Trends and shock persistence in precious metal prices

Abstract

How fast, if ever, does the price of precious metals recover from a shock? Considering the industrial importance of precious metals, as well as investors' requirements, measures of shock persistence can provide essential benchmarks. This study investigates the shock persistence in four major precious metal prices (gold, silver, palladium, and platinum) and two equity indices (Nasdaq and DJIA) reflecting technological and industrial development. After accounting for structural breaks, the persistence of a shock in prices can be assessed through the magnitude of autoregressive parameters and expressed in terms of cumulative impulse response (CIR) and half-life of a shock (HLS). We use weekly data from 2003 through 2019, and state-of-the-art methods known to yield unbiased estimates. Our findings suggest a breakpoint in mid-2008 indicating a regime change. Gold prices are found to recover quickly from shocks. Our findings thus contribute to the discussion whether gold is a "safe haven" for investors.

Full text

Motivation
Data
Methodology
Empirical results
Summary and conclusions
Trends and shock persistence
in precious metal prices
ISF 2019, Thessaloniki
Harald Schmidbauer
Shanxi University of Finance and Economics, Taiyuan, China
Angi R¨osch
FOM University of Applied Sciences, Munich, Germany
copyright c
Harald Schmidbauer / Angi R¨osch, 2019
Trends and shock persistence in precious metal prices —Harald Schmidbauer / Angi R¨osch 1 of 19

Motivation
Data
Methodology
Empirical results
Summary and conclusions
Motivation
How do precious metal prices behave?
Suppose you own gold / silver / platinum / palladium.
There is a price shock. What to do?
Wait for the price to stabilize again?
Makes sense if effect of shock is short-lived.
Adapt to the new price level?
Makes sense if effect of shock lasts long.
How long will it take for a price shock to dissipate?
How do precious metal prices compare to other asset prices
in this respect?
Trends and shock persistence in precious metal prices —Harald Schmidbauer / Angi R¨osch 2 of 19

Motivation
Data
Methodology
Empirical results
Summary and conclusions
Four precious metals
gold
usage: jewelry, electronics, medicine, etc.
recent price (2019-06-13): 1335.90 USD per fine troy ounce
Schmidbauer / R¨osch:
The impact of festivities on gold price expectation and volatility.
International Review of Financial Analysis, 2018
silver
usage: jewelry / silverware, electronics, medicine, etc.
recent price (2019-06-13): 14.795 USD per fine troy ounce
platinum
usage: catalysis, jewelry, electronics, medicine, etc.
recent price (2019-06-13): 809.00 USD per fine troy ounce
palladium
usage: catalysis, electronics, hydrogen storage, etc.
recent price (2019-06-13): 1438.00 USD per fine troy ounce
Trends and shock persistence in precious metal prices —Harald Schmidbauer / Angi R¨osch 3 of 19

Motivation
Data
Methodology
Empirical results
Summary and conclusions
Precious metal prices
Other asset prices
Precious metal prices
0
2
4
6
8
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
gold
silver
platinum
palladium
weekly prices from 2003-01-07 to 2019-03-05
prices in USD, normed: 2003-01-07 ≡1
data source: London Bullion Market Association
break in trend (Zivot/Andrews test): 2013-02-05 (gold)
Trends and shock persistence in precious metal prices —Harald Schmidbauer / Angi R¨osch 4 of 19

Motivation
Data
Methodology
Empirical results
Summary and conclusions
Precious metal prices
Other asset prices
Other asset prices
0
2
4
6
8
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
dji
ndx
eurusd
wti
weekly prices from 2003-01-07 to 2019-03-05
prices in USD, normed: 2003-01-07 ≡1
data sources: Yahoo! Finance; ECB; US EIA
breaks in trend (Zivot/Andrews test): 2009-05-13 (dji), 2008-08-05 (ndx)
Trends and shock persistence in precious metal prices —Harald Schmidbauer / Angi R¨osch 5 of 19

Motivation
Data
Methodology
Empirical results
Summary and conclusions
The basic model
Special cases
Persistence of a shock
Simulation examples
Statistical inference
The basic model
Linear trend plus noise:
zt=µ+βt+ut
ut=α1ut−1+· · · +αput−p+t
(The series (zt) is the logarithmic price series.)
(t): white noise
(ut): AR or unit-root process
This model has different variants of nonstationarity.
Trends and shock persistence in precious metal prices —Harald Schmidbauer / Angi R¨osch 6 of 19

