Cycle shapes

While it was recognized that with CW and CCW two main motions exist in the way cy-cles progress (cf. section 7.1.6), different pat-terns can be distinguished therein. As we can see in figure 7.7, those patterns can be cate-gorized as I - circles, II - arches, III - loops, and IV - ramparts. The patterns are present in both, clockwise and counterclockwise motions and will be discussed now.

Figure 7.7: Major observed cycle types

I - Circles

The circle pattern seen in figure 7.7 is an exam-ple of how an ideal commodity cycle unfolds. A good example for a clockwise cycle is uranium between February 2001 and November 2016 (cf.

cycle V in figure 7.6). In figure 7.8 we can see that the cycle starts in February 2001 with the uranium market at the trough of the cycle. Its prices are bottoming out and overall returns are negative (cf. table 7.3). Prices then slowly in-crease from its low of 16,292 USD/t with their volatility decreasing further.

Figure 7.8: A CW circle - Uranium 2001-2016 Hope is spreading and the cycle crosses into sustained positive return area by May 2003. Af-ter a long period of low volatility but steadily improving returns, the market finds its peak in June 2007. The prices are at their maximum at 300,314 USD/t. The boom times last for another couple of months but the contraction of the market has already set in. By December 2011 pessimism spreads and the market enters into negative return area, but the worst is still to come when prices reach 40,785 USD/t at the end of the cycle in November 2016.

Risk Return Price

Date % % USD/t

Feb-2001 4.18 -1.17 16,292 May-2003 3.64 0.09 24,030 Jun-2007 5.16 4.59 300,314 Dec-2011 8.94 0.16 115,037 Nov-2016 5.03 -1.62 40,786 Table 7.3: Statistics of a clockwise U cycle

II - Arches

Arches as seen in figure 7.7, closely resemble those of circles. However, these cycles are sub-stantially different with respect to the location of the starting and ending point of the cycle.

For a clockwise cycle the associated risk of the end point is higher than it is at the starting point. The reverse is true for the counterclock-wise cycle.

A good example for a clockwise cycle can be observed for zinc between August 2002 and De-cember 2011 in figure 7.9. The cycle starts with prices at 747.60 USD/t and negative returns (cf. table 7.4).

Figure 7.9: A CW arch - Zinc 2002-2011 As the cycle progresses, it enters into sus-tained positive return area more than two years later in November 2004, with prices sitting at 1095.64 USD/t. The cycle is now entering its boom phase with prices and price volatility in-creasing together. In December 2006 the cycle top is reached that coincides with a price max-imum of 4405.40 USD/t - almost six times the price of the previous cycle bottom. As time progresses, the volatility of the returns increase further while the returns themselves start to fall. The cycle started to contract now and en-tered negative growth domain in April 2011.

Prices sit now at 2362.22 USD/t, roughly half of what they were at the peak. The contraction continues with the cycle ending at its bottom in December 2011 with prices sitting at 1904.73 USD/t. Table 7.4: Statistics of a CW zinc arch An example for a counterclockwise arch can also be given for zinc. Starting at the end of the previous clockwise arch, returns are still negative but increase while the volatility also decreases (cf. figure 7.10 and table 7.5). In May 2013 the cycle enters sustained positive return area and the boom peaks in February 2014. After this, returns fall again with volatil-ity still diminishing. In January 2016 the cycle finally ends in a new trough with prices sitting at 1507.05 USD/t.

Figure 7.10: A CCW arch - Zinc 2011-2016 The entire cycle lasted 50 months with a maximum monthly return of 1.22% at its peak.

This contrasts strongly with the clockwise arch for zinc described earlier where the cycle lasts 113 months and a maximum return of 3.18%.

Risk Return Price Table 7.5: Statistics of a zinc CCW arch

III - Loops

While an arch is essentially a circle with its end members (i.e. cycle start and end) spread apart, a loop represents the contrary, its end members are crossing each other. When a CW motion prevails, the end point therefore will ex-hibit less volatility than at its starting point.

Subsequently, the opposite holds for the CCW motion.

A good clockwise motion example is the MVT ore type between 1962 and 1969. When look-ing at figure 7.11 we can observe that the cycle starts at its nadir in January 1962. The cy-cle slowly moves within its third quadrant Qiii

while its returns become ever less negative and volatile (cf. table 7.6). Along the way prices find their cycle minimum in August 1962 with 14.15 USD/tore. In December 1962 returns fi-nally turn positive and a short year later in De-cember 1963 it sees its lowest volatility (σ = 2.56%). From then on volatility starts to in-crease again, along with the returns. In July 1964 the cycle peak is reached with an average

return of 0.9%.

