Wednesday, 19 July 2017

Review of gold price volatility: 1973 till 2017

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 bullion ETF’s...

All of this is a mixture of facts and myths, causes and consequences, hidden motives and secrecy, disinformation, 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 17:00 pm Eastern time (22:00 in London).

Volatility is defined as the standard deviation on a series of daily fluctuations. If prices were stable or if they rose or declined at a steady pace, volatility would fall to zero.  The total series 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 of daily percentage variations of the gold price D/D-1 (%)

Fig 1:  Bars are 0.5% wide; the central bar with gold price variations between -0.25% and +0.25% accounts
for more than a quarter of all observations.

'MOMENTS' of the Distribution (Univariate Procedure)
Distribution analysis of: D/D-1 (%)


Moments
N
11165
Sum Weights
11165
Mean
0.00034714
Sum Observations
3.87586965
Std Deviation
0.01308285
Variance
0.00017116
Skewness
0.4168864
Kurtosis
11.001672
Uncorrected SS
1.91218769
Corrected SS
1.9108422
Coeff Variation
3768.7043
Std Error Mean
0.00012381

What do those data mean? N is the number of trading days (11165), 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 $1219.1 on 12 July 2017 from the $65.10 on 2 Jan 1973 only is 0.026246% every trading day. Some high school algebra is enough to understand that the observed mean (0.0347%) must be higher than that value.
The standard deviation of 1.308% is the main measure of day-to-day volatility. It is equivalent to an annualized volatility of 20.79%.

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 11 implies that the distribution is not Gaussian.  A distribution with high kurtosis (or 'peakedness') 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. Most visually striking is the dominantly frequent number of tiny fluctuations:  those smaller than +0.25% (the central bar) amount to over 25% of the total number of trading days.



'Goodness-of-fit'


In the above graph, the equivalent (closest fitting) Gaussian distribution is drawn along with the frequency bars. I've visually rejected the normal distribution and commented on the distribution 'moments'. Following ‘goodness-of-fit’ tests reject the normal (Gaussian) distribution with only a tiny false rejection probability: below 1% for the less sensitive Kolmogorov-Smirnov test and below 0.5% for both the Cramer-von Mises and Anderson-Darling tests.


Goodness-of-Fit Tests for Normal Distribution
Test
Statistic
p Value
Kolmogorov-Smirnov
D
0.088887
Pr > D
<0.010
Cramer-von Mises
W-Sq
41.768758
Pr > W-Sq
<0.005
Anderson-Darling
A-Sq
236.932033
Pr > A-Sq
<0.005


The last test heavily weighs any error occurring in the tail ends, where the Gaussian distribution quickly fades to zero. With the calculated standard deviation at 1.31%,  the Gaussian distribution allows no more than 1 observation on 1000 outside the interval [-4.31%,+4.31%].  The more elevated number of such rallies and swoons invalidates the Gaussian distribution. This brings us to following item:

Extreme swoons and rallies 


Following tables gives an overview of the 25 biggest swoons and the 25 largest rallies of the gold price since 1973 and additionally of the 20 largest swoons and rallies since the turn of the century. (Note that some extreme swoons and rallies are off chart on the above frequency distribution graph; nevertheless they have been taken into account for all calculations!)


Table 2 and 3: Extreme swoons and rallies since the start of observations in Jan 1973

Date POG D/D-1 (%) Date POG D/D-1 (%)
22/01/1980 737.5 -13.24% 03/01/1980 634 13.32%
28/02/1983 408.5 -12.10% 03/11/1976 125.85 11.87%
15/04/2013 1416 -8.53% 16/01/1980 760 11.11%
02/11/1976 112.5 -8.24% 03/09/1982 454.75 10.98%
20/03/2008 913.5 -8.21% 18/01/1980 830 10.67%
17/03/1980 484 -7.46% 28/11/1973 101.5 10.33%
26/03/1980 507.5 -7.26% 7/02/2000 316.6 10.12%
04/01/1980 588 -7.26% 18/09/2008 864.25 10.03%
25/08/2011 1716.5 -7.22% 21/02/1980 665 9.74%
14/11/1973 90 -7.12% 16/08/1973 103 9.57%
20/02/1980 606 -7.09% 19/03/1980 527 9.45%
25/01/1980 668 -6.83% 02/01/1980 559.5 9.28%
26/09/2011 1615 -6.65% 22/02/1973 86.5 9.08%
28/02/1974 162.5 -6.61% 08/04/1980 528 8.70%
28/01/1980 624 -6.59% 20/08/1982 386.5 8.37%
28/09/1981 421.5 -6.44% 28/12/1979 512 8.22%
21/03/1980 525 -6.42% 29/01/1980 674.25 8.05%
11/12/1980 558 -6.38% 07/01/1980 633.5 7.74%
14/08/1973 95.5 -6.37% 24/11/2008 816.75 7.68%
12/08/2008 808.75 -6.37% 15/05/1973 110 7.58%
01/06/1983 410 -6.29% 10/10/1979 413 7.05%
01/11/1978 227.5 -6.22% 25/04/1980 551.5 6.94%
02/01/1975 175 -6.17% 28/09/1999 301.5 6.91%
15/04/1980 497.5 -6.09% 18/09/1979 375.75 6.82%
14/03/1980 523 -6.02% 26/03/1973 90 6.51%


