Bubble Strategies (Fordham)

Identifying Commodity Price Bubbles
Potential Risk and Rewards of Holding Commodities for Retail Investor
Portfolios
David De Wolf
Fordham University
June, 17 2016
David De Wolf (Fordham University) Identifying Commodity Price Bubbles June, 17 2016 1 / 27

Table of Contents
1 Research question
2 Data
3 Econometric tests
SADF (PWY)
GSADF (PSY)
4 Results
Bubble tests
Portfolio creation
5 Conclusion

Research question
Research Question
1 Can we detect bubbles in commodity markets based on the PWY and
PSY test during the past 26 years?
2 If we can detect bubbles, can we build protable trading strategies
based on historical information that we have obtained?

Data
Data Selection
Source: Thompson Reuters Datastream
Four commodities: Gold, Oil, Corn and Soybean
Data frame: 03/04/1990 - 29/04/2016
Frequency: daily observations (6544 full sample)
Continuous Futures prices

Econometric tests SADF (PWY)
Sup Augmented Dickey Fuller (PWY)
Supremum Augmented Dickey Fuller Test (SADF) proposed by
Phillips, Wu, and Yu (2011)
The SADF test is an extension of RADF test using a xed rolling
window
Determinants:
rw denotes the size of the window
r0 represents the xed initial window (0.01 + 1.8/
√
T)Ö T = 211
r1 denotes the window starting point
r2 denotes the window ending point

Sup Augmented Dickey Fuller (SADF) - PWY
Expanding window
6544 observations
6333 windows
Mathematically, this boils down to
Pt = µ + β+
ρ
i=1
γ Pt−i + εt (1)
where
Pt is the daily log prices of the commodities
µ is the intercept
β denotes the slope coecient
ρ is the maximum number of lags
εt is the error term

Sup Augmented Dickey Fuller (SADF) - PWY
SADF is the supremum of ADF
Mathemetically this boils down to:
SADF(r0) = sup{ADFr2 } (2)
A bubble is detected when SADF values cross the critical values
re = infr2 [,r0,T ] r2 : ADFr2 cvΘ
r2
(3)
rf = infr2 [,r1e,+h,T] r2 : ADFr2 cvΘ
r2
(4)

Econometric tests GSADF (PSY)
Generalized Sup Augmented Dickey Fuller (GSADF) - PSY
The PSY model is a modied, expanded version of the SADF
Duration of the rst bubble is important to detect the second
Mathematcially the rst step is to equivalent to:
∆Pt = αr1,r2 + βr1,r2 Pt+
ρ
i=1
γi
r1,r2
∆Pt + εt (5)
where
r0denotes the minimum window size
r1denotes the estimation starting point and varies between the rst
observation and observation r2 − r0(+1)
r2denotes the estimation end point
ρ denotes the number of lags
β denotes the bubble component

Estimate an auto regressive model with a null hypothesis: βr1,r2
= 0
(no bubble).
The alternative hypothesis is as follows: βr1,r2
0 (speculative
bubble) in the time series
Test statistic is calculated as: ADFr1,r2
=
βr1,r2
SE(βr1,r2 )
and is used to test
for signicance

In a second phase, the BSADF values are computed
Backwards looking instead of forward looking
Bubble origination and end dates of the bubbles will be computed as follows:
r1e = infr2 [,r0,T ] r2 : BSADFr2 (r0) scvΘ
r2
(6)
r1f = infr2 [,r1e,+h,T] r2 : BSADFr2 (r0) scvΘ
r2
(7)
where
scvΘ
r2
are the 100Θ% critical values using BSADF test statistics
based on r2 observations
minimum dened bubble length of h.
Θ is the desired level of signicance.

BSADF Test statistics
P∗
t = Pt+
ρ
i=1
ˆγi
r1,r2
∆P∗
t−i + ε∗
t (8)
where
P∗
t are generated using equation 8 for t = 1, 2, ...T.
ˆγi
r1,r2
is the estimated autoregressive coecient
residuals ˆεt are found for each commodity time series
ˆε∗
t =εtηt. ηt is an i.i.d. sequence from a standard normal distribution
or N (0, 1)

Overview SADF/BSADF/GSADF
Generally the GSADF and SADF are computed as follows:
GSADF(r0) = sup{BSADFr2
(r0)} (9)
SADF(r0) = sup{ADFr2
} (10)
where
r2 is the end of the sample
r0 is the window size

Results Bubble tests
Introduction to the SADF and GSADF
SADF/ GSADF test statistics and critical values
lagged order of 1
95 % condence levels
200 and 500 bootstrapping iterations
Trade o between daily and weekly observations

