Tuesday, 7 May 2013

Volatility in the gold market

It’s often heard that gold takes the staircase up, but the elevator down. A gold rally would then consist in a gradual process of relatively small but consistent daily upward moves. The gold cartel (bullion banks and investment banks, backed by the FED) would not allow gold to rally over 2% daily.

Once ignited, swoons in precious metals are thought to aggravate by forced liquidation of future long positions and the redemption of leveraged products and bullion ETF’s...

All of this is a mixture of facts and myths, causes and consequences, hidden motives and secrecy, misinformation, manipulation and opportunism. While I can do very little about most of those, I will try to clarify some of the facts in order to eliminate a few of the myths.

Volatility

The tool of preference to determine how fast prices fluctuate is called volatility. We need to distinguish between intra-day volatility and longer term volatility. For this second case, we need a long term series of closing or fixing prices. About the only series of daily gold prices publicly available is the London fix, with data going back to the beginning of 2000.

While much shorter than many stock index series, this is largely enough for our purpose. There are two daily fixing prices. On days preceding a holiday, there may be only an AM-fix. In order to maximize the information available for calculation, I’ve chosen the London AM-fix. Observe that there’s nearly a 12 hour delay between the London AM fix and the Comex (NY-Globex) close at 17:15 pm Eastern time (22:15 in London).

Volatility is defined as the standard deviation on a series of daily fluctuations. If prices were stable or the daily rise or decline remained completely constant, volatility would fall to zero.

The total series of daily fluctuations allows some in depth analysis on the distribution of daily fluctuations, including a long term historic volatility. This will allow checking some of the hypotheses put forward in the introduction.

 

Distribution analysis

Table 1:  'Moments' of the distribution

N
3369  
Sum Weights
3369  
Mean
0.056421 %  
Sum Observations
1.90084015 
Std Deviation
1.206049 %  
Variance
0.00014546 
Skewness
-0.0552065  
Kurtosis
7.16371153 
Uncorrected SS
0.49096657  
Corrected SS
0.48989409  
Coeff. Variation
2137.57062  
Std Error Mean
0.00020779  

What do those data mean? N is the number of observations (3369), each of them is equivalent, so the weights also total N. 'Mean' is the average price fluctuation. It’s positive, which corresponds to a long term price appreciation. For your information: the required rate for gold to trend up to the $1476.5 on 3 May 2013 from the $282.05 at the first AM fix on 4 Jan 2000 only is 0.0491% every trading day. Some high school knowledge of algebra is enough to understand that the observed mean (0.0564%) must be higher than that value. The standard deviation of 1.206% is the main measure of volatility.
The negative skewness implies that the distribution has more observations in its left tail (large swoons) than in its right tail (large rallies). The effect is however small: extreme observations do occur on either side: one myth has gone.
In the right column, the excess kurtosis of 7.16 implies that the distribution is not normal bell-shaped. A distribution with high kurtosis has a slender top and initially drops off faster than does the corresponding normal distribution with the same standard deviation. However it has fatter tails. Extreme variations are far more frequent than predicted by the normal Gaussian distribution.

Figure: Frequency of occurrence of daily fluctuations of the gold price. (In fractions: 0.01 corresponds to 1%) The black curve is the best fitting normal distribution. 
Very small variations are more frequent than predicted by a normal distribution. Fluctuations smaller than +0.25% (the central bar) amount to over 20% of the total number of trading days. This is the most striking result of the high excess kurtosis mentioned above. Small advances are more frequent than small declines. The situation reverses further away from the center as larger swoons occur more often than larger rallies. Yet paradoxically, the two single largest moves are two rallies discussed below.

Extreme observations

Following table gives an overview of the 10 largest rallies and the 10 biggest swoons since the turn of the century. Apart from the date, the AM fix of gold is also added for each day. (Dates use the European format: Day/Month/Year.)

