The document presents a methodology for assessing risk in commodity markets using semi-nonparametric specifications. It evaluates Value-at-Risk and Expected Shortfall for commodity exchange-traded funds using ARMA-EGARCH models with skewed-t and Gram-Charlier distributions. Backtesting shows the semi-parametric models have better coverage and performance than more traditional distributions. The Gram-Charlier distribution provides a closed-form expression for Expected Shortfall and is recommended for mitigating concerns about commodity market risk assessment. Future work could apply other risk measures to commodity assets and compare results with additional backtesting methods.

1. Motivation
Models and Methodology
Application
Conclusion
Risk assessment in commodity markets with
semi-nonparametric specifications
Esther B. Del Brio, Andr´es Mora-Valencia, Javier Perote
I Network de M´etodos Cuantitativos en Econom´ıa - AFADECO, November 10,
2017
Afadeco November 10,2017 Risk assessment in commodity markets

2. Motivation
Models and Methodology
Application
Conclusion
Outline
1 Motivation
2 Models and Methodology
3 Application
4 Conclusion
Afadeco November 10,2017 Risk assessment in commodity markets

3. Motivation
Models and Methodology
Application
Conclusion
Introduction
Commodity prices experienced a boom in the mid-2000s.
With the boom of commodity prices, several Exchange
Traded Funds (ETFs) were created in order to track the price
of main commodities such as gold, silver and oil.
Financial institutions and regulators - e.g. Financial Stability
Board (FSB) and Bank for International Settlements (BIS) -
expressed their concerns about the potential systemic
impact of the ETFs industry in 2011.
Commodity assets may present higher volatilities than equity
assets even in “relatively” calm periods.
Recently, there has been a sharp decline in the price of
these assets affecting developed markets based on mining and
energy industries like Canada and Australia, based metals
businesses in Deutsche Bank and JP Morgan, among others .
Afadeco November 10,2017 Risk assessment in commodity markets

4. Motivation
Models and Methodology
Application
Conclusion
Risk Measures
Value-at-risk (VaR) has been the standard market risk
measure to assess regulatory capital requirements since 1996.
VaR has been criticized since they do not fulfill the
subadditivity property and its inability to accurately capture
tail risk.
Expected Shortfall (ES) provides coherent risk measures.
Basel 2.5 (2012) proposes to replace VaR by ES.
ES is very sensitive to extreme events and may result in
unstable capital numbers at high confidence levels.
ES does not satisfy the elicitability property, which generated
debate on whether ES can be backtestable.
VaR satisfies elicitability property and there are very
well-known backtesting methods for this measure.
Afadeco November 10,2017 Risk assessment in commodity markets

5. Motivation
Models and Methodology
Application
Conclusion
Literature Review
Authors Asset (Variable) Best Model
Giot & Laurent (2003) Several commodity markets APARCH + skewed-t innovations
Hung et al. (2008) Energy commodities GARCH + heavy tail model
Chiu et al. (2010) Brent and WTI crude oil prices Hull-White model
Aloui & Mabrouk (2010) Oil and gas commodities prices FIAPARCH + skewed-t innovations
Youssef et al. (2015) Crude oil and gasoline market FIAPARCH + EVT
Andriosopoulos
Nomikos(2015)
8 spot energy commodities and SEI MC simulations
Steen et al. (2015) 19 commotity futures Quantile regression
Aloui & Jammazi (2015) Oil-exchange rate pairs Wavelet-based models
Lu et al. (2014) Crude oil futures and natural gas futures t-Copula & skewed-t for mgnls
Afadeco November 10,2017 Risk assessment in commodity markets

6. Motivation
Models and Methodology
Application
Conclusion
VaR/ES-ARMA(1,1)-EGARCH(1,1)
Rt+1 = µt+1 + σt+1Zt+1:
µt+1 = µ + φ1µt + θ t + t+1,
t+1 = Zt+1σt+1 Zt+1 ∼ G(0, 1),
logσ2
t+1 = ω + α (|zt| − E [|zt|]) + γzt + β log σ2
t ,
VaR = µt+1 + σt+1qγ(Zt+1),
ES = µt+1 + σt+1ESγ(Zt+1).
Afadeco November 10,2017 Risk assessment in commodity markets

7. Motivation
Models and Methodology
Application
Conclusion
Distributions (...for G)
1 Normal
2 Student’s t
3 Skewed t
4 GC Type A
Afadeco November 10,2017 Risk assessment in commodity markets

8. Motivation
Models and Methodology
Application
Conclusion
Normal, Student’s t and Skewed-t
Normal:
φ (zt) = 1√
2π
exp −z2
t
2 .
Student’s t:
t (zt) =
Γ(ν+1
2 )√
π(ν−2)Γ(ν
2 )
1 + z2
t
ν−2
−ν+1
2
,
Skewed t (Fernandez and Steel, 1998):
g (zt) =



