Investing in Gold: Individual Asset Risk in the Long Run

Transcription

1 CENTRAL BANK OF CYPRUS EUROSYSTEM WORKING PAPER SERIES Invesing in Gold: Individual Asse Risk in he Long Run Anonis Michis June 2014 Working Paper

2 Cenral Bank of Cyprus Working Papers presen work in progress by cenral bank saff and ouside conribuors. They are inended o simulae discussion and criical commen. The opinions expressed in he papers do no necessarily reflec he views of he Cenral Bank of Cyprus or he Eurosysem Address 80 Kennedy Avenue CY-1076 Nicosia, Cyprus Posal Address P. O. Box CY-1395 Nicosia, Cyprus publicaions@cenralbank.gov.cy Websie hp:// Fax Papers in he Working Paper Series may be downloaded from: hp:// Cenral Bank of Cyprus, Reproducion is permied provided ha he source is acknowledged. 2

3 Invesing in gold: individual asse risk in he long run Anonis Michis 1 Absrac This sudy examines gold s conribuion o porfolio risk over differen ime scales. The analysis is based on wavele decomposiions of he variances and covariances associaed wih a porfolio ha includes gold, socks, 10-year governmen bonds and hree-monh Treasury bills. The resuls sugges ha gold provides he lowes conribuion o porfolio risk only when considered over medium- and long-erm invesmen horizons. Keywords: gold; asse risk; waveles; covariance JEL classificaion: G11; G15 1 The opinions expressed in his paper are hose of he auhor and do no necessarily reflec he views of he Cenral Bank of Cyprus or he Eurosysem. The auhor would like o hank Alex Michaelides, Chrisos Savva and Panayiois Theodossiou for helpful commens and suggesions. Correspondence: Anonis A. Michis, Saisics Deparmen, Cenral Bank of Cyprus, 80 Kennedy Avenue, P.O.Box 25529, CY-1395, Nicosia, Cyprus. AnonisMichis@cenralbank.gov.cy 3

4 1. Inroducion Unlike mos financial asses used for diversificaion, gold does no bear a couner-pary risk. I is a universally acceped asse ha is commonly used as a sore of value and is characerized by high liquidiy. An imporan diversificaion propery of gold is is negaive correlaion wih many asse classes commonly used in invesmen porfolios. This is paricularly rue for US socks and porfolios having a large porion of equiies. Technically, gold has been associaed wih hree main properies when used in a porfolio conex. Firs, i reduces negaive skewness and he impac of ouliers on he disribuion of reurns, providing a closer approximaion o he normal disribuion. Second, is diversificaion properies are no negaed during periods of unanicipaed inflaion. Third, i improves porfolio performance during periods of financial sress (see, Sco-Ram, 2002, p. 137). In his sudy, a wavele analysis is used o obain ime scale decomposiions of he variances and covariances associaed wih a porfolio of asses ha includes gold, socks, 10-year governmen bonds and hree-monh reasury bills. The ime scale decomposiions generaed by waveles permi an evaluaion of gold s conribuion o porfolio risk over differen cycles. The resuls sugges ha gold provides he lowes conribuion o porfolio risk and is an effecive diversifier only when considered over medium- and long-erm invesmen horizons. 2. Diversificaion properies and invesmen horizon Wih regard o inflaion, gold is known o provide a good hedge only when considered over long periods of ime (see, Fraser-Sampson, 2011, p. 169). Over shor periods, he 4

