- Email: [email protected]
Diamonds versus precious metals: What gleams most against USD exchange rates?
Finance Research Letters xxx (xxxx) xxx–xxx
Contents lists available at ScienceDirect
Finance Research Letters journal homepage: www.elsevier.com/locate/frl
Diamonds versus precious metals: What gleams most against USD exchange rates? Rihab Bedouia,b,1, Khaled Guesmic, Saoussen Kalaia, Thomas Porcherd,
⁎
a
The Institute of Higher Business Studies of Sousse, Sousse, Tunisia University of Paris Ouest Nanterre La Défense, 200 avenue de la République, 92000 Nanterre Cedex, France Climate Change and Energy Transition Chair, IPAG Business School Paris, Visiting Professor, Telfer School of Management, University of Ottawa, Ottawa, Canada d Paris School of Business, PSB, 59 Rue Nationale, 75013, Paris, France b c
ARTICLE INFO
ABSTRACT
Keywords: Copulas Diamonds Precious metals Alternative asset Safe-haven, Hedge USD depreciation
Historically, commodity market, particularly the metal market has been used as a hedge for stock market and currencies during time of distress. In this paper, we shed light on a new alternative asset and examine the hedging and safe haven ability of diamonds and five precious metals that is, gold, silver, palladium, platinum and rhodium by using copula process. Then, we compare the performance of diamond versus metals in terms of hedging and safe haven against USD depreciation. Our empirical results show that gold, silver, palladium and platinum outperform diamonds and rhodium in term of hedging against USD movement. Our finding for safe haven study reveals that both precious metals and diamonds serve as a weak safe haven.
1. Introduction The developments of financial markets as well as the globalization have increased the uncertainty and therefore the risk of exchange rates which lead investors to focus more and look for “the flight to quality effect”.2 Indeed, investors often consider the precious metals especially gold as an alternative investment to market volatility, exchange rate and inflation. Historically, the financial mediahave considered that gold can act as a safe haven in financial markets. Therefore, Baur and Lucey (2010) examine the usefulness of gold as a safe haven in extreme stock market volatility. Moreover, some papers have studied the gold's safe haven status with respect to stock market, bond market, currencies, as well as exchange movements (Capie et al. (2005), Baur and Lucey (2010); Baur and McDermott (2010); Joy (2011); Pukthuanthong and Roll (2011); Ciner et al. (2013); Pullen et al. (2014)).On the other side, a handful of studies investigate the role of other precious metals as a hedge and safe haven (Conovor et al. (2009); Lucey and Li (2013); Hood and Malik (2013); Agyei et al. (2014). Currently, the gemstones especially the diamond has been attracted by the financial media. In this order, Renneboog and Spaenjers (2012); Auer and Schumacher (2013) analyze the role of this new asset in the global financial system. They show that an investment in a diversified diamond portfolio can outperform a diversified stock market investment in a period of generally frail stock market. However, in turmoil market, gold has long been used as a safe haven against currency devaluation, inflation, and stock market crashes. It has historically been valuable, expensive, long lasting and an asset that
Corresponding author. E-mail address: [email protected] (T. Porcher). 1 Member of the Research laboratory for Economy, Management and Quantitative Finance LaReMFiQ 2 The Flight to quality is the act of moving capital away from “risky” investment and toward “safer” investment due to uncertainty about the overall economy. ⁎
https://doi.org/10.1016/j.frl.2019.08.001 Received 3 May 2019; Received in revised form 20 July 2019; Accepted 7 August 2019 1544-6123/ © 2019 Elsevier Inc. All rights reserved.
Please cite this article as: Rihab Bedoui, et al., Finance Research Letters, https://doi.org/10.1016/j.frl.2019.08.001
Finance Research Letters xxx (xxxx) xxx–xxx
R. Bedoui, et al.
holds its value when other assets are crashing. In the weakness of 2008–2009 Global Financial Crises “GFC”, investors have been attracted by diamonds. The great increase of gold demand after the GFC raised drastically the gold price, consequently created a potential bubble in the market. Thus, investors who want to protect their wealth seek an alternative investment, which is free risk and not yet overrun. Therefore, diamonds have introduced as an interesting alternative investment to secure investor's wealth. An analysis of the range of potential scenarios outlined by Goodman et al. (2014) suggest that the diamond industry can be a robust and profitable sector, which encourage more investors to use the asset as an alternative investment. Moreover, Auer (2014) examines the performance of diamond returns against precious metals and finds that a diversified diamond portfolio outperforms an investment in gold and silver in term of low risks. Therefore, it is interesting to study the usefulness of diamond as a safe haven and hedge against stock market crashes and exchange rate devaluation as well as to compare its performance with five precious metals (Gold, Silver, Palladium, Platinum and Rhodium). In this Paper, we examine the hedging and safe haven capacity of diamonds versus precious metals against USD movement using copula theory. Indeed, we find evidence that investing in precious metals rather than diamonds is better choice for investors seeking to protect their investment against USD depreciation value. Our finding is crucial because in our knowledge this is the first work that uses physical diamond (investment direct) and diamond indices (investment indirect) as well as five precious metals in context of hedging against exchange rates. Moreover, in this research we give more importance by extracting turbulence sub period and seeking a haven capacity of diamonds and precious metals at extreme movement and in period with high uncertainty that is not shown in other articles. This finding is of highly interest and importance for investors who are interested in diamonds to deal with risk management during extreme market volatility. Also, as diamond is a new addition to investment field, it is important to benefit from understanding the respective interaction between diamond index, diamond prices and the market. So, we use daily spot prices over the period from January 2, 2002 to July 19th, 2016. We estimate the copula parameters by using the Canonical Maximum Likelihood (CML) method and select the adequate copula by using goodness-of fit test. The paper is organized as follows: In Section 2, we discuss our empirical methodology and define the copula theory and its properties. In Section 3, we describe our data set. In Section 4, we study the safe haven and the hedge effect using copulas. Finally in Section 4, we give our conclusions and future extensions. 2. Methodology Our primary goal of this study is to explore the safe haven and hedging properties of diamonds versus precious metals against the exchange rate. Past studies investigate the hedge and safe haven properties without distinguishing between average and extreme shocks. Kaul and Sapp (2007) define the safe haven asset as an asset that investors acquire during periods of uncertainty. This asset does not co-move with the other asset during turmoil while Baur and Lucey (2010) provide a definition and a clear distinction between hedge and safe haven. Then, Baur and McDermott (2011) extend the research of Baur and Lucey (2010) by giving discrimination between the strong and weak safe haven and hedge properties as bellow: A weak (strong) hedge is defined as an asset that is uncorrelated (negatively correlated) with another asset or portfolio on average. A weak (strong) safe haven is defined as an asset that is uncorrelated (negatively correlated) with another asset or portfolio during extreme movement. Thus, in our work we follow these definitions to discriminate between hedge and safe haven abilities of precious metals and diamond. We use Copulas to model average and tail dependence and examine the hedge and safe haven abilities of precious metals and diamonds against USD exchange rates. For this we will follow the same methodology developed in Bedoui et al. (2018).Thus we use the Canonical Maximum likelihood (CML) to estimate the parameter of a panel of possible copula. Firstly, we estimate the margins using empirical distribution: T 1 F^i (x) = T t = 1 1I{Xi x } I = 1,....,p; where I is the indicator function. Then we apply the CML method. The procedure of this in two step:
• Transformation of the initial sample set into uniform variables, using the empirical marginal distribution: u^t = (u^1 , ….,u^N ) = (F^1 (x1t ), …, F^N (xNt ))
(1)
• Estimation of the copula parameters via the following relation: ^CLM = arg max
T t=1
LnC (u^1 , ….,u^N , )
(2)
For the marginal distribution, we consider the Golsten–Jagannathan–Rankle GARCH (GJR–GARCH) represented by Glosten et al., 1993. The GJR–GARCH models the asymmetry, but on the conditional variance. It gives more weight to negative shocks than the positive one which is the fact in financial series. Hence, The GJR–GARCH model is defined as: t
(3)
= z t t , z t followsawhitenoiseprocess
where: 2
Finance Research Letters xxx (xxxx) xxx–xxx
R. Bedoui, et al. q 2 t w
p
+
(
i
+ i It
2 i < 0) t i
2 j t j,
+
i=1
i = 1…p and j = 1…q
j=1
(4)
with:
w, q i=1
i
+
0 i, i and j q p + j=1 j i=1 i
<1
(5)
β j are the conditional variance term, γi are the asymmetric effect coefficient.and
It
i
=
1 if 0 if
t i t i
<0 >0
(6)
2.1. The goodness of fit testing It is important to determine how well the model fits the data and which model is the best. Therefore, there are different ways to select the adequate copula that gives the best dependence structure. 2.1.1. Graphical criterion This Scatter plot allows for a graphical overview about the adequacy quality of an estimated parametric copula and the empirical copula. Although it provides a view of the dependence structure, this graphical method can be used solely in the bivariate case whereas; our study is about the multivariate case. 2.1.2. Information criteria We select the model that minimizes the amount of Kullback–Leibler's inforamation. Among the many criterions that have been proposed in literature, the most commonly used are: a Bayesian Information Criterion (BIC)
BIC =
(7)
2l( ) + Kln (n)
where l(θ) is the log-likelihood of the estimated parameter θ, K is the number of parameters in the model and n is the size of the sample. a Akaike's Information Criterion (AIC)
AIC = 2k
(8)
2l ( )
where l(θ) is the log-likelihood of the estimated parameter θ, K is the number of estimated parameters in the model. The information criterions do not present a robust tool to judge the adequacy quality of the chosen copula; hence it is essential to use more powerful tools. The decision rule is as follows: We select the appropriate copula which maximises the log likelihood and minimises the AIC and BIC criterion 2.1.3. Goodness-of-fit test of Rémillard and Scaillet 2009 According to Genest et al. (2009), the Goodness-of-fit test is the most powerful test which based on the distance between the empirical copula and the parametric copula estimated by the null hypothesis. The Rémillard and Scaillet test is based on the statistic obtained by the parametric boostrap and presents a main drawback which is the computational cost when dealing with large sample. To reduce the time of computing from days to minutes, we follow the step of Ivan Kojadinovic et al. (2011) and use the goodnessof-fit based on the multiplier central limit theorems inspired by the work of The Rémillard and Scaillet (2009). Therefore, this test is based on comparing between the empirical copula Cn and the parametric estimated copula C n . n
=
n (Cn
C
n)
The test statictics lay on the Von–Mises distances:
Sn =
(u)2dCn (u )
More Sn is higher, the probability to reject H0 increase. The p-value of the test is given by specially adopted Monte Carlo methods. 3