 Table 2: Top 10 extreme rallies and swoons in 21st century daily fluctuations of gold
 

Date
Gold price
Rally

Date
Gold price
Swoon
7/02/2000
316.6
10.12%

15/04/2013
1416
-8.53%
18/09/2008
864.25
10.03%

20/03/2008
913.5
-8.21%
24/11/2008
816.75
7.68%

25/08/2011
1716.5
-7.22%
21/05/2001
288.35
5.97%

26/09/2011
1615
-6.65%
7/10/2008
881.75
5.41%

12/08/2008
808.75
-6.37%
29/12/2008
881
5.29%

15/08/2008
784.75
-5.82%
6/06/2012
1633.25
5.20%

13/10/2008
865
-5.77%
17/05/2006
713
4.70%

31/10/2008
728.5
-5.67%
30/01/2009
918.5
4.55%

22/05/2006
645.5
-5.35%
11/12/2008
821
4.49%

7/12/2009
1147.5
-4.63%

First three rallies are even larger than their counterpart among the swoons. It takes us to the fourth observation and downwards to consistently see the swoon more severe than the rally with the same ranking. The 15 April 2013 beating was the worst of the century so far. We find quite a few 2008 observations (both summer and autumn) at both sides. This made volatility rise to an unequalled level over the period immediately preceding and during the culmination of the financial crisis.

The most stunning 10.12% rally in February 2000 followed a report which made clear the detrimental influence of generalized hedging by producers and of gold leasing by central banks on the gold price trend. The rally didn’t however break the back of the gold bear market yet: nearly all of the gains vaporized during the following months. The 18 September 2008 double digit rise was the main ripple effect of the Lehman Brothers bankruptcy declared earlier that week. At that moment the global financial system seemed on the brink. This was before hedge funds were forced to sell whatever they could get a bid on in order to meet margin requirements. Most often that was gold, which contributed to the extended gold swoon we witnessed in autumn 2008. The March 2008 single day swoon follows gold breaking above $1000 for the first time ever. We find two more similar swoons in 2011 as gold came off its double top in August and September 2011.
What makes the 15 April swoon so exceptional is that it isn’t preceded by any significant precious metal rally, on the contrary. Nor did it happen during a stock market crisis as it happened in fall 2008. Instead it was an orchestrated sell-off after several reports giving gold a bad press. Future longs were taken to the woodshed and forced to sell into weakness.

Read also the postings: Sudden swoons are the fate of precious metal prices, The puke moment for precious metals and miners and Honestly, you don't want to know...
 

Monitoring volatility

Monitoring volatility requires a moving series of daily fluctuations on which the standard deviation is calculated. We use a 21 trading day period for this, which generally corresponds to one month’s data. The volatility measure was annualised.

In order for the graphs to show better detail, the period covered was split. The first graph covers the decade 2000-2009, with the onset of the secular gold bull market and ending with the 2008 breakdown during the financial crisis and the onset of the recovery:

Fig 1: Gold price (USD/Oz): the blue graph on the left axis; Volatility of the gold price: the red graph on the right axis.
You may situate the dates of extreme gold rallies and swoons on this very long scale. Only the February 2000 volatility spike was the result of a sudden 10% gold rally as the report on the consequences of gold miner hedging and gold leasing by central banks was disclosed in congress.

The second graph starts in 2008 and covers the final gold bull run till 2011 followed by the three year bear market until new year 2015.

Fig 2: Gold price (USD/Oz): the blue graph on the left axis; Volatility of the gold price: the red graph on the right axis. - Graph updated on Jan 05, 2015

The volatility culminates in autumn 2008 with a series of gold price swoons alternated with rallies. Despite the largest swoon on April 15 of 2013, volatility stays considerably below the level reached in autumn 2008. Back then, volatility surged, reaching multiple tops as the gold price behaved erratically during the financial crisis, with a succession of few manic rallies and more frequent major swoons. Volatility spikes have nearly always coincided with a severe correction or downtrend for gold. During the 2009-11 gold rally whereby the price more than doubled, volatility remained fairly low and even then any temporary rise was due to a short correction of the gold price. The autumn 2011 volatility peak marks the breakdown of the gold price after its early September all time high. For the sake of clarity, a last updated gold price and volatitliy graph since June 2012, with ample detail on the more recent cyclical gold bear market, extending into 2015. Volatility peaks now are lower than during the 2013 smash down. This does not imply gold strengthening as gold corrections have become more frequent, tearing apart any nascent gold rally before it gets rooted.


Fig 3: Gold price (USD/Oz): the blue graph on the left axis; Volatility of the gold price: the red graph on the right axis. - Graph updated on Jun 22, 2015

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