Motivation
Data
Methodology
Empirical results
Summary and conclusions
The basic model
Special cases
Persistence of a shock
Simulation examples
Statistical inference
Special cases
Order 1: zt=µ+βt+ut
ut=αut−1+t
Then:
zt=µ?+β?t+αzt−1+t
with µ?=µ(1 −α) + αβ and β?=β(1 −α)
Extreme cases:
α=0: xt=µ+βt+t(trend stationary process)
α=1: yt=β+yt−1+t(difference stationary process)
Trends and shock persistence in precious metal prices —Harald Schmidbauer / Angi R¨osch 7 of 19

Motivation
Data
Methodology
Empirical results
Summary and conclusions
The basic model
Special cases
Persistence of a shock
Simulation examples
Statistical inference
Persistence of a shock
Model:
zt=µ?+β?t+αzt−1+t
(The series (zt) is the logarithmic price series.)
Effect of a one-unit change in ton zt+i:αi(i = 0, 1, . . . )
Half-life of a shock:
HLS = log(1/2)
log(α)
Cumulative impulse response:
CIR = X
i≥0
αi=1
1−α
Trends and shock persistence in precious metal prices —Harald Schmidbauer / Angi R¨osch 8 of 19

Motivation
Data
Methodology
Empirical results
Summary and conclusions
The basic model
Special cases
Persistence of a shock
Simulation examples
Statistical inference
Simulation example I: different parameters
0 20 40 60 80 100
0 20 40 60 80
trend stationary (α = 0)
trend stationary (α = 0.95)
difference stationary (α = 1)
Trends and shock persistence in precious metal prices —Harald Schmidbauer / Angi R¨osch 9 of 19

Motivation
Data
Methodology
Empirical results
Summary and conclusions
The basic model
Special cases
Persistence of a shock
Simulation examples
Statistical inference
Simulation example II: different parameters, with shock
0 20 40 60 80 100
0 20 40 60 80
trend stationary (α = 0)
trend stationary (α = 0.95)
difference stationary (α = 1)
Trends and shock persistence in precious metal prices —Harald Schmidbauer / Angi R¨osch 10 of 19

Motivation
Data
Methodology
Empirical results
Summary and conclusions
The basic model
Special cases
Persistence of a shock
Simulation examples
Statistical inference
We use Andrews-Chen median-unbiased estimation for AR models
(as implemented in Kim’s R package BootPR).
Trends and shock persistence in precious metal prices —Harald Schmidbauer / Angi R¨osch 11 of 19

Motivation
Data
Methodology
Empirical results
Summary and conclusions
Asset prices and their shock sensitivity
Robustness with respect to the existence of a trend break
Asset prices and their shock sensitivity
name from to AR order alpha HLS CIR
gold1 2003-01-07 2013-01-29 1 0.9571 15.8 23.3
gold2 2013-02-12 2019-03-05 1 0.9532 14.5 21.4
silver 2003-01-07 2019-03-05 1 0.9998 3745.2 5403.7
platinum 2003-01-07 2019-03-05 1 0.9980 339.8 490.7
palladium 2003-01-07 2019-03-05 1 0.9925 92.5 133.9
wti 2003-01-07 2019-03-05 1 0.9956 158.3 228.8
eurusd 2003-01-07 2019-03-05 1 0.9912 78.8 114.2
dji1 2003-01-07 2008-05-13 1 0.9668 20.5 30.1
dji2 2008-05-27 2019-03-05 1 0.9554 15.2 22.4
ndx1 2003-01-07 2008-08-05 1 0.9628 18.3 26.9
ndx2 2008-08-19 2019-03-05 1 0.9443 12.1 17.9
Trends and shock persistence in precious metal prices —Harald Schmidbauer / Angi R¨osch 12 of 19

Motivation
Data
Methodology
Empirical results
Summary and conclusions
Asset prices and their shock sensitivity
Robustness with respect to the existence of a trend break
standard deviation and kurtosis of weekly returns
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2 3 4 5
1.5 2.0 2.5 3.0 3.5 4.0 4.5
standard deviation
kurtosis
gold1 (2003 Jan − 2013 Jan)
gold2 (2013 Jan − 2019 Mar)
silver
platinum
palladium
wti
eurousd
dji1 (2003 Jan − 2008 May)
dji2 (2008 May − 2019 Mar)
ndx1 (2003 Mar − 2008 Aug)
ndx2 (2008 Aug − 2013 Mar)
Trends and shock persistence in precious metal prices —Harald Schmidbauer / Angi R¨osch 13 of 19