Finance Research Letters xxx (xxxx) xxx–xxx
R. Bedoui, et al.
The adequate copula is the copula with the highest p-value. 3. Data Our primary goal of this study is to explore the safe haven and hedging properties of diamonds versus precious metals against the exchange rate to evaluate diamonds as a viable investment alternative. So, we use daily prices of five precious metals (gold, silver, platinum, palladium and rhodium), two diamond prices (D Flawless grade, 1 carat and 3 carat respectively); four polished diamond indices prices: 1 carat Commercial diamond index (1 ct com), 1 carat Fine diamond index (1ct Fine), 0.5 carat Commercial diamond index (0.5 ct com), 0.5 carat Fine diamond index (0.5 ct fine); as well as three USD nominal exchange rates and USD effective exchange rate over the period from January 1st, 2002 to July 19th, 2016. All the prices of diamonds, diamond indices and precious metals are measured in the US dollar per troy ounce except silver, which is priced in cent per troy ounce. Exchange rates are expressed in terms of USD per unit of foreign currency. In our case, it corresponds to the amount of USD per one unit of each of three major currencies in international trade: the Euro (EUR), The British pound Sterling (GBP), the Japanese Yen (JPY). Thus, an appreciation in the nominal exchange rate leads to depreciation in USD. Diamond prices are extracted from Data stream and the USD effective rate is extracted from the bank of England while the remaining data are downloaded from the “Quandl's Data Collections”. There are cases where stock markets in different countries were closed on some days during the observation period. To eliminate this discordance, we only deal with the daily data for days where all markets are open. We finally get 3388 valid observations.3 Fig. 1 presents the dynamics of the daily traded of diamond prices, diamond indices, precious metals and exchange rates. From Fig. 1, we can remark that all variables vary over time. Regarding diamond price, it is clear that the 1 carat diamond prices are less volatile than 3 carat prices while the movement of diamond indices is heavily influenced by the development of 1 carat indices. Moreover, Fig. 1 shows that after the global financial crisis 2008, all precious metals exhibit severity in the trend changes except gold, which is the more stable commodity comparing to other while rhodium exhibits the largest drop in price. However, as shown in Fig. 1 the USD nominal and effective exchange rates are unstable in time and exhibit more volatility than other variables. According to Tables 1a–c we show that the kurtosis for all variables is greater than three. Thus, all our distributions are Leptokurtic and having fat tail. Therefore, the probabilities of extremely realizations are higher than the normal distributions case. The skewness measures the asymmetry of the distribution. Negative skewness means that the distribution is skewed to left while positive skewness means that the distribution is skewed to the right. And zero values of skewness indicate symmetric distribution. In our case, Tables 1a–c, show that 1 carat diamond price; Gold; Silver; Palladium; Platinum; GBP/USD and USD effective rate have a negative skewness which indicates that the extreme values are located on the left side of the mean. While, all remaining variables have a positive skewness which means that the most values concentrated on the left side of the mean and extreme values are on the right side. 4. Empirical results To measure the degree of interdependence between variables with copula, it's important as a first step to fit our returns to deal with the autocorrelation and heteroskedasticity then we filter the log negative returns into an approximately i.i.d series. To capture the volatility cluster, we use the GJR–GARCH. This model gives more weight to negative movement, which is styled in the financial series means that negative shocks have a more important influence on volatility than positive ones. The GJR–GARCH (1, 1): the (1, 1) in parentheses is a standard notation in which the first number refers to how many autoregressive lags (ARCH terms) and the second one refers to the number of the moving average lags. According to Table 2, all variables fit to an AR (1)-GJR (1, 1)-GARCH (1, 1) model except the palladium and the platinum which are fitted to an AR (0)-GJR-GARCH (1, 1) model. In addition, Table 2 shows that the maximum likelihood results for β is very significant (approximately equal to 0.9) for all variables except the 1 carat diamond prices and 3 carat diamond prices (approximately is closed to 0). Therefore, the conditional volatility is past-dependent and very persistent over time for all series except the diamond prices (1 carat and 3 carat) 4.1. The study of the hedging effect by using copulas The copula is considered as the most appropriate tool to model the dependence between variables. We use the Canonical Maximum likelihood (CML) to estimate the parameter of the copula. Table 3 shows the results for the parametric copula model described above. Parameter estimates for the elliptical copula is negative for the pairs of USD effective rate and all diamond index and prices metals (except the 1 carat fine diamond index and the rhodium) while we find the opposite results for the EUR/USD rate. Moreover, we remark that the degrees of freedom for the t-copula are very large for mostly diamond prices and indices (v → ∞), then the t-copula converge to the normal copula. The estimated parameter values for the Placket copula (Placket, 1965) are all positive (for all pairs). Whereas, Frank copula (Frank, 1979) show evidence of positive and negative dependence. Examining (Clayton, 1978) and (Gumbel, 1960) copulas, the estimated parameters are quite equal to zero (1.4509*10−6) for Clayton copula and equal to one for Gumbel copula which admit independence structure for various pairs. After the copula fitting, an important question arises: Which copula to choose? To answer this question we use the AIC 3 There are cases where stock markets in different countries were closed on some days during the observation period. To eliminate this discordance, we only deal with the daily data for days where all markets are open. We finally get 3388 valid observations.
4
Finance Research Letters xxx (xxxx) xxx–xxx
R. Bedoui, et al.
Fig. 1. Dynamics of the daily traded of diamonds prices, diamond indices, precious metals and exchange rates.
(Akaike information criterion) and BIC (Bayesian information criterion) criterion as well as the Goodness-of-fit test. From Table 4, we observe that in the case of the pairs USD effective rate-precious metals, the Elliptical copulas offer the best performance and negative dependence with all metals except the rhodium. While for the case of USD effective rate-diamonds, the Archimedean copulas (Frank for 1ct diamond price, Gumbel for 3ct diamonds price, Clayton4 for 1ct commercial, 1ct fine and 0.5ct fine diamond indices) and placket copula (for 0.5ct commercial diamond index) perform better and admit a positive dependence structure except for 1ct and 4
(see Clayton, 1978). 5
Finance Research Letters xxx (xxxx) xxx–xxx
R. Bedoui, et al.
Table 1a Descriptive statistics for diamonds and diamond indices.
1 carat 3 carat 1 carat commercial 1 carat Fine 0.5 carat commercial 0.5 carat Fine
Mean(%)
S.deviation
Skewness
Kurtosis
Maximum
Minimum
Median(%)
0.00219 0.01663 −0.00008 0.00369 −0.00418 0.00048
0.0703 0.0356 0.0302 0.0356 0.0265 0.0348
−0.2812 0.2485 0.0912 0.0374 0.7205 0.4367
20 123 8.1 8.2 17.9 8.7
0.5527 0.5979 0.1930 0.2065 0.2561 0.1975
−0.6243 −0.6071 −0.2072 −0.1937 −0.2462 −0.2062
0 0 0 0 0 0
Table 1b Descriptive statistics for Precious metals.
Gold Silver Palladium Platinum Rhodium
Mean(%)
S.deviation
Skewness
Kurtosis
Maximum
Minimum
Median(%)
0.04621 0.04345 0.01184 0.02405 −0.01121
0.0122 0.0228 0.0220 0.0151 0.0203
−0.3070 −0.4676 −0.4518 −0.7522 0.1337
7.7 11.5 7.6 12 44
0.0759 0.1828 0.1092 0.0843 0.3127
−0.0960 −0.1869 −0.1786 −0.1728 −0.2336
0.05971 0.05739 0 0.05935 0
Table 1c Descriptive statistics for exchange rates.