5 price of gold is highly volaile and hus less useful for hedging. Gold is herefore no very appropriae for invesors adoping a shor-erm, sraegic approach for quick reurns. In conras, i is highly valuable o invesors wih a long-erm orienaion and a passive sraegy of holding heir asses for long periods of ime. In addiion o inflaion, gold is also known o provide a good hedge agains he US dollar over periods when he value of he dollar weakens (Joy, 2011). Such periods are closely linked wih he macroeconomic condiions in he US economy, which are usually associaed wih business cycles ha expand over several monhs or years. In his case, posiions in gold are also more meaningful when considered as medium- o long-erm invesmens. Using copula mehods, Reboredo (2013) demonsraed ha gold provides boh a valuable hedge and a safe haven asse in periods of exreme US dollar movemens and effecively reduces risk in currency porfolios. A number of sudies have empirically invesigaed he diversificaion properies of gold. Gold s performance as a hedge or safe haven asse varies by asse class and marke. For example, Baur and McDermo (2010) showed ha gold is a good hedge and a safe haven for socks from maor European counries and he US, bu he same is no rue for Ausralia, Canada, Japan and he BRIC counries. Wih regard o bonds, Baur and Lucey (2010) showed ha gold canno be considered a safe haven for bonds from he US, he UK and Germany. In addiion, Agyei- Ampomah e al. (2014) found ha gold provides an effecive hedge for bonds from counries wih deb issues (e.g., Greece and Porugal) bu exhibis posiive co-movemen wih UK and German bonds in periods of high marke volailiy. This finding suggess ha invesors view high qualiy bonds and gold as subsiues. 5

6 Given he above menioned cyclical characerisics of gold as an invesmen asse, i is of ineres o examine is conribuion o porfolio risk across he cycle. Mos sudies invesigae he diversificaion properies of gold using acual marke- level daa. However, such daa canno provide any insigh wih regard o he diversificaion properies of gold over differen ime scales (or cycles). As a resul, i is no possible o examine how gold s individual asse risk in he conex of a porfolio differs among shor-, medium- and longerm cycles. This is an imporan disincion in he examinaion of gold as an invesmen asse. 3. Individual asse risk by ime scale 3.1. Wavele variance and covariance Square-inegrable funcions or signals can be decomposed a differen ime scales using sequences of local basis funcions ermed faher ( ) and moher ( ) waveles. They are defined as follows (see, Gallegai e. al., 2011): / 2 2 k, k 2 2 and / 2 2 k, k 2. 2 A decrease in he value of reduces he widh and doubles he frequency of he moher wavele, which enables a beer represenaion of he shor-erm, high-frequency oscillaions in he signal. In conras, he faher wavele is no affeced by changes in. I is designed o represen he smooh rend behavior in he daa. Changes in he value of k 6

7 shif he locaion of boh he faher and moher waveles, hus enabling beer adapaion o he local feaures of he daa. Using he faher and moher waveles, a muliresoluion approximaion of a signal can be formed as follows: k s ) d ( ).. d ( )... d ( ). (1) J, k J, k ( J, k J, k, k, k 1, k 1, k k k k The wavele coefficiens in equaion (1) are based on he following inegrals: sj, k J, k ( ) d and d, k, k ( ) d. The faher wavele coefficiens ( s J, k signal, and he moher wavele coefficiens ( ) capure he low-frequency rend behavior in he d, k ) capure all high-frequency, shor-erm oscillaions from he rend. Therefore, ime scales corresponding o higher values of are associaed wih long-erm cycles in he daa, and ime scales corresponding o small values of are associaed wih shor-erm cycles in he daa. A wavele muliresoluion analysis can be performed using eiher a discree wavele ransform (DWT) or a maximal overlap discree wavele ransform (MODWT). The DWT provides an orhogonal decomposiion of he signal bu is associaed wih wo limiaions: he sample size mus be of dyadic lengh (a power of 2) and he faher and moher wavele coefficiens are no shif-invarian (as a resul of he decimaion operaions hey are sensiive o circular shifs). 7