Motivation
Data
Methodology
Empirical results
Summary and conclusions
Asset prices and their shock sensitivity
Robustness with respect to the existence of a trend break
HLS in prices and standard deviation of weekly returns
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2345
HLS (weeks)
standard deviation
5 10 50 100 500 1000 5000
gold1 (2003 Jan − 2013 Jan)
gold2 (2013 Jan − 2019 Mar)
silver
platinum
palladium
wti
eurousd
dji1 (2003 Jan − 2008 May)
dji2 (2008 May − 2019 Mar)
ndx1 (2003 Mar − 2008 Aug)
ndx2 (2008 Aug − 2013 Mar)
Trends and shock persistence in precious metal prices —Harald Schmidbauer / Angi R¨osch 14 of 19

Motivation
Data
Methodology
Empirical results
Summary and conclusions
Asset prices and their shock sensitivity
Robustness with respect to the existence of a trend break
HLS in prices and kurtosis of weekly returns
●
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●
●
●
●
●
●
●
●
●
1.5 2.0 2.5 3.0 3.5 4.0 4.5
HLS (weeks)
kurtosis
5 10 50 100 500 1000 5000
gold1 (2003 Jan − 2013 Jan)
gold2 (2013 Jan − 2019 Mar)
silver
platinum
palladium
wti
eurousd
dji1 (2003 Jan − 2008 May)
dji2 (2008 May − 2019 Mar)
ndx1 (2003 Mar − 2008 Aug)
ndx2 (2008 Aug − 2013 Mar)
Trends and shock persistence in precious metal prices —Harald Schmidbauer / Angi R¨osch 15 of 19

Motivation
Data
Methodology
Empirical results
Summary and conclusions
Asset prices and their shock sensitivity
Robustness with respect to the existence of a trend break
Robustness with respect to the existence of a trend break
How robust are the HLS results with respect to the existence of a
trend break?
What if we treat gold and silver prices the same way?
There is no trend break in gold prices. OR:
There is a trend break in silver prices.
Results are shown in the following scatterplots.
Trends and shock persistence in precious metal prices —Harald Schmidbauer / Angi R¨osch 16 of 19

Motivation
Data
Methodology
Empirical results
Summary and conclusions
Asset prices and their shock sensitivity
Robustness with respect to the existence of a trend break
HLS in prices and standard deviation of weekly returns
●
●
●
●
●
●
●
●
●
●
●
●
●
●
2345
HLS (weeks)
standard deviation
5 10 50 100 500 1000 5000
gold
gold1 (2003 Jan − 2013 Jan)
gold2 (2013 Jan − 2019 Mar)
silver
silver1 (2003 Jan − 2010 Aug)
silver2 (2010 Sep − 2019 Mar)
platinum
palladium
wti
eurousd
dji1 (2003 Jan − 2008 May)
dji2 (2008 May − 2019 Mar)
ndx1 (2003 Mar − 2008 Aug)
ndx2 (2008 Aug − 2013 Mar)
Trends and shock persistence in precious metal prices —Harald Schmidbauer / Angi R¨osch 17 of 19

Motivation
Data
Methodology
Empirical results
Summary and conclusions
Asset prices and their shock sensitivity
Robustness with respect to the existence of a trend break
HLS in prices and kurtosis of weekly returns
●
●
●
●
●
●
●
●
●
●
●
●
●
●
1.5 2.0 2.5 3.0 3.5 4.0 4.5
HLS (weeks)
kurtosis
5 10 50 100 500 1000 5000
gold
gold1 (2003 Jan − 2013 Jan)
gold2 (2013 Jan − 2019 Mar)
silver
silver1 (2003 Jan − 2010 Aug)
silver2 (2010 Sep − 2019 Mar)
platinum
palladium
wti
eurousd
dji1 (2003 Jan − 2008 May)
dji2 (2008 May − 2019 Mar)
ndx1 (2003 Mar − 2008 Aug)
ndx2 (2008 Aug − 2013 Mar)
Trends and shock persistence in precious metal prices —Harald Schmidbauer / Angi R¨osch 18 of 19

Motivation
Data
Methodology
Empirical results
Summary and conclusions
Summary and conclusions
We analyzed weekly price series of
precious metals: gold, silver, platinum, palladium
other assets: dji, ndx, euro/USD, wti
over the period 2003 – 2019 with respect to their shock persistence.
A significant trend break was found for gold, but not for silver,
platinum, or palladium.
Silver, platinum, palladium have a high HLS.
(Investors: Get used to a new price level!)
The results depend on how we treat trend breaks.
Trends and shock persistence in precious metal prices —Harald Schmidbauer / Angi R¨osch 19 of 19