GBP/USD JPY/USD EUR/USD USD*
Mean(%)
S.deviation
Skewness
Kurtosis
Maximum
Minimum
Median(%)
−0.00295 0.00646 0.00604 -xw0.00549
0.0062 0.0084 0.0081 0.0047
−1.0284 0.5983 0.6405 −0.2806
16.1 103 90.2 6.3
0.0354 0.1685 0.1596 0.0228
−0.0849 −0.1629 −0.1433 −0.0415
0 0 0.01293 −0.00093
Notes: The Kurtosis represents the fourth moment of the random variable. It is a measure of the “heavy tails”. We use this measure to compare the distribution to the normal one which had a kurtosis equal to three. Therefore, distributions with a kurtosis more than three are “Leptokurtic” and kurtosis less than three are “Platykurtic”. ⁎ mean effective rate. Table 2 GJR estimation. C 1 carat 3 carat 1 carat Commercial 1carat Fine 0.5 carat Commercial 0.5 carat Fine Gold Silver Palladium Platinum Rhodium GBP/USD JPY/USD EUR/USD USD*
AR(1) −11
−1.5542×10 −5.8253×10−9 −6.3898×10−5 −6.1466×10−5 −2.6855×10−5 −4.3712e×10−5 0.00067433 0.00072299 0.00029695 0.0005666 2.4712×10−9 0.00011779 −3.3631×10−5 0.0002141 −2.7994×10−5
W −6
−1.0327×10 2.4591×10−7 −0.040551 −0.049438 −0.0061665 −0.021429 −0.010181 −0.085838 0.056457 0.03562 −0.060308 −0.0077321 −0.030371
−7
2 × 10 2 × 10−7 2 × 10−7 2 × 10−7 2 × 10−7 2 × 10−7 1.2212×10−6 2.9633×10−6 5.889×10−6 2.8138×10−6 2 × 10−7 2 × 10−7 1.2541×10−6 4.5469×10−7 2 × 10−7
β
α
v
δ
0 0.007254 0.87008 0.85491 0.88644 0.84401 0.95119 0.95407 0.90266 0.91868 0.028806 0.945 0.90453 0.9479 0.95324
0.86999 1.9658×10−5 0.25984 0.29018 0.22712 0.31199 0.052406 0.060476 0.10416 0.078427 1.0181 0.045246 0.077773 0.035854 0.040831
2 2 2.557 2.5972 2.2218 2.386 5.572 4.6768 4.3957 5.9129 2.0654 8.1053 4.6543 5.4795 7.2644
0.26003 7.2747×10−5 −0.25984 −0.29018 −0.22712 −0.31199 −0.02119 −0.035975 −0.016728 −0.015465 −0.093818 0.01234 −0.010397 0.012384 −0.0045927
Notes: W is a Constant. β and α are GARCH(1) and ARCH(1) processes. v and δ are the degree of freedom Leverage (1).
0.5ct fine diamond indices where the parameters values of Clayton are close to 0 which indicate an independence structure. Our results reveal that precious metals except rhodium can be a strong hedge whereas only 1ct and 0.5ct fine diamond indices serve as a weak hedge against the USD effective rate. For the case of EUR/USD (i.e. GBP/USD and JPY/USD)5 exchange rate, we find different adequate copulas. These copulas reveal an independence structure with some diamond indices and Rhodium which indicate that diamond indices and rhodium can act as a weak hedge against USD movement. On the other hand, the relationship between precious
5
The tables of GBP/USD and JPY/USD are available on request. 6
Finance Research Letters xxx (xxxx) xxx–xxx
R. Bedoui, et al.
Table 3 Estimates of the dependence parameters for different copula models.
1 carat –USD effective rate 3 carat-USD effective rate 1 carat commercial-USD effective rate 1 carat fine –USD effective rate 0.5 carat commercial- USD effective rate 0.5 carat fine-USD effective rate Gold-USD effective rate Silver-USD effective rate Palladium-USD effective rate Platinum-USD effective rate Rhodium-USD effective rate 1 carat –EUR/USD 3 carat-EUR/USD 1 carat commercial-EUR/USD 1 carat fine –EUR/USD 0.5 carat commercial –EUR/USD 0.5 carat fine-EUR/USD Gold-EUR/USD Silver-EUR/USD Palladium-EUR/USD Platinum-EUR/USD Rhodium-EUR/USD
Normal ρ
Student-t ρ
v
Plackett θ
Frank θ
Clayton θ
Gumbel θ
0.0272 0.0261 −0.0021 0.0030 −0.0397 −0.0045 −0.4826 −0.3054 −0.2678 −0.3274 0.0545 −0.0323 −0.0322 0.0199 −0.0197 0.0036 0.0092 0.2757 0.1988 0.1655 0.2254 −0.0485
0.0286 0.0262 −0.0018 0.0030 −0.0409 −0.0038 −0.4886 −0.3092 −0.2734 −0.3325 0.0547 −0.0330 −0.0329 0.0201 −0.0189 0.0043 0.0093 0.2778 0.1999 0.1695 0.2278 −0.0487
68.2725 70396 154.1428 1161300 40.5573 37.0889 6.9470 16.5020 14.3433 13.9094 4669200 39.2000 74.6154 37.1022 23.3169 24.4374 14.8911 12.235 26.9497 20.3712 20.7027 4669100
1.1281 1.0709 0.9698 0.9516 0.8949 0.9743 0.2716 0.4205 0.4780 0.4082 1.1442 0.8495 0.8576 1.0459 1.0119 1.0760 1.0410 2.0321 1.6038 1.5961 1.8351 0.9382
0.2124 0.1578 0.0129 2.1950×10−4 −0.2624 −0.0147 −3.2583 −1.8953 −1.6794 −2.0538 0.3439 −0.2114 −0.2141 0.1325 −0.0836 0.0455 0.0649 1.6661 1.1533 1.0258 1.3554 −0.2813
0.0218 0.0183 0.0106 1.4509×10−6 1.4509×10−6 1.4509×10−6 1.4509×10−6 1.4509×10−6 1.4509×10−6 1.4509×10−6 0.0504 1.4509×10−6 1.4509×10−6 0.0194 1.4509×10−6 0.0071 0.0180 0.3132 0.1977 0.1714 0.2416 1.4509×10−6
1.0091 1.0105 1.0008 1.0041 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0165 1.0000 1.0000 1.0099 1.0000 1.0043 1.0097 1.1931 1.1226 1.1024 1.1476 1.0000
Notes: The results of other variables database are available on request. The results of the AIC and BIC criterion are available on request. Table 4 Results of Goodness-of-fit test for different copulas.
1 carat –USD effective rate 3 carat-USD effective rate 1 carat commercial-USD effective rate 1 carat fine –USD effective rate 0.5 carat commercial- USD effective rate 0.5 carat fine-USD effective rate Gold-USD effective rate Silver-USD effective rate Palladium-USD effective rate Platinum-USD effective rate Rhodium-USD effective rate 1 carat –EUR/USD 3 carat-EUR/USD 1 carat commercial-EUR/USD 1 carat fine –EUR/USD 0.5 carat commercial –EUR/USD 0.5 carat fine-EUR/USD Gold-EUR/USD Silver-EUR/USD Palladium-EUR/USD Platinum-EUR/USD Rhodium-EUR/USD
Normal
Student-t
Frank
Plackett
Clayton
Gumbel
0.01648 0.1224 0.473 0.1993 0.8237 0.6998 0.07742 0.1943 0.512 0.2183 0.05544 0.2652 0.4091 0.5729 0.1474 0.6389 0.8307 0.2512 0.6069 0.3691 0.7098 0.524
0.01049 0.1314 0.451 0.2273 0.7957 0.6968 0.3651 0.1224 0.7128 0.1983 0.05145 0.2193 0.3801 0.5799 0.1933 0.8237 0.9925 0.4311 0.4141 0.4151 0.7308 0.519
0.02647 0.06543 0.4461 0.1484 0.8516 0.6149 0.0004995 0.015485 0.02647 0.004496 0.02248 0.2772 0.3971 0.6179 0.1084 0.7408 0.8467 0.0004995 0.04545 0.7547 0.1513 0.2672
0.02348 0.08841 0.4421 0.1454 0.8796 0.6159 0.0004995 0.05145 0.05644 0.01049 0.02248 0.2742 0.4061 0.6439 0.13424 0.7438 0.8197 0.002498 0.05245 0.7997 0.1813 0.2672
0.007493 0.07143 0.6429 0.3002 0.07443 0.7727 0.0004995 0.0004995 0.0004995 0.0004995 0.02048 0.03746 0.1044 0.491 0.3981 0.7977 0.8776 0.0004995 0.0004995 0.0004995 0.0004995 0.6149
0.007493 0.1643 – – – – – – – – 0.0004995 – – 0.473 – 0.8207 0.9535 0.0004995 0.007493 0.001499 0.0004995 –
metals (except rhodium) and nominal exchange rates is a positive which means that precious metals are strong hedge against USD movement. To summarize, diamonds and rhodium show a weak hedging ability against nominal exchange rates. On the other side, only 1 carat and 0.5 carat fine indices serve a weak hedge for the USD effective rate. While, precious metals exhibit a strong hedging ability against both nominal and effective exchange rates. Hence, we can conclude that gold, silver, palladium and platinum outperform diamonds and rhodium in terms of hedge against USD movement. These results mean that when the value of USD decreases the value of gold (silver, palladium and platinum) increases. 4.2. The study of the safe haven effect by using extremely dependence measures and copulas Firstly, we have studied the hedging ability of diamond prices and precious metals. Now, we concentrate in the safe haven properties where safe haven assets mean 2 assets are uncorrelated (weak safe haven) or negatively correlated (strong safe haven) during time of incertitude. We examine the capacity of precious metals and diamonds to cover against the extreme movement of USD 7
Finance Research Letters xxx (xxxx) xxx–xxx
R. Bedoui, et al.
Table 5 Tail dependence coefficients.