8 Alhough no exacly orhogonal, he MODWT is more efficien han he DWT and is also characerized by he following advanages: (i) for each ime scale i generaes vecors of wavele coefficiens ha have equal lengh wih he acual ime series, (ii) i can be used o analyze ime series of any lengh, and (iii) i is ranslaion-invarian; herefore, he wavele coefficiens are no affeced by shifs in he signal (see Kim and In, 2010). In pracice, he MODWT is compued wih a pyramid algorihm ha ieraively filers he ime series wih a scaling (low-pass) and a wavele (high-pass) filer o produce he vecors of wavele coefficiens (see, Gencay e. al., 2002, pp ). When working wih monhly ime series of lengh observaions, he generaed wavele coefficiens a scale 1 ( d 1) capure cyclical variaion over duraions of 2-4 monhs. Accordingly, he wavele coefficiens a scales 2 ( d 2 ) and 3 ( d 3 ) capure cyclical variaion over duraions of 4-8 and 8-16 monhs, respecively. This is he case up o level 8. For non-dyadic lengh ime series, he daa can be padded wih he las value of he series o increase he lengh o he nex power of 2, and hen perform he MODWT (see, Gencay e al., 2002, p. 144). Using he wavele coefficiens generaed by he MODWT, he wavele variance of a saionary process ( ), a ime scale, can be esimaed as follows (see, Percival and Walden, 2000, p. 306): T 1 ( L ~ 1 ( ) d, ). (2) T 8

9 The variances generaed by he wavele coefficiens a each ime scale effecively capure he variance of he acual ime series. As before, d, represens he scale wavele coefficiens of he process generaed by he MODWT. L ( 2 1)( L 1) 1 is he lengh of he wavele filer used o generae he scale wavele coefficiens and ~ T T L 1 refers o he number of coefficiens unaffeced by he boundary. Consequenly, he coefficiens ha make use of he periodic boundary condiions are no included in he variance esimaor. Similarly, he wavele covariance esimaor decomposes he covariance beween wo saionary processes ( and y ) ino differen ime scales as follows: T 1 L 1, ~ 1 y y ( ) d, d,. (3) T In his case, coefficiens ha make use of he periodic boundary condiions are also no included in he esimaor. These wavele variance and covariance esimaors were used by Gencay e al. (2005) o esimae he sysemaic risk (bea) of socks and by Kim and In (2010) o analyze opimal porfolio allocaion by ime scale Individual asse risk In his subsecion, he expressions for he wavele variance and covariance repored in equaions (2) and (3) above are used in he conex of he mean-variance porfolio framework o obain esimaes of he risk associaed wih a single asse (e.g., gold). To see his, consider a porfolio of N risky asses. The variance of he porfolio is equal o he 9

10 sum of all possible weighed covariances associaed wih he reurns ( r ) of he N risky asses: N N V r ) i1 h1 ( w w i h ih. To evaluae he conribuion of a single risky asse o oal porfolio risk, Copeland e al. (2005, p. 139) suggesed calculaing he parial derivaive of he porfolio variance wih respec o he weigh of he asse ( w is he percenage invesed in he i -h risky asse) as follows: i V ( r) w i N 2 2w 2 w. (4) i i h1 h ih Using he parial derivaive in (4) and he expressions for he wavele variance and covariance in (2) and (3), he risk associaed wih asse i, a ime scale, can be esimaed as follows: N 2 risk( i, ) 2w ( ) 2 w ( ). (5) i i h1 h ih In he nex secion, expression (5) is used in he conex of a porfolio of asses o calculae he risk associaed wih each class of asses. 10

11 4. Resuls and discussion In his secion, an equally weighed porfolio is considered ha includes gold, socks, 10- year governmen bonds and hree-monh Treasury bills (T-bills). The daa consis of monhly reurns for he period of Sepember 1991 o December Three maor economies are represened in he asse classes of he porfolio: Germany, he UK and he US. The daa for gold reurns were obained from he World Gold Council. For he oher asse classes he daa were obained from he OECD saisical daabase. Summary saisics of he reurns associaed wih each asse class are included in Table 1. Table 1 Summary saisics of reurns Germany UK US Socks Bonds T-bills Socks Bonds T-bills Socks Bonds T-bills Gold Mean S. Dev Min Max The reurns of he en asse classes included in Table 1 were analyzed wih he MODWT using a Daubechies leas asymmeric wavele filer of lengh 8. This filer was also used by Gencay e al. (2005) and Kim and In (2010) o analyze similar daa, and provided good resoluions of he daa used in his sudy. Following he wavele ransform, all possible wavele variances and covariances beween he en asse classes were esimaed for eigh ime scales using he esimaors in equaions (2) and (3). The esimaes were hen incorporaed ino expression (5) o calculae he individual risk associaed wih each asse class by ime scale. The resuls are presened in Table 2. 11