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 couple of tables:


Table 4 and 5: Twenty extreme swoons and rallies in the 21st century

Date POG D/D-1 (%) Date POG D/D-1 (%)
15/04/2013 1416 -8.53% 7/02/2000 316.6 10.12%
20/03/2008 913.5 -8.21% 18/09/2008 864.25 10.03%
25/08/2011 1716.5 -7.22% 24/11/2008 816.75 7.68%
26/09/2011 1615 -6.65% 21/05/2001 288.35 5.97%
12/08/2008 808.75 -6.37% 7/10/2008 881.75 5.41%
15/08/2008 784.75 -5.82% 29/12/2008 881 5.29%
13/10/2008 865 -5.77% 6/06/2012 1633.25 5.20%
31/10/2008 728.5 -5.67% 19/09/2013 1363.5 4.90%
22/05/2006 645.5 -5.35% 17/05/2006 713 4.70%
7/12/2009 1147.5 -4.63% 30/01/2009 918.5 4.55%
24/10/2008 692.5 -4.61% 11/12/2008 821 4.49%
20/06/2013 1303.25 -4.59% 22/09/2008 873 4.24%
5/02/2010 1052.25 -4.56% 26/08/2011 1787 4.11%
15/05/2006 693 -4.51% 27/10/2008 720.5 4.04%
18/04/2008 908.75 -4.49% 24/06/2016 1314.675 4.01%
26/06/2013 1229 -4.36% 26/01/2009 906.5 3.84%
5/10/2011 1600 -4.31% 11/02/2016 1232.125 3.83%
1/04/2008 897 -4.29% 19/08/2011 1862 3.76%
8/02/2000 303.15 -4.25% 10/05/2006 704.3 3.61%
23/10/2008 726 -4.16% 8/10/2008 913 3.54%

After singling out the 21st century observations, we witness that, although the three largest single day rallies were more vigorous than their counterparts among swoons were severe, this doesn't count for the continuation of the list. In the 21st century swoons with the same 'ranking' were generally more severe than rallies were vigorous.  Moreover many 'high ranking' swoons have been relatively recent.


The 2011-2015 bear market left its footprint

The April 15, 2013 beating still stands as the worst of the century so far. 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.


Onset and break-down of the secular gold rally

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.

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 swoon and rally sides. This made volatility rise to a level unprecedented in the 21st century.

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 followed 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.

Key Gold Price levels and Dates

Apart from major rallies and swoons, monitoring key gold price levels and related dates also is interesting. As this would take us too far outside the framework of this article on volatility, I have summarized that information in a separate document; click here to read.

I should apologize all key price levels are in USD. Since we go back to 1980, the euro is not a valid alternative. The USD has been trending down against the Swiss Franc over the long run as it also was weakening against the hard currencies (Deutsche Mark, Austrian Schilling, Dutch Guilder) which merged into the euro and against the Japanese Yen. Over the long haul, the green back strengthened relative to all other world currencies.

Evidently as exchange rates have been fluctuating, key gold price levels in other currencies were attained at different dates. Even the Aug 2011 all time high in USD may not be the all time high in other currencies.

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 2: Gold price (USD/Oz): the blue graph on the left axis; Volatility of the gold price: the red graph  on the right axis
(click any of the graphs to view true size)
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 volatility culminates in autumn 2008 with a series of gold price swoons alternating with rallies. 

The second graph starts in Jan 2008 and covers the final gold bull run till 2011 followed by the three years of the four year bear market.


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 running to new year 2015
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 2009-2011 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 and completeness, a last gold price and volatility graph since June 2012. It includes ample detail on the more recent cyclical gold bear market, extending to December 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 got rooted.

The 2016 gold recovery brought 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 2016 gold recovery only has entailed a modest and temporary rise of volatility: once at its onset in winter 2016 and a second time at its culmination and break-down in summer 2016.

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
(click any of the graphs to view true size)

As the following severe correction brought the yellow metal back below $1130 before any turn-around, volatility rose moderately. Since February 2017 the yellow metal keeps meandering between a hard to break $1300 resistance level and a relatively firm support at $1200. As a result, volatility is fading.


Back to the epic days of the 20th century

A historic overview of volatility during the 1973-1980 gold bull market and its aftermath during the remainder of the 1980's has been discussed before. Click the link in the paragraph title to view the article. The 20th century gold bull is discussed in the last chapter.

1 comment:

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