1 carat –USD effective rate 3 carat-USD effective rate 1 carat commercial-USD effective rate 1 carat fine –USD effective rate 0.5ct fine-USD effective rate 0.5 carat commercial-USD effective rate Gold-USD effective rate Silver-USD effective rate Palladium-USD effective rate Platinum-USD effective rate Rhodium-USD effective rate 1 carat –EUR/USD 3 carat-EUR/USD 1 carat fine –EUR/USD 1 carat fine-EUR/USD 0.5 carat commercial –EUR/USD 0.5 carat fine-EUR/USD Gold-EUR/USD Silver-EUR/USD Palladium-EUR/USD Platinum-EUR/USD Rhodium-EUR/USD
Copula
Lower tail
Upper tail
Frank Gumbel Clayton Clayton Plackett Clayton Student Normal Student Normal Normal Frank Normal Plackett Clayton Student Student Student Normal Plackett Student Clayton
0 0.01435 0 0 0 0 0.00137188 0 0.0001030574 0 0 0 0 0 0 3.361909×10−5 0.001161447 0.01679122 0 0 0.00128912 0
0 0 3.989733×10−29 0 0 0 0.00137188 0 0.0001030574 0 0 0 0 0 0 3.361909×10−5 0.001161447 0.01679122 0 0 0.00128912 0
exchanges rates. Copula has capacity to detect the dependence of extreme movements between the two variables studied. According to Table 5,6 we observe that for all pairs the tail dependence close or equal to zero. Hence, we can say that all diamonds and precious metals serve as a weak safe haven asset for USD depreciation. Now, we apply a less statistical and more arbitrary approach to deal with the safe haven property. We will focus on period of crises and high incertitude. We define the sub period of subprime crisis in 2007 and peaked in September until February 17 th 2011, thus we get 840 observations. We will study the dependence structure between diamonds and USD rates against precious metals and USD rates during the window of 25 days and the whole sub period to investigate if the safe haven property is due to a panic reaction of the investors. The 25 window days are considered the 25 first trading days of crisis and are from September 2nd to October 7th 2008. In light of the results of Table 6, we remark that diamonds exhibit safe haven ability against USD movement only during the window period. This may be due to an exhaustive swap for investors from risky assets to safer ones. Moreover, gold keeps its role as a weak safe haven against all exchange rates during the whole period and the window of 25 first trading days whereas, platinum, palladium and rhodium have not capacity to act as a safe haven for the USD depreciation against JPY7during the subprime crisis. That is due to the decreasing of platinum (palladium and rhodium) trades since the peak of 2008 in Japan. To conclude, in time of market turbulence gold offers better protection than diamond for investors who seek to protect against USD movement. 5. Conclusion The developments of financial markets as well as the globalization have grown the amount of uncertainty and volatility which impact the investor's decisions. Therefore, they seek to reduce the volatility by holding “the flight to quality effect” where they diversify their portfolio with safe assets. Recently, precious metals have played an important role as an alternative asset due to several criteria which present a security for investors especially gold. Indeed, gold has long been used as a safe haven against currency devaluations. However, the increasing of gold prices after the global financial crisis leads investors looking for the new alternative investment where diamonds have been introduced as an interesting alternative investment. Our results show that diamonds and rhodium have a weak hedging ability against the nominal USD exchange rates. On the other side, only 1 ct and 0.5 ct fine diamond indices serve as a weak hedge against USD effective rate. While precious metals (except rhodium) show a strong hedging ability against both nominal and effective USD rate. Hence, gold, silver, palladium and platinum outperform diamonds and rhodium in terms of hedging ability against USD movement. Our finding for the safe haven study reveals that all pairs have a tail independence structure. Therefore, precious metals and diamonds serve as a weak safe haven assets against US dollar depreciation. Finally, we examine the tail dependence in high moment of uncertainty, we conclude that both precious metals and diamonds act as a weak safe haven against USD movement. Our study gives a new insight in the relation between diamonds and exchange rates on average, as well as during extreme movement and increasing incertitude. Indeed, we find evidence that investing in precious metals rather than diamonds is better choice for investors seeking to protect their investment against USD depreciation value.Hence, diamonds tend not to function well as 6 7
The tables of GBP/USD and JPY/USD are available on request. The rank correlation for JPY/USD and GBP/USD are available on request. 8
Finance Research Letters xxx (xxxx) xxx–xxx
R. Bedoui, et al.
Table 6 Rank correlation between diamond, precious metals and exchange rates during the subprime crisis.
1 carat 3 carat 1 carat commercial 1carat fine 0.5 carat commercial 0.5 carat fine Gold Silver Palladium Platinum Rhodium
Sub period September 2008 to February 2011 EUR/USD USD (effective rate) Spearman Kendall Spearman Kendall
Window of 25 days EUR/USD Spearman Kendall
USD (effective rate) Spearman Kendall
0.0100 0.0080 0.0276 −0.0554 −0.0029 −0.0090 0.2912 0.1965 0.2376 0.2493 0.0016
0.0786 0.0009 0.2520 0.3053 0.1678 0.6591 0.3123 0.1215 0.4176 0.4407 0.2774
0.2215 0.0060 −0.2767 −0.1719 −0.2880 −0.3962 −0.6364 −0.5514 −0.3677 −0.4298 −0.3663
0.0076 0.0064 0.0190 −0.0359 −0.0026 −0.0056 0.2003 0.1326 0.1616 0.1704 5.7×10−4
0.0163 0.0262 0.0060 −0.0121 −0.0285 0.0022 −0.4681 −0.3502 −0.3987 −0.3761 −7.3×10−4
0.0128 0.0209 0.0050 −0.0076 −0.0178 7.4548×10−4 −0.3328 −0.2418 −0.2760 −0.2623 −4.3×10−4
0.0523 0.0036 0.1621 0.2174 0.1008 0.4862 0.2332 0.0672 0.3327 0.3123 0.2055
0.1663 0.0026 −0.2095 −0.1225 −0.1896 −0.2806 −0.4704 −0.3992 −0.2693 −0.3123 −0.2413
a safe haven and hedge for USD movement, but should still be included within a portfolio as an effective diversifier. For future researches, it may be interesting to study the hedging and safe haven properties of precious metals and diamond against other currencies. Supplementary materials Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.frl.2019.08.001. References Agyei, S.A., Gounopoulos, D., Mazouz, K., 2014. Does gold offer a better protection against losses in sovereign debt bonds than other metals? J. Bank. Financ. 40, 507–521. Auer, B.R., 2014. Could diamonds become an investor's best friend? Rev. Managerial Sci. 8 (3), 351–383. Auer, B.R., Schuhmacher, F., 2013. Diamonds—A precious new asset? Int. Rev. Financ. Anal. 28, 182–189. Baur, D., Lucey, B., 2010. Is gold a hedge or safe haven? An analysis of stocks bonds and gold. Financial Rev. 45, 217–229. Baur, D.C., McDermott, T.K., 2010. Is gold a safe haven? International evidence. J. Bank. Financ. 34, 1886–1898. Bedouia, R., Braeik, Goutte, S., Guesmi, K., 2018. On the study of conditional dependence structure between oil, gold and USD exchange rates. Int. Rev. Financ Anal. 59, 134–146. Capie, F., Mills, T.C., Wood, G., 2005. Gold as a hedge against the Dollar. J. Int. Financ. Mark. Instit. Money 15 (4), 343–352. Ciner, C., Gurdgiev, C., Lucey, B.M., 2013. Hedges and safe havens: an examination of stocks, bonds, gold, oil and exchange rates. Int. Rev. Financ. Anal. 29, 202–211. Clayton, D.G., 1978. A model for association in bivariate life tables and itsapplication in epidemiological studies of familial tendency in chronic disease incidence. Biometrika 65, 141–152. Conover, C.M., Jensen, G.R., Johnson, R.R., Mercer, J.M., 2009. Can precious metals make your portfolio shine? J. Invest. 18 (1), 75–86. Frank, M.J., 1979. On the simultaneous associativity of F(x; y) and x + y- F(x; y). Aequationes Math. 19, 194–226. Genest, C., Rivest, L., 2009). Goodness-of-fit tests for copulas: a review and a power study. Insurance: Math. Econ. 44 (2), 199–213. Glosten, L.R., Jagannathan, R., Runkle, D.E., 1993. On the relation between the expected value and the volatility of the nominal excess return on stocks. J. Fnance 48 (5), 1779–1801. Goodman, S., M. Bratt, and L. Brantberg. Perspectives on the Diamond Industry. McKinsey & Company, 2014. Gumbel, E.J., 1960. Bivariate exponential distributions. J. Am. Stat. Assoc. 55, 698–707. hood, M., Malik, F., 2013. Is gold the best hedge and a safe haven under changing stock market volatility? Rev. Financ. Econ. 22, 47–52. Joy, M., 2011. Gold and the US Dollar: hedge or haven? Financ. Res. Lett. 8 (3), 130–131. Kojadinovic, I., Yan, J., 2011). A goodness-of-fit test for multivariate multiparameter copulas based on multiplier central limit theorems. Stat. Comput. 21 (1), 17–30. Lucey, B.M., Li., S., 2013. What precious metals act as safe havens, and when? some us evidence. In: SSRN Scholarly Paper ID 2335402. Rochester, NY. Social Science Research. Plackett, R.L., 1965. A class of bivariate distributions. J. Am. Stat. Assoc. 60, 516–522. Pukthuanthong, K., Roll, R., 2011. Gold and the Dollar (and the euro, pound, and yen). J. Bank. Financ. 35 (8), 2070–2083. Pullen, T., Benson, K., Faff, R., 2014. A comparative analysis of the investment characteristics of alternative gold assets. Abacus 50 (1), 76–92. Renneboog, L., Spaenjers, C., 2012. Hard assets: the returns on rare diamonds and gems. Financ. Res. Lett. 9 (4), 220–230. Rémillard, B., Scaillet, O., 2009). Testing for equality between two copulas. J. Multivariate Anal. 100 (3), 377–386.