12 The shaded areas indicae he minimum values (lowes conribuions o risk) by ime scale. Gold provides he lowes conribuion o porfolio risk in ime scales 5-8 (negaive values indicae reducion of risk). These ime scales are associaed wih cyclical movemens of lengh monhs and are herefore more relevan o invesors wih a medium- o long-erm orienaion. Wih regard o ime scales 1-4 ha are associaed wih cyclical movemens of lengh 2-32 monhs, he lowes conribuion o risk is provided by US Treasury bills. Gold s conribuion o risk in ime scale 1 (cycles of lengh 2-4 monhs) is similar o socks, and in ime scales 2 and 3, exceeds ha of bonds. Table 2 Individual asse risk by ime scale Time Germany UK US Scale Socks Bonds T-bills Socks Bonds T-bills Socks Bonds T-bills Gold The shaded areas indicae minimum values. Furhermore, he resuls in ime scales 5-8 sugges ha socks are less risky when considered over long ime horizons. This finding is consisen wih he sudy of Kim and In (2010), who sugges he allocaion of greaer weighing o socks as he invesmen horizon lenghens, due o he mean revering propery ha characerizes sock reurns (see Barberis, 2000). 12

13 The resuls for gold confirm he findings presened in Secion 2. The price of gold is highly volaile in he shor erm and herefore enails a high conribuion o porfolio risk when considered over shor-erm invesmen horizons. Therefore, i is no appropriae for invesors adoping a shor-erm, sraegic approach o invesmens. In he long erm, gold is very useful for hedging due o is negaive correlaion wih he oher asse classes and effecively reduces porfolio risk. Therefore, i is highly valuable o invesors wih a long-erm orienaion. References Agyei-Ampomah, S., Gounopoulos, D., Mazouz, K., Does gold offer a beer proecion agains losses in sovereign deb bonds han oher meals? Journal of Banking and Finance, 40, Barberis, N., Invesing for he long-run when reurns are predicable. Journal of Finance, 55, Baur, D.G., Lucey, B.M., Is gold a hedge or a safe haven? An analysis of socks, bonds and gold. Financial Review, 45, Baur, D.G., McDermo, T.K., Is gold a safe haven? Inernaional evidence. Journal of Banking and Finance, 34, Copeland, T., Weson, J., Shasri, K., Financial Theory and Corporae Policy, fourh ed. Pearson Addison Wesley, Mass. Fraser-Sampson, G., Alernaive asses: invesmens for a pos-crisis world. John Wiley and Sons, Chicheser, UK. 13

14 Gallegai, M., Gallegai, M., Ramsey, J.B., Semmler, W., The US Wage Phillips Curve across Frequencies and over Time. Oxford Bullein of Economics and Saisics, 73, Gencay, R., Selcuk, F., Whicher, B., Muliscale sysemaic risk. Journal of Inernaional Money and Finance, 24, Gencay, R., Selcuk, F., Whicher B., An Inroducion o Waveles and Oher Filering Mehods in Finance and Economics. Academic Press, New York. Joy, M., Gold and he US dollar: hedge or heaven? Finance Research Leers, 8, Kim, S., In, F., Porfolio allocaion and he invesmen horizon: a muliscaling approach. Quaniaive Finance, 10, Percival, D.B., Walden, A.T., Wavele Mehods for Time Series Analysis. Cambridge Universiy Press, Cambridge. Reboredo, J.C., Is gold a safe haven of a hedge for he US dollar? Implicaions for risk managemen. Journal of Banking and Finance 37, Sco-Ram, R., Invesing in gold and precious meals, in: Jobman, D.R., (Ed.), The Handbook of Alernaive Asses, New York, John Wiley and Sons. 14