Friday, 26 June 2015

Review of gold price volatility

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. A publicly available series of daily gold prices is the London fix, with data going back to the beginning of 2000. Here 20th century data are included going back to January 1973.

This is comparable to many stock index series and largely enough for our purpose. For the 21st century data the average of the two LBMA daily fixing prices is made. On days preceding a holiday, there may be only an 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

Moments
N
10643  
Sum Weights
10643 
Mean
0.000361  
Sum Observations
3.840 
Std Deviation
0.01330  
Variance
0.000177 
Skewness
0.40308  
Kurtosis
10.747 
Uncorrected SS
1.885  
Corrected SS
1.884 
Coeff Variation
3687.53  
Std Error Mean
0.000129 

What do those data mean? N is the number of observations (10643), 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 $1189.6 on 22 Jun 2015 from the $65.10 on 2 Jan 1973 only is 0.0273% every trading day. Some high school knowledge of algebra is enough to understand that the observed mean (0.0361%) must be higher than that value. 
The standard deviation of 1.330% is the main measure of day-to-day volatility. It is equivalent to an annualized volatility of 21.11%.
The slightly positive skewness implies that the distribution has more observations in its right tail (large rallies) than in its left tail (large swoons). The effect is small: extreme observations do occur on either side: one myth has gone.
In the right column, the excess kurtosis of 10.747 implies that the distribution is not Gaussian.  A distribution with high kurtosis has a slender top and initially drops off faster than does the corresponding Gaussian or 'normal' distribution with the same standard deviation. However it has fatter tails. Extreme variations are far more frequent than predicted by the Gaussian distribution.


Figure: Frequency of occurrence of daily fluctuations of the gold price.  The red curve is the best fitting normal distribution. (click to enlarge)

Very small variations are more frequent than predicted by a normal distribution. Fluctuations smaller than +0.25% (the central bar) amount to over 25% of the total number of trading days. This is the most striking result of the high excess kurtosis mentioned above.

Extreme observations

Following tables gives an overview of the 20 largest rallies and the 20 biggest swoons of the gold price since 1973 and additionally of the 10 largest rallies and swoons since the turn of the century. (Note that the top 2 swoons and top 12 rallies are off chart on the above frequency distribution graph.)

Table 2: Top 20 extreme swoons and rallies of gold since 1973

Date Swoon
Date Rally
1/22/1980 -13.24% 1 1/3/1980 13.32%
2/28/1983 -12.10% 2 11/3/1976 11.87%
4/15/2013 -8.53% 3 1/16/1980 11.11%
11/2/1976 -8.24% 4 9/3/1982 10.98%
3/20/2008 -8.21% 5 1/18/1980 10.67%
3/17/1980 -7.46% 6 11/28/1973 10.33%
3/26/1980 -7.26% 7 2/7/2000 10.12%
1/4/1980 -7.26% 8 9/18/2008 10.03%
8/25/2011 -7.22% 9 2/21/1980 9.74%
11/14/1973 -7.12% 10 8/16/1973 9.57%
2/20/1980 -7.09% 11 3/19/1980 9.45%
1/25/1980 -6.83% 12 1/2/1980 9.28%
9/26/2011 -6.65% 13 2/22/1973 9.08%
2/28/1974 -6.61% 14 4/8/1980 8.70%
1/28/1980 -6.59% 15 8/20/1982 8.37%
9/28/1981 -6.44% 16 12/28/1979 8.22%
3/21/1980 -6.42% 17 1/29/1980 8.05%
12/11/1980 -6.38% 18 1/7/1980 7.74%
8/14/1973 -6.37% 19 11/24/2008 7.68%
8/12/2008 -6.37% 20 5/15/1973 7.58%

Observations dating in the 20th century dominate the list on both sides: gold price volatility has been unprecedented in the 1970's and 1980's. Yet the 1990's apparently has been a dull decade for gold traders. Singling out 21st century observations, we obtain one last table:

Table 3: Top 10 extreme gold swoons and rallies in 21st century

Date Gold Price Swoon
Date Gold Price Rally
04/15/2013 1416.0 -8.53% 1 02/07/2000 316.6 10.12%
03/20/2008 913.5 -8.21% 2 09/18/2008 864.3 10.03%
08/25/2011 1716.5 -7.22% 3 11/24/2008 816.8 7.68%
09/26/2011 1615.0 -6.65% 4 05/21/2001 288.4 5.97%
08/12/2008 808.8 -6.37% 5 10/07/2008 881.8 5.41%
08/15/2008 784.8 -5.82% 6 12/29/2008 881.0 5.29%
10/13/2008 865.0 -5.77% 7 06/06/2012 1633.3 5.20%
03/30/2015 1186.5 -5.76% 8 09/19/2013 1363.5 4.90%
10/31/2008 728.5 -5.67% 9 05/17/2006 713.0 4.70%
05/22/2006 645.5 -5.35% 10 01/30/2009 918.5 4.55%


Apart from the date, the gold price also is added for each day.  First two rallies are larger than their counterpart among the swoons. It takes us to the third observation and downwards to consistently see the swoon more severe than the rally with the same ranking. The April 15, 2013 beating was the worst of the century so far.  We find quite a few 2008 observations (both summer and autumn, over the period immediately preceding and during the culmination of the financial crisis) at both sides. This made volatility rise to a level unequaled in the 21st century .
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 April 15, 2013 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 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 annualized .

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 running to new year 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 gold price and volatility 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 in 2015 gold corrections have become more frequent, tearing apart any nascent gold rally before it gets rooted.

The recent gold recovery we witnessed since Jan 20, 2016 brings gold back into its trading range from June 2013 - June 2015. The yellow metal has been able to curb the latest leg down experienced since summer 2015, when prices dropped below $1200 without any prompt recovery back to that level.  The gold recovery only has entailed a modest rise of volatility.


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 Oct 21, 2016

Back to the epic days of the 20th century

As an illustration and in order to compare the 21st century gyrations of the gold price to those several decades ago, you find below the gold price and its volatility during the 1970's (1970-78) and during the 1980's (1979-1989). The graphs are split at year end 1978 in order to avoid the hectic January 1980 days occurring at the very left of the graph.

Fig 3: Gold price in USD/Oz (monthly observations from Jan 1970 till Dec 1972 and daily from Jan 1973 onward). Annualized volatility in percentage on the right scale. (click to enlarge)
The 1972-1974 gold rally makes volatility rise as does the short cyclical gold bear towards the end of 1976.  If a volatility scale leading limited at 60% is sufficient for the 21st century (and only 45% for the last few gold bear years), we need to extend that volatility scale to 70% on the first 1970's graph. Volatility even spiked to 115% in January 1980 !

Fig 4: Gold price (USD/Oz): the blue graph on the left axis; Volatility of the gold price: the red graph on the right axis. Gold price daily observations from Jan 1979 onward till Jan 1989. Annualized volatility in percentage (click to enlarge)
Volatility dropped during the latter half of the 1980's and was to remain low for most of the next decade.

4 comments:



  1. Thanks for sharing, I will bookmark and be back again


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