9
Contents lists available at ScienceDirect
Finance Research Letters journal homepage: www.elsevier.com/locate/frl
Diamonds versus precious metals: What gleams most against USD exchange rates? Rihab Bedouia,b,1, Khaled Guesmic, Saoussen Kalaia, Thomas Porcherd,
⁎
a
The Institute of Higher Business Studies of Sousse, Sousse, Tunisia University of Paris Ouest Nanterre La Défense, 200 avenue de la République, 92000 Nanterre Cedex, France Climate Change and Energy Transition Chair, IPAG Business School Paris, Visiting Professor, Telfer School of Management, University of Ottawa, Ottawa, Canada d Paris School of Business, PSB, 59 Rue Nationale, 75013, Paris, France b c
ARTICLE INFO
ABSTRACT
Keywords: Copulas Diamonds Precious metals Alternative asset Safe-haven, Hedge USD depreciation
Historically, commodity market, particularly the metal market has been used as a hedge for stock market and currencies during time of distress. In this paper, we shed light on a new alternative asset and examine the hedging and safe haven ability of diamonds and five precious metals that is, gold, silver, palladium, platinum and rhodium by using copula process. Then, we compare the performance of diamond versus metals in terms of hedging and safe haven against USD depreciation. Our empirical results show that gold, silver, palladium and platinum outperform diamonds and rhodium in term of hedging against USD movement. Our finding for safe haven study reveals that both precious metals and diamonds serve as a weak safe haven.
1. Introduction The developments of financial markets as well as the globalization have increased the uncertainty and therefore the risk of exchange rates which lead investors to focus more and look for “the flight to quality effect”.2 Indeed, investors often consider the precious metals especially gold as an alternative investment to market volatility, exchange rate and inflation. Historically, the financial mediahave considered that gold can act as a safe haven in financial markets. Therefore, Baur and Lucey (2010) examine the usefulness of gold as a safe haven in extreme stock market volatility. Moreover, some papers have studied the gold's safe haven status with respect to stock market, bond market, currencies, as well as exchange movements (Capie et al. (2005), Baur and Lucey (2010); Baur and McDermott (2010); Joy (2011); Pukthuanthong and Roll (2011); Ciner et al. (2013); Pullen et al. (2014)).On the other side, a handful of studies investigate the role of other precious metals as a hedge and safe haven (Conovor et al. (2009); Lucey and Li (2013); Hood and Malik (2013); Agyei et al. (2014). Currently, the gemstones especially the diamond has been attracted by the financial media. In this order, Renneboog and Spaenjers (2012); Auer and Schumacher (2013) analyze the role of this new asset in the global financial system. They show that an investment in a diversified diamond portfolio can outperform a diversified stock market investment in a period of generally frail stock market. However, in turmoil market, gold has long been used as a safe haven against currency devaluation, inflation, and stock market crashes. It has historically been valuable, expensive, long lasting and an asset that
Corresponding author. E-mail address: [email protected] (T. Porcher). 1 Member of the Research laboratory for Economy, Management and Quantitative Finance LaReMFiQ 2 The Flight to quality is the act of moving capital away from “risky” investment and toward “safer” investment due to uncertainty about the overall economy. ⁎
https://doi.org/10.1016/j.frl.2019.08.001 Received 3 May 2019; Received in revised form 20 July 2019; Accepted 7 August 2019 1544-6123/ © 2019 Elsevier Inc. All rights reserved.
Please cite this article as: Rihab Bedoui, et al., Finance Research Letters, https://doi.org/10.1016/j.frl.2019.08.001
Finance Research Letters xxx (xxxx) xxx–xxx
R. Bedoui, et al.
holds its value when other assets are crashing. In the weakness of 2008–2009 Global Financial Crises “GFC”, investors have been attracted by diamonds. The great increase of gold demand after the GFC raised drastically the gold price, consequently created a potential bubble in the market. Thus, investors who want to protect their wealth seek an alternative investment, which is free risk and not yet overrun. Therefore, diamonds have introduced as an interesting alternative investment to secure investor's wealth. An analysis of the range of potential scenarios outlined by Goodman et al. (2014) suggest that the diamond industry can be a robust and profitable sector, which encourage more investors to use the asset as an alternative investment. Moreover, Auer (2014) examines the performance of diamond returns against precious metals and finds that a diversified diamond portfolio outperforms an investment in gold and silver in term of low risks. Therefore, it is interesting to study the usefulness of diamond as a safe haven and hedge against stock market crashes and exchange rate devaluation as well as to compare its performance with five precious metals (Gold, Silver, Palladium, Platinum and Rhodium). In this Paper, we examine the hedging and safe haven capacity of diamonds versus precious metals against USD movement using copula theory. Indeed, we find evidence that investing in precious metals rather than diamonds is better choice for investors seeking to protect their investment against USD depreciation value. Our finding is crucial because in our knowledge this is the first work that uses physical diamond (investment direct) and diamond indices (investment indirect) as well as five precious metals in context of hedging against exchange rates. Moreover, in this research we give more importance by extracting turbulence sub period and seeking a haven capacity of diamonds and precious metals at extreme movement and in period with high uncertainty that is not shown in other articles. This finding is of highly interest and importance for investors who are interested in diamonds to deal with risk management during extreme market volatility. Also, as diamond is a new addition to investment field, it is important to benefit from understanding the respective interaction between diamond index, diamond prices and the market. So, we use daily spot prices over the period from January 2, 2002 to July 19th, 2016. We estimate the copula parameters by using the Canonical Maximum Likelihood (CML) method and select the adequate copula by using goodness-of fit test. The paper is organized as follows: In Section 2, we discuss our empirical methodology and define the copula theory and its properties. In Section 3, we describe our data set. In Section 4, we study the safe haven and the hedge effect using copulas. Finally in Section 4, we give our conclusions and future extensions. 2. Methodology Our primary goal of this study is to explore the safe haven and hedging properties of diamonds versus precious metals against the exchange rate. Past studies investigate the hedge and safe haven properties without distinguishing between average and extreme shocks. Kaul and Sapp (2007) define the safe haven asset as an asset that investors acquire during periods of uncertainty. This asset does not co-move with the other asset during turmoil while Baur and Lucey (2010) provide a definition and a clear distinction between hedge and safe haven. Then, Baur and McDermott (2011) extend the research of Baur and Lucey (2010) by giving discrimination between the strong and weak safe haven and hedge properties as bellow: A weak (strong) hedge is defined as an asset that is uncorrelated (negatively correlated) with another asset or portfolio on average. A weak (strong) safe haven is defined as an asset that is uncorrelated (negatively correlated) with another asset or portfolio during extreme movement. Thus, in our work we follow these definitions to discriminate between hedge and safe haven abilities of precious metals and diamond. We use Copulas to model average and tail dependence and examine the hedge and safe haven abilities of precious metals and diamonds against USD exchange rates. For this we will follow the same methodology developed in Bedoui et al. (2018).Thus we use the Canonical Maximum likelihood (CML) to estimate the parameter of a panel of possible copula. Firstly, we estimate the margins using empirical distribution: T 1 F^i (x) = T t = 1 1I{Xi x } I = 1,....,p; where I is the indicator function. Then we apply the CML method. The procedure of this in two step:
• Transformation of the initial sample set into uniform variables, using the empirical marginal distribution: u^t = (u^1 , ….,u^N ) = (F^1 (x1t ), …, F^N (xNt ))
(1)
• Estimation of the copula parameters via the following relation: ^CLM = arg max
T t=1
LnC (u^1 , ….,u^N , )
(2)
For the marginal distribution, we consider the Golsten–Jagannathan–Rankle GARCH (GJR–GARCH) represented by Glosten et al., 1993. The GJR–GARCH models the asymmetry, but on the conditional variance. It gives more weight to negative shocks than the positive one which is the fact in financial series. Hence, The GJR–GARCH model is defined as: t
(3)
= z t t , z t followsawhitenoiseprocess
where: 2
Finance Research Letters xxx (xxxx) xxx–xxx
R. Bedoui, et al. q 2 t w
p
+
(
i
+ i It
2 i < 0) t i
2 j t j,
+
i=1
i = 1…p and j = 1…q
j=1
(4)
with:
w, q i=1
i
+
0 i, i and j q p + j=1 j i=1 i
<1
(5)
β j are the conditional variance term, γi are the asymmetric effect coefficient.and
It
i
=
1 if 0 if
t i t i
<0 >0
(6)
2.1. The goodness of fit testing It is important to determine how well the model fits the data and which model is the best. Therefore, there are different ways to select the adequate copula that gives the best dependence structure. 2.1.1. Graphical criterion This Scatter plot allows for a graphical overview about the adequacy quality of an estimated parametric copula and the empirical copula. Although it provides a view of the dependence structure, this graphical method can be used solely in the bivariate case whereas; our study is about the multivariate case. 2.1.2. Information criteria We select the model that minimizes the amount of Kullback–Leibler's inforamation. Among the many criterions that have been proposed in literature, the most commonly used are: a Bayesian Information Criterion (BIC)
BIC =
(7)
2l( ) + Kln (n)
where l(θ) is the log-likelihood of the estimated parameter θ, K is the number of parameters in the model and n is the size of the sample. a Akaike's Information Criterion (AIC)
AIC = 2k
(8)
2l ( )
where l(θ) is the log-likelihood of the estimated parameter θ, K is the number of estimated parameters in the model. The information criterions do not present a robust tool to judge the adequacy quality of the chosen copula; hence it is essential to use more powerful tools. The decision rule is as follows: We select the appropriate copula which maximises the log likelihood and minimises the AIC and BIC criterion 2.1.3. Goodness-of-fit test of Rémillard and Scaillet 2009 According to Genest et al. (2009), the Goodness-of-fit test is the most powerful test which based on the distance between the empirical copula and the parametric copula estimated by the null hypothesis. The Rémillard and Scaillet test is based on the statistic obtained by the parametric boostrap and presents a main drawback which is the computational cost when dealing with large sample. To reduce the time of computing from days to minutes, we follow the step of Ivan Kojadinovic et al. (2011) and use the goodnessof-fit based on the multiplier central limit theorems inspired by the work of The Rémillard and Scaillet (2009). Therefore, this test is based on comparing between the empirical copula Cn and the parametric estimated copula C n . n
=
n (Cn
C
n)
The test statictics lay on the Von–Mises distances:
Sn =
(u)2dCn (u )
More Sn is higher, the probability to reject H0 increase. The p-value of the test is given by specially adopted Monte Carlo methods. 3