Gold SADF vs GSADF
Figure: SADF GSADF Bubble Test for Gold

Oil SADF vs GSADF
Figure: SADF GSADF Bubble Test for Oil

Corn SADF vs GSADF
Figure: SADF GSADF Bubble test for Corn

Soybean SADF vs GSADF
Figure: SADF GSADF Bubble test for Soybean

General overview
Figure: General overview bubbles detection

Results Portfolio creation
Introduction to Portfolio Creation
Equally weighted portfolios
Seven dierent assets
Franklin Templeton Global Growth Fund
Barclays U.S. Aggregate
Goldman Sachs Commodity Index
Goldman Sachs Commodity Index Gold, Oil, Corn and Soybean
Four dierent strategies:
Buy and Hold
Daily rebalancing
Monthly rebalancing
Yearly rebalancing
Performance measures: Sharpe, Sortino and Omega ratio
Transaction costs: 50 bp

Portfolio Description
Portfolio 1: only global equities via the Templeton Global Growth Fund
Portfolio 2: equally weighted portfolio of Global Equities and U.S. Fixed
Income securities
Portfolio 3: equally weighted portfolio of Gobal Equities, U.S. Fixed income
and the Broad Commodity Index
Portfolio 4: equally weighted portfolio of Global Equities, U.S. Fixed income
and the Gold Commodity Index
Portfolio 5: Equally weighted portfolio of Global Equities, U.S. Fixed income
and the Gold - , Oil - , Corn - and Soybeans Commodity Index.
Portfolio 6: Equally weighted portfolio made up of the Gold, Oil, Corn, and
Soybeans Commodity Indexes

Portfolio Back Test
Table: Performance Measures EW BH Strategy
Buy and Hold: Equally Weighted
Portfolio Mean Median Std Dev. Skewness Ex. Kurtosis Sharpe Sortino Omega
1 5.499 5.881 12.987 1.373 4.896 0.179 0.344 1.685
2 3.363 3.323 7.093 0.895 3.057 0.026 0.041 1.074
3 3.061 3.838 6.506 -0.705 0.712 -0.018 -0.023 0.952
4 3.426 4.129 5.567 0.042 -0.203 0.044 0.064 1.120
5 3.449 4.949 7.057 -0.211 -0.793 0.038 0.055 1.095
6 3.748 6.601 10.268 -0.043 -0.572 0.055 0.081 1.140

Portfolio Back Test
Table: Performance Measures EW Yearly Rebalanced Strategy
Yearly Rebalanced: Equally Weighted
1 5.499 5.881 12.987 1.373 4.896 0.179 0.344 1.685
2 5.185 5.535 13.255 1.321 4.599 0.151 0.283 1.550
3 5.255 5.252 13.156 0.017 0.851 0.158 0.249 1.524
4 6.128 5.599 13.341 0.956 1.619 0.221 0.442 1.852
5 8.735 9.323 22.254 0.493 -0.018 0.250 0.486 1.867
6 9.443 11.181 29.153 0.781 1.080 0.215 0.423 1.746

Portfolio Back Test for Bubble Strategies
Table: Four Commodity Strategy Risk On and Risk O
Four Commodity Bubble Strategy: Risk O
3 2.603 4.232 8.184 -1.787 5.215 -0.070 -0.081 0.809
4 3.086 3.930 6.353 -0.767 1.391 -0.015 -0.029 0.960
5 2.636 5.634 9.809 -1.778 5.126 -0.055 -0.065 0.857
6 3.040 6.696 11.829 -0.599 0.324 -0.012 -0.015 0.971
Four Commodity Bubble Strategy: Risk On
3 3.088 3.797 6.303 -0.547 0.289 -0.015 -0.019 0.962
4 3.324 4.150 5.688 -0.264 -0.086 0.025 0.035 1.068
5 3.009 5.429 8.177 -0.949 1.411 -0.021 -0.026 0.948
6 3.746 6.601 10.243 -0.039 -0.551 0.055 0.081 1.140

Table: Three Commodity Strategy Risk On and Risk O
Three Commodity Bubble Strategy: Risk O
3 2.362 4.197 7.809 -1.146 2.206 -0.105 -0.123 0.747
4 2.892 4.122 6.104 -0.223 -0.312 -0.047 -0.062 0.886
5 2.121 5.046 9.022 -0.777 0.557 -0.117 -0.139 0.746
6 2.653 6.447 11.039 -0.145 -0.532 -0.048 -0.063 0.893
Three Commodity Bubble Strategy: Risk On
3 3.150 3.538 5.862 -0.167 -0.434 -0.005 -0.007 0.987
4 3.321 3.622 5.303 0.083 -0.316 0.027 0.039 1.071
5 2.928 5.046 7.048 -0.134 -0.651 -0.036 -0.048 0.918
6 3.746 6.601 10.243 -0.039 -0.551 0.055 0.081 1.140

Figure: Portfolio values

Conclusion
Conclusion
Based on the GSADF (PSY Test) we nd:
17 bubbles in Gold
15 bubbles in Oil
12 bubbles in Corn
11 bubbles in Soybeans
Longest bubble in Gold and lasted for 912 days
Shortest bubble in both Oil as Gold and lasted for 8 days
TC's play an improtant role in portfolio rebalancing
Yearly rebalanced and EW portfolios deliver the best result
Bubble strategies in EW portfolios fail to deliver satisfying results

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