivated by something as simple as looking at a normal quantile plot.


Richard Waterman. 09/10/97.