Finance Research Letters xxx (xxxx) xxx–xxx
R. Bedoui, et al.
The adequate copula is the copula with the highest p-value. 3. Data Our primary goal of this study is to explore the safe haven and hedging properties of diamonds versus precious metals against the exchange rate to evaluate diamonds as a viable investment alternative. So, we use daily prices of five precious metals (gold, silver, platinum, palladium and rhodium), two diamond prices (D Flawless grade, 1 carat and 3 carat respectively); four polished diamond indices prices: 1 carat Commercial diamond index (1 ct com), 1 carat Fine diamond index (1ct Fine), 0.5 carat Commercial diamond index (0.5 ct com), 0.5 carat Fine diamond index (0.5 ct fine); as well as three USD nominal exchange rates and USD effective exchange rate over the period from January 1st, 2002 to July 19th, 2016. All the prices of diamonds, diamond indices and precious metals are measured in the US dollar per troy ounce except silver, which is priced in cent per troy ounce. Exchange rates are expressed in terms of USD per unit of foreign currency. In our case, it corresponds to the amount of USD per one unit of each of three major currencies in international trade: the Euro (EUR), The British pound Sterling (GBP), the Japanese Yen (JPY). Thus, an appreciation in the nominal exchange rate leads to depreciation in USD. Diamond prices are extracted from Data stream and the USD effective rate is extracted from the bank of England while the remaining data are downloaded from the “Quandl's Data Collections”. There are cases where stock markets in different countries were closed on some days during the observation period. To eliminate this discordance, we only deal with the daily data for days where all markets are open. We finally get 3388 valid observations.3 Fig. 1 presents the dynamics of the daily traded of diamond prices, diamond indices, precious metals and exchange rates. From Fig. 1, we can remark that all variables vary over time. Regarding diamond price, it is clear that the 1 carat diamond prices are less volatile than 3 carat prices while the movement of diamond indices is heavily influenced by the development of 1 carat indices. Moreover, Fig. 1 shows that after the global financial crisis 2008, all precious metals exhibit severity in the trend changes except gold, which is the more stable commodity comparing to other while rhodium exhibits the largest drop in price. However, as shown in Fig. 1 the USD nominal and effective exchange rates are unstable in time and exhibit more volatility than other variables. According to Tables 1a–c we show that the kurtosis for all variables is greater than three. Thus, all our distributions are Leptokurtic and having fat tail. Therefore, the probabilities of extremely realizations are higher than the normal distributions case. The skewness measures the asymmetry of the distribution. Negative skewness means that the distribution is skewed to left while positive skewness means that the distribution is skewed to the right. And zero values of skewness indicate symmetric distribution. In our case, Tables 1a–c, show that 1 carat diamond price; Gold; Silver; Palladium; Platinum; GBP/USD and USD effective rate have a negative skewness which indicates that the extreme values are located on the left side of the mean. While, all remaining variables have a positive skewness which means that the most values concentrated on the left side of the mean and extreme values are on the right side. 4. Empirical results To measure the degree of interdependence between variables with copula, it's important as a first step to fit our returns to deal with the autocorrelation and heteroskedasticity then we filter the log negative returns into an approximately i.i.d series. To capture the volatility cluster, we use the GJR–GARCH. This model gives more weight to negative movement, which is styled in the financial series means that negative shocks have a more important influence on volatility than positive ones. The GJR–GARCH (1, 1): the (1, 1) in parentheses is a standard notation in which the first number refers to how many autoregressive lags (ARCH terms) and the second one refers to the number of the moving average lags. According to Table 2, all variables fit to an AR (1)-GJR (1, 1)-GARCH (1, 1) model except the palladium and the platinum which are fitted to an AR (0)-GJR-GARCH (1, 1) model. In addition, Table 2 shows that the maximum likelihood results for β is very significant (approximately equal to 0.9) for all variables except the 1 carat diamond prices and 3 carat diamond prices (approximately is closed to 0). Therefore, the conditional volatility is past-dependent and very persistent over time for all series except the diamond prices (1 carat and 3 carat) 4.1. The study of the hedging effect by using copulas The copula is considered as the most appropriate tool to model the dependence between variables. We use the Canonical Maximum likelihood (CML) to estimate the parameter of the copula. Table 3 shows the results for the parametric copula model described above. Parameter estimates for the elliptical copula is negative for the pairs of USD effective rate and all diamond index and prices metals (except the 1 carat fine diamond index and the rhodium) while we find the opposite results for the EUR/USD rate. Moreover, we remark that the degrees of freedom for the t-copula are very large for mostly diamond prices and indices (v → ∞), then the t-copula converge to the normal copula. The estimated parameter values for the Placket copula (Placket, 1965) are all positive (for all pairs). Whereas, Frank copula (Frank, 1979) show evidence of positive and negative dependence. Examining (Clayton, 1978) and (Gumbel, 1960) copulas, the estimated parameters are quite equal to zero (1.4509*10−6) for Clayton copula and equal to one for Gumbel copula which admit independence structure for various pairs. After the copula fitting, an important question arises: Which copula to choose? To answer this question we use the AIC 3 There are cases where stock markets in different countries were closed on some days during the observation period. To eliminate this discordance, we only deal with the daily data for days where all markets are open. We finally get 3388 valid observations.
4
Finance Research Letters xxx (xxxx) xxx–xxx
R. Bedoui, et al.
Fig. 1. Dynamics of the daily traded of diamonds prices, diamond indices, precious metals and exchange rates.
(Akaike information criterion) and BIC (Bayesian information criterion) criterion as well as the Goodness-of-fit test. From Table 4, we observe that in the case of the pairs USD effective rate-precious metals, the Elliptical copulas offer the best performance and negative dependence with all metals except the rhodium. While for the case of USD effective rate-diamonds, the Archimedean copulas (Frank for 1ct diamond price, Gumbel for 3ct diamonds price, Clayton4 for 1ct commercial, 1ct fine and 0.5ct fine diamond indices) and placket copula (for 0.5ct commercial diamond index) perform better and admit a positive dependence structure except for 1ct and 4
(see Clayton, 1978). 5
Finance Research Letters xxx (xxxx) xxx–xxx
R. Bedoui, et al.
Table 1a Descriptive statistics for diamonds and diamond indices.
1 carat 3 carat 1 carat commercial 1 carat Fine 0.5 carat commercial 0.5 carat Fine
Mean(%)
S.deviation
Skewness
Kurtosis
Maximum
Minimum
Median(%)
0.00219 0.01663 −0.00008 0.00369 −0.00418 0.00048
0.0703 0.0356 0.0302 0.0356 0.0265 0.0348
−0.2812 0.2485 0.0912 0.0374 0.7205 0.4367
20 123 8.1 8.2 17.9 8.7
0.5527 0.5979 0.1930 0.2065 0.2561 0.1975
−0.6243 −0.6071 −0.2072 −0.1937 −0.2462 −0.2062
0 0 0 0 0 0
Table 1b Descriptive statistics for Precious metals.
Gold Silver Palladium Platinum Rhodium
Mean(%)
S.deviation
Skewness
Kurtosis
Maximum
Minimum
Median(%)
0.04621 0.04345 0.01184 0.02405 −0.01121
0.0122 0.0228 0.0220 0.0151 0.0203
−0.3070 −0.4676 −0.4518 −0.7522 0.1337
7.7 11.5 7.6 12 44
0.0759 0.1828 0.1092 0.0843 0.3127
−0.0960 −0.1869 −0.1786 −0.1728 −0.2336
0.05971 0.05739 0 0.05935 0
Table 1c Descriptive statistics for exchange rates.