− 2
γ+ 1
γ
t (γzt) zt < 0,
2
γ+ 1
γ
t zt
γ zt ≥ 0,
.
Afadeco November 10,2017 Risk assessment in commodity markets

9. Motivation
Models and Methodology
Application
Conclusion
Gram-Charlier Type A
GC Type A density:
f (zt, d) = 1 +
n
s=1
dsHs (zt) φ (zt) ,
where:
φ (zt) is the normal pdf,
d = (d1, . . . , ds) ∈ Rs, and
Hs is the sth Hermite polynomial (HP) of order, which is
computed in terms of the sth order derivative of the Gaussian
pdf:
ds φ(zt )
dzs
t
= (−1)s
Hs (zt) φ (zt) .
Afadeco November 10,2017 Risk assessment in commodity markets

10. Motivation
Models and Methodology
Application
Conclusion
GC Type A
First four HP:
H1 (zt) = zt
H2 (zt) = z2
t − 1
H3 (zt) = z3
t − 3zt
H4 (zt) = z4
t − 6z2
t + 3
These polynomials form an orthonormal basis:
Hs (zt) Hj (zt) φ (zt) dzt = 0 ∀s = j
Afadeco November 10,2017 Risk assessment in commodity markets

11. Motivation
Models and Methodology
Application
Conclusion
Fitted Densities
0
0,005
0,01
0,015
0,02
0,025
Fig. 2. Fitted densities (left tails)
Histogram Normal
Gram-Charlier Student's t
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1
Fig. 1. Fitted densities
Histogram Normal
Gram-Charlier Student's t
Afadeco November 10,2017 Risk assessment in commodity markets

12. Motivation
Models and Methodology
Application
Conclusion
GC Type A ES
ESα =
−
φ(ϕ−1(α))
α 1 +
S
s=2
ds Hs ϕ−1
(α) + sHs−2 ϕ−1
(α)
where
φ is the pdf of standard normal
and
ϕ−1 (α) is the α-quantile of the GC Type A distribution
Afadeco November 10,2017 Risk assessment in commodity markets

13. Motivation
Models and Methodology
Application
Conclusion
Backtesting methods
We compute one-step ahead forecasts for VaR and ES through a rolling
window of size T and compare the model performance according to:
Backtesting methods for VaR
1 Bernoulli coverage test
2 Relative comparison for VaR
Backtesting methods for ES
1 t-test
2 Relative comparison for ES
Afadeco November 10,2017 Risk assessment in commodity markets

14. Motivation
Models and Methodology
Application
Conclusion
Commodity ETFs Prices
Sample: Daily prices form January 2007 to January 2016 for Gold, Silver,
Oil, Agriculture, Energy abd Broad Commodity ETFs
Afadeco November 10,2017 Risk assessment in commodity markets

15. Motivation
Models and Methodology
Application
Conclusion
Commodity ETFs Returns
Return data exhibits: volatility clustering, leptokurtosis, skewness,
leverage effects
Afadeco November 10,2017 Risk assessment in commodity markets

16. Motivation
Models and Methodology
Application
Conclusion
Coverage test: 99%-VaR
Skewed-t and GC outperform the rest of the models. Result is
corroborated by the Diebold Mariano test for relative performance
(pairwise comparison).
Afadeco November 10,2017 Risk assessment in commodity markets

17. Motivation
Models and Methodology
Application
Conclusion
t-test: 97.5%-ES
Skewed-t and GC outperform the rest of the models. Result is
corroborated by the Diebold Mariano test for relative performance
(pairwise comparison).
Afadeco November 10,2017 Risk assessment in commodity markets

18. Motivation
Models and Methodology
Application
Conclusion
Conclusion
We applied backtesting methods for both VaR and ES to
different Commodity ETFs.
We compare the performance of different parametric and
semi-nonparametric specifications both in univariate
framework.
Coverage and relative performance tests show that the skewed
t and Gram-Charlier outperform other more traditional density
specifications.
We show that the Gram-Charlier distribution is very tractable
for empirical purposes and provide a closed expression for ES
with GC distribution.
We recommend the application of this distribution to mitigate
regulation concerns about global financial stability and
commodities risk assessment.
Afadeco November 10,2017 Risk assessment in commodity markets

19. Motivation
Models and Methodology
Application
Conclusion
Future Work
Applications of other risk measures such as median shortfall
(it is also elicitable), spectral risk measures.
Compare results with other tests (Acerbi and Szekely, 2014).
Other commodity assets: Commodity Leveraged-ETFs.
Afadeco November 10,2017 Risk assessment in commodity markets

20. Motivation
Models and Methodology
Application
Conclusion
Thank you!
Andr´es Mora-Valencia
a.mora262@uniandes.edu.co
Afadeco November 10,2017 Risk assessment in commodity markets