Figure 7.11: A CW loop - MVT.TRI 1962-1969 This is also when the ore value is with 29.98 USD/tore at its highest during the cycle, more than double the value of the minimum just two years earlier. After peaking, prices and returns start to fall, while volatilities keep increasing.

They finally find their peak in November 1965 with a σ of 3.85%. From now on, prices, returns and volatility keep falling and prices bottom out in March 1968 at 21.02 USD/tore. The cycle finds its end in July 1969 after dipping into neg-ative growth territory only three months ear-lier. By then its Rmin sits at -0.33% with a Table 7.6: Statistics of a CW loop - MVT.TRI

IV - Ramparts

ramparts are special arches that appear only during the lead up and aftermath of the sec-ond world war. They exist for CCW and CW motions, with the former usually followed by the latter. The key difference of these pat-terns compared to those described earlier, is that they either do not finish their cycle in neg-ative return area (CCW) or do not start within

it (CW). This would disqualify them to be con-sidered in this analysis according to the guide-lines discussed on page 49. However, it was decided that such cycles were included never-theless, with their lowest returns assigned as ei-ther the end point (CCW) or the starting point (CW) for their respective cycle. The reason for this decision is the understanding that these ab-normalities are caused by the temporary freeze of prices during the second world war⁴. This freeze resulted in a drop of returns and volatil-ities in prices while not allowing the returns to go negative. When price freezes were finally lifted, the returns as well as volatilities started to increase once again until the next cycle peak was reached. The price freeze during the war can therefore be considered to be a pause but-ton on metal market economics.

An example for a counterclockwise cycle is that for the Kidd Creek ore type (VMS.KID) be-tween 1936 and 1946. As can be seen in fig-ure 7.12, the first cycle starts in July 1932 at a return minimum of -1.22%.

Figure 7.12: A CCW rampart - VMS.KID 1932-1946

From this low point where with 5.07 USD/tore prices are also at their lowest, the CCW cycle gradually improves and volatilities increase (cf. table 7.7). They reach their maxi-mum with 5.61% in October 1933. In June 1935 the cycle enters sustained positive growth but volatilities fall already. In March 1937 maxi-mum prices are reached with 13.42 USD/tore. Shortly after, in July 1937, the cycle maximum is reached. From now on volatilities and re-turns decrease until the cycle end is reached in March 1946 (see also normalized cycle chart in figure 7.5). At this point, average returns sit

4In fact the price freeze allowed the allied war effort to be planned better and gave the industry an incentive to produce set metal quotas at acceptable profit margins. By this action, price spikes as in WWI were avoided and metal producers could not be accused of price profiteering during WWII, as they did during WWI.

at 0.17% with a σ of 0.79%.

Risk Return Price

Date % % USD/t

Jul-1932 3.76 -1.22 5.07 Jun-1935 4.99 0.03 8.6 Jul-1937 4.85 1.6 12.36 Mar-1946 0.79 0.17 13.3 Table 7.7: Statistics of a VMS.KID CCW ram-part

The subsequent clockwise cycle starts where the previous left off (cf. fig. 7.13), with returns and volatilities increasing as time progresses (cf. table 7.8).

Figure 7.13: A CW rampart - VMS.KID 1946-1954

The next cycle peak is at hand in August 1951 with an Rmax of 1.56%. This is also the time when prices peak at 33.12 USD/tore, a fourfold increase over the last Pmin of 8.21 USD/tore in June 1938. Very shortly after this peak, the cycle loses steam and returns fall un-til they become negative in August 1953. Five months later the cycle ends with a return of -0.38% and a σ of 5.30%. It is also the time when the prices find their new low with Pmin=18.90 USD/tore.

Risk Return Price

Date % % USD/t

Mar-1946 0.79 0.17 13.30 Aug-1951 5.32 1.56 33.12 Aug-1953 5.35 -0.20 18.99 Jan-1954 5.30 -0.38 18.90 Table 7.8: Statistics of a VMS.KID CW ram-part

Summary & Discussion

As we have seen, four main cycle styles can be described that are relevant for both CW and CCW motions. While these styles are prevail-ing in the data set in various forms, from tiny to squished, to various forms of distortions, there is a small fraction (≈ 5%) that was hard to as-sign any type of style to. This however was not considered to be of a great concern for the out-come of this study, since no matter what style, it was more important to understand what mo-tion prevailed in the considered cycles. This was always possible since styles and types of motions were determined to be independent features of the data set.