GBP/USD JPY/USD EUR/USD USD*
Mean(%)
S.deviation
Skewness
Kurtosis
Maximum
Minimum
Median(%)
−0.00295 0.00646 0.00604 -xw0.00549
0.0062 0.0084 0.0081 0.0047
−1.0284 0.5983 0.6405 −0.2806
16.1 103 90.2 6.3
0.0354 0.1685 0.1596 0.0228
−0.0849 −0.1629 −0.1433 −0.0415
0 0 0.01293 −0.00093
Notes: The Kurtosis represents the fourth moment of the random variable. It is a measure of the “heavy tails”. We use this measure to compare the distribution to the normal one which had a kurtosis equal to three. Therefore, distributions with a kurtosis more than three are “Leptokurtic” and kurtosis less than three are “Platykurtic”. ⁎ mean effective rate. Table 2 GJR estimation. C 1 carat 3 carat 1 carat Commercial 1carat Fine 0.5 carat Commercial 0.5 carat Fine Gold Silver Palladium Platinum Rhodium GBP/USD JPY/USD EUR/USD USD*
AR(1) −11
−1.5542×10 −5.8253×10−9 −6.3898×10−5 −6.1466×10−5 −2.6855×10−5 −4.3712e×10−5 0.00067433 0.00072299 0.00029695 0.0005666 2.4712×10−9 0.00011779 −3.3631×10−5 0.0002141 −2.7994×10−5
W −6
−1.0327×10 2.4591×10−7 −0.040551 −0.049438 −0.0061665 −0.021429 −0.010181 −0.085838 0.056457 0.03562 −0.060308 −0.0077321 −0.030371
−7
2 × 10 2 × 10−7 2 × 10−7 2 × 10−7 2 × 10−7 2 × 10−7 1.2212×10−6 2.9633×10−6 5.889×10−6 2.8138×10−6 2 × 10−7 2 × 10−7 1.2541×10−6 4.5469×10−7 2 × 10−7
β
α
v
δ
0 0.007254 0.87008 0.85491 0.88644 0.84401 0.95119 0.95407 0.90266 0.91868 0.028806 0.945 0.90453 0.9479 0.95324
0.86999 1.9658×10−5 0.25984 0.29018 0.22712 0.31199 0.052406 0.060476 0.10416 0.078427 1.0181 0.045246 0.077773 0.035854 0.040831
2 2 2.557 2.5972 2.2218 2.386 5.572 4.6768 4.3957 5.9129 2.0654 8.1053 4.6543 5.4795 7.2644
0.26003 7.2747×10−5 −0.25984 −0.29018 −0.22712 −0.31199 −0.02119 −0.035975 −0.016728 −0.015465 −0.093818 0.01234 −0.010397 0.012384 −0.0045927
Notes: W is a Constant. β and α are GARCH(1) and ARCH(1) processes. v and δ are the degree of freedom Leverage (1).
0.5ct fine diamond indices where the parameters values of Clayton are close to 0 which indicate an independence structure. Our results reveal that precious metals except rhodium can be a strong hedge whereas only 1ct and 0.5ct fine diamond indices serve as a weak hedge against the USD effective rate. For the case of EUR/USD (i.e. GBP/USD and JPY/USD)5 exchange rate, we find different adequate copulas. These copulas reveal an independence structure with some diamond indices and Rhodium which indicate that diamond indices and rhodium can act as a weak hedge against USD movement. On the other hand, the relationship between precious
5
The tables of GBP/USD and JPY/USD are available on request. 6
Finance Research Letters xxx (xxxx) xxx–xxx
R. Bedoui, et al.
Table 3 Estimates of the dependence parameters for different copula models.
1 carat –USD effective rate 3 carat-USD effective rate 1 carat commercial-USD effective rate 1 carat fine –USD effective rate 0.5 carat commercial- USD effective rate 0.5 carat fine-USD effective rate Gold-USD effective rate Silver-USD effective rate Palladium-USD effective rate Platinum-USD effective rate Rhodium-USD effective rate 1 carat –EUR/USD 3 carat-EUR/USD 1 carat commercial-EUR/USD 1 carat fine –EUR/USD 0.5 carat commercial –EUR/USD 0.5 carat fine-EUR/USD Gold-EUR/USD Silver-EUR/USD Palladium-EUR/USD Platinum-EUR/USD Rhodium-EUR/USD
Normal ρ
Student-t ρ
v
Plackett θ
Frank θ
Clayton θ
Gumbel θ
0.0272 0.0261 −0.0021 0.0030 −0.0397 −0.0045 −0.4826 −0.3054 −0.2678 −0.3274 0.0545 −0.0323 −0.0322 0.0199 −0.0197 0.0036 0.0092 0.2757 0.1988 0.1655 0.2254 −0.0485
0.0286 0.0262 −0.0018 0.0030 −0.0409 −0.0038 −0.4886 −0.3092 −0.2734 −0.3325 0.0547 −0.0330 −0.0329 0.0201 −0.0189 0.0043 0.0093 0.2778 0.1999 0.1695 0.2278 −0.0487
68.2725 70396 154.1428 1161300 40.5573 37.0889 6.9470 16.5020 14.3433 13.9094 4669200 39.2000 74.6154 37.1022 23.3169 24.4374 14.8911 12.235 26.9497 20.3712 20.7027 4669100
1.1281 1.0709 0.9698 0.9516 0.8949 0.9743 0.2716 0.4205 0.4780 0.4082 1.1442 0.8495 0.8576 1.0459 1.0119 1.0760 1.0410 2.0321 1.6038 1.5961 1.8351 0.9382
0.2124 0.1578 0.0129 2.1950×10−4 −0.2624 −0.0147 −3.2583 −1.8953 −1.6794 −2.0538 0.3439 −0.2114 −0.2141 0.1325 −0.0836 0.0455 0.0649 1.6661 1.1533 1.0258 1.3554 −0.2813
0.0218 0.0183 0.0106 1.4509×10−6 1.4509×10−6 1.4509×10−6 1.4509×10−6 1.4509×10−6 1.4509×10−6 1.4509×10−6 0.0504 1.4509×10−6 1.4509×10−6 0.0194 1.4509×10−6 0.0071 0.0180 0.3132 0.1977 0.1714 0.2416 1.4509×10−6
1.0091 1.0105 1.0008 1.0041 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0165 1.0000 1.0000 1.0099 1.0000 1.0043 1.0097 1.1931 1.1226 1.1024 1.1476 1.0000
Notes: The results of other variables database are available on request. The results of the AIC and BIC criterion are available on request. Table 4 Results of Goodness-of-fit test for different copulas.
1 carat –USD effective rate 3 carat-USD effective rate 1 carat commercial-USD effective rate 1 carat fine –USD effective rate 0.5 carat commercial- USD effective rate 0.5 carat fine-USD effective rate Gold-USD effective rate Silver-USD effective rate Palladium-USD effective rate Platinum-USD effective rate Rhodium-USD effective rate 1 carat –EUR/USD 3 carat-EUR/USD 1 carat commercial-EUR/USD 1 carat fine –EUR/USD 0.5 carat commercial –EUR/USD 0.5 carat fine-EUR/USD Gold-EUR/USD Silver-EUR/USD Palladium-EUR/USD Platinum-EUR/USD Rhodium-EUR/USD
Normal
Student-t
Frank
Plackett
Clayton
Gumbel
0.01648 0.1224 0.473 0.1993 0.8237 0.6998 0.07742 0.1943 0.512 0.2183 0.05544 0.2652 0.4091 0.5729 0.1474 0.6389 0.8307 0.2512 0.6069 0.3691 0.7098 0.524
0.01049 0.1314 0.451 0.2273 0.7957 0.6968 0.3651 0.1224 0.7128 0.1983 0.05145 0.2193 0.3801 0.5799 0.1933 0.8237 0.9925 0.4311 0.4141 0.4151 0.7308 0.519
0.02647 0.06543 0.4461 0.1484 0.8516 0.6149 0.0004995 0.015485 0.02647 0.004496 0.02248 0.2772 0.3971 0.6179 0.1084 0.7408 0.8467 0.0004995 0.04545 0.7547 0.1513 0.2672
0.02348 0.08841 0.4421 0.1454 0.8796 0.6159 0.0004995 0.05145 0.05644 0.01049 0.02248 0.2742 0.4061 0.6439 0.13424 0.7438 0.8197 0.002498 0.05245 0.7997 0.1813 0.2672
0.007493 0.07143 0.6429 0.3002 0.07443 0.7727 0.0004995 0.0004995 0.0004995 0.0004995 0.02048 0.03746 0.1044 0.491 0.3981 0.7977 0.8776 0.0004995 0.0004995 0.0004995 0.0004995 0.6149
0.007493 0.1643 – – – – – – – – 0.0004995 – – 0.473 – 0.8207 0.9535 0.0004995 0.007493 0.001499 0.0004995 –
metals (except rhodium) and nominal exchange rates is a positive which means that precious metals are strong hedge against USD movement. To summarize, diamonds and rhodium show a weak hedging ability against nominal exchange rates. On the other side, only 1 carat and 0.5 carat fine indices serve a weak hedge for the USD effective rate. While, precious metals exhibit a strong hedging ability against both nominal and effective exchange rates. Hence, we can conclude that gold, silver, palladium and platinum outperform diamonds and rhodium in terms of hedge against USD movement. These results mean that when the value of USD decreases the value of gold (silver, palladium and platinum) increases. 4.2. The study of the safe haven effect by using extremely dependence measures and copulas Firstly, we have studied the hedging ability of diamond prices and precious metals. Now, we concentrate in the safe haven properties where safe haven assets mean 2 assets are uncorrelated (weak safe haven) or negatively correlated (strong safe haven) during time of incertitude. We examine the capacity of precious metals and diamonds to cover against the extreme movement of USD 7
Finance Research Letters xxx (xxxx) xxx–xxx
R. Bedoui, et al.
Table 5 Tail dependence coefficients.
1 carat –USD effective rate 3 carat-USD effective rate 1 carat commercial-USD effective rate 1 carat fine –USD effective rate 0.5ct fine-USD effective rate 0.5 carat commercial-USD effective rate Gold-USD effective rate Silver-USD effective rate Palladium-USD effective rate Platinum-USD effective rate Rhodium-USD effective rate 1 carat –EUR/USD 3 carat-EUR/USD 1 carat fine –EUR/USD 1 carat fine-EUR/USD 0.5 carat commercial –EUR/USD 0.5 carat fine-EUR/USD Gold-EUR/USD Silver-EUR/USD Palladium-EUR/USD Platinum-EUR/USD Rhodium-EUR/USD
Copula
Lower tail
Upper tail
Frank Gumbel Clayton Clayton Plackett Clayton Student Normal Student Normal Normal Frank Normal Plackett Clayton Student Student Student Normal Plackett Student Clayton
0 0.01435 0 0 0 0 0.00137188 0 0.0001030574 0 0 0 0 0 0 3.361909×10−5 0.001161447 0.01679122 0 0 0.00128912 0
0 0 3.989733×10−29 0 0 0 0.00137188 0 0.0001030574 0 0 0 0 0 0 3.361909×10−5 0.001161447 0.01679122 0 0 0.00128912 0
exchanges rates. Copula has capacity to detect the dependence of extreme movements between the two variables studied. According to Table 5,6 we observe that for all pairs the tail dependence close or equal to zero. Hence, we can say that all diamonds and precious metals serve as a weak safe haven asset for USD depreciation. Now, we apply a less statistical and more arbitrary approach to deal with the safe haven property. We will focus on period of crises and high incertitude. We define the sub period of subprime crisis in 2007 and peaked in September until February 17 th 2011, thus we get 840 observations. We will study the dependence structure between diamonds and USD rates against precious metals and USD rates during the window of 25 days and the whole sub period to investigate if the safe haven property is due to a panic reaction of the investors. The 25 window days are considered the 25 first trading days of crisis and are from September 2nd to October 7th 2008. In light of the results of Table 6, we remark that diamonds exhibit safe haven ability against USD movement only during the window period. This may be due to an exhaustive swap for investors from risky assets to safer ones. Moreover, gold keeps its role as a weak safe haven against all exchange rates during the whole period and the window of 25 first trading days whereas, platinum, palladium and rhodium have not capacity to act as a safe haven for the USD depreciation against JPY7during the subprime crisis. That is due to the decreasing of platinum (palladium and rhodium) trades since the peak of 2008 in Japan. To conclude, in time of market turbulence gold offers better protection than diamond for investors who seek to protect against USD movement. 5. Conclusion The developments of financial markets as well as the globalization have grown the amount of uncertainty and volatility which impact the investor's decisions. Therefore, they seek to reduce the volatility by holding “the flight to quality effect” where they diversify their portfolio with safe assets. Recently, precious metals have played an important role as an alternative asset due to several criteria which present a security for investors especially gold. Indeed, gold has long been used as a safe haven against currency devaluations. However, the increasing of gold prices after the global financial crisis leads investors looking for the new alternative investment where diamonds have been introduced as an interesting alternative investment. Our results show that diamonds and rhodium have a weak hedging ability against the nominal USD exchange rates. On the other side, only 1 ct and 0.5 ct fine diamond indices serve as a weak hedge against USD effective rate. While precious metals (except rhodium) show a strong hedging ability against both nominal and effective USD rate. Hence, gold, silver, palladium and platinum outperform diamonds and rhodium in terms of hedging ability against USD movement. Our finding for the safe haven study reveals that all pairs have a tail independence structure. Therefore, precious metals and diamonds serve as a weak safe haven assets against US dollar depreciation. Finally, we examine the tail dependence in high moment of uncertainty, we conclude that both precious metals and diamonds act as a weak safe haven against USD movement. Our study gives a new insight in the relation between diamonds and exchange rates on average, as well as during extreme movement and increasing incertitude. Indeed, we find evidence that investing in precious metals rather than diamonds is better choice for investors seeking to protect their investment against USD depreciation value.Hence, diamonds tend not to function well as 6 7
The tables of GBP/USD and JPY/USD are available on request. The rank correlation for JPY/USD and GBP/USD are available on request. 8
Finance Research Letters xxx (xxxx) xxx–xxx
R. Bedoui, et al.
Table 6 Rank correlation between diamond, precious metals and exchange rates during the subprime crisis.
1 carat 3 carat 1 carat commercial 1carat fine 0.5 carat commercial 0.5 carat fine Gold Silver Palladium Platinum Rhodium
Sub period September 2008 to February 2011 EUR/USD USD (effective rate) Spearman Kendall Spearman Kendall
Window of 25 days EUR/USD Spearman Kendall
USD (effective rate) Spearman Kendall
0.0100 0.0080 0.0276 −0.0554 −0.0029 −0.0090 0.2912 0.1965 0.2376 0.2493 0.0016
0.0786 0.0009 0.2520 0.3053 0.1678 0.6591 0.3123 0.1215 0.4176 0.4407 0.2774
0.2215 0.0060 −0.2767 −0.1719 −0.2880 −0.3962 −0.6364 −0.5514 −0.3677 −0.4298 −0.3663
0.0076 0.0064 0.0190 −0.0359 −0.0026 −0.0056 0.2003 0.1326 0.1616 0.1704 5.7×10−4
0.0163 0.0262 0.0060 −0.0121 −0.0285 0.0022 −0.4681 −0.3502 −0.3987 −0.3761 −7.3×10−4
0.0128 0.0209 0.0050 −0.0076 −0.0178 7.4548×10−4 −0.3328 −0.2418 −0.2760 −0.2623 −4.3×10−4
0.0523 0.0036 0.1621 0.2174 0.1008 0.4862 0.2332 0.0672 0.3327 0.3123 0.2055
0.1663 0.0026 −0.2095 −0.1225 −0.1896 −0.2806 −0.4704 −0.3992 −0.2693 −0.3123 −0.2413
a safe haven and hedge for USD movement, but should still be included within a portfolio as an effective diversifier. For future researches, it may be interesting to study the hedging and safe haven properties of precious metals and diamond against other currencies. Supplementary materials Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.frl.2019.08.001. References Agyei, S.A., Gounopoulos, D., Mazouz, K., 2014. Does gold offer a better protection against losses in sovereign debt bonds than other metals? J. Bank. Financ. 40, 507–521. Auer, B.R., 2014. Could diamonds become an investor's best friend? Rev. Managerial Sci. 8 (3), 351–383. Auer, B.R., Schuhmacher, F., 2013. Diamonds—A precious new asset? Int. Rev. Financ. Anal. 28, 182–189. Baur, D., Lucey, B., 2010. Is gold a hedge or safe haven? An analysis of stocks bonds and gold. Financial Rev. 45, 217–229. Baur, D.C., McDermott, T.K., 2010. Is gold a safe haven? International evidence. J. Bank. Financ. 34, 1886–1898. Bedouia, R., Braeik, Goutte, S., Guesmi, K., 2018. On the study of conditional dependence structure between oil, gold and USD exchange rates. Int. Rev. Financ Anal. 59, 134–146. Capie, F., Mills, T.C., Wood, G., 2005. Gold as a hedge against the Dollar. J. Int. Financ. Mark. Instit. Money 15 (4), 343–352. Ciner, C., Gurdgiev, C., Lucey, B.M., 2013. Hedges and safe havens: an examination of stocks, bonds, gold, oil and exchange rates. Int. Rev. Financ. Anal. 29, 202–211. Clayton, D.G., 1978. A model for association in bivariate life tables and itsapplication in epidemiological studies of familial tendency in chronic disease incidence. Biometrika 65, 141–152. Conover, C.M., Jensen, G.R., Johnson, R.R., Mercer, J.M., 2009. Can precious metals make your portfolio shine? J. Invest. 18 (1), 75–86. Frank, M.J., 1979. On the simultaneous associativity of F(x; y) and x + y- F(x; y). Aequationes Math. 19, 194–226. Genest, C., Rivest, L., 2009). Goodness-of-fit tests for copulas: a review and a power study. Insurance: Math. Econ. 44 (2), 199–213. Glosten, L.R., Jagannathan, R., Runkle, D.E., 1993. On the relation between the expected value and the volatility of the nominal excess return on stocks. J. Fnance 48 (5), 1779–1801. Goodman, S., M. Bratt, and L. Brantberg. Perspectives on the Diamond Industry. McKinsey & Company, 2014. Gumbel, E.J., 1960. Bivariate exponential distributions. J. Am. Stat. Assoc. 55, 698–707. hood, M., Malik, F., 2013. Is gold the best hedge and a safe haven under changing stock market volatility? Rev. Financ. Econ. 22, 47–52. Joy, M., 2011. Gold and the US Dollar: hedge or haven? Financ. Res. Lett. 8 (3), 130–131. Kojadinovic, I., Yan, J., 2011). A goodness-of-fit test for multivariate multiparameter copulas based on multiplier central limit theorems. Stat. Comput. 21 (1), 17–30. Lucey, B.M., Li., S., 2013. What precious metals act as safe havens, and when? some us evidence. In: SSRN Scholarly Paper ID 2335402. Rochester, NY. Social Science Research. Plackett, R.L., 1965. A class of bivariate distributions. J. Am. Stat. Assoc. 60, 516–522. Pukthuanthong, K., Roll, R., 2011. Gold and the Dollar (and the euro, pound, and yen). J. Bank. Financ. 35 (8), 2070–2083. Pullen, T., Benson, K., Faff, R., 2014. A comparative analysis of the investment characteristics of alternative gold assets. Abacus 50 (1), 76–92. Renneboog, L., Spaenjers, C., 2012. Hard assets: the returns on rare diamonds and gems. Financ. Res. Lett. 9 (4), 220–230. Rémillard, B., Scaillet, O., 2009). Testing for equality between two copulas. J. Multivariate Anal. 100 (3), 377–386.
9