wgc - gold - hedging against tail risks

8/3/2019 WGC - Gold - Hedging Against Tail Risks

1/20

GOLD: HEDGING AGAINST TAIL RISK


2/20

The World Gold Councils mission is to stimulateand sustain the demand or gold and to createenduring value or its stakeholders. The organisationrepresents the worlds leading gold miningcompanies, who produce approximately 60% oglobal corporate gold mining production andwhose Chairmen and CEOs orm the Board o theWorld Gold Council (WGC).

As the gold industrys key market developmentbody, WGC works with multiple partners to create

structural shits in demand and to promote theuse o gold in all its orms; as an investment byopening new market channels and making goldswealth preservation qualities better understood;in jewellery through the development o the premiummarket and the protection o the mass market; inindustry through the development o the electronicsmarket and the support o emerging technologiesand in government aairs through engagement inmacro-economic policy issues, lowering regulatorybarriers to gold ownership and the promotion ogold as a reserve asset.

The WGC is a commercially-driven organisation andis ocussed on creating a new prominence or gold.It has its headquarters in London and operationsin the key gold demand centres o India, China,the Middle East and United States. The WGC isthe leading source o independent research andknowledge on the international gold market andon golds role in meeting the social and economicdemands o society.

About The World Gold Council


3/20

Gold: Hedging against tail risk

Executive summary 3

Why hedging against tail risk matters 5

The role o gold in reducing a potential loss 7

Asset and period selection 7

Finding optimal portolios 10

Reducing expected losses in a portolio by

using gold 11

The golden touch: managing risk

in periods o fnancial stress 12

Out-o-sample considerations:

past and present 13

Conclusion 14

Appendix 15

Contents

October 200


4/20


5/20



Executive summary

Gold plays many roles within an investors portolio. Itserves as a portolio diversier: it tends to have lowcorrelations to most assets usually held by institutionaland individual investors. It preserves wealth: goldis typically considered a hedge against infation,but it also acts as a currency hedge, in particular

against the dollar with which gold correlatesnegatively. Moreover, it helps to manage risk moreeectively by protecting against inrequent or unlikelybut consequential negative events, oten reerred toas tail risks. Here we explore this particular role.

In periods o economic expansion, and especiallyprior to 2007, many investors concentrated on returnseeking strategies at the expense o incurringhigher risk. While these kinds o strategies mayprove eective in some time periods, events such asthe recent 2007-2009 nancial crisis have broughtback into perspective alternative strategies thatplace more emphasis on risk management. Byusing lessons learned during these tough times,investors may be better prepared when a newunoreseen event occurs. It is not a matter o beingoverly cautious; these events may not be very likely,but they can substantially impact investors capitaland should be protected against. Moreover, thereare cost-eective strategies that can provide suchprotection without sacricing return. We show thatgold can be an integral part o these strategies orboth short- and long-term investors.

We believe golds role extends beyond aordingprotection in extreme circumstances. In previousstudies, the WGC has shown that including goldin a portolio can reduce the volatility o a portoliowithout necessarily sacricing expected returns.However, we now nd that portolios which include

gold are not only optimal in the sense o deliveringbetter risk-adjusted returns, but that they can alsohelp to reduce the potential loss. Specically, weshow that gold can decrease the Value at Risk(VaR). We nd that even relatively small allocations togold, ranging between 2.5% and 9.0%,1 helpreduce the weekly 1% and 2.5% VaR o a portolioby between 0.1% and 18.5% based on datarom December 87 to July 10. Moreover, lookingat past events typically considered to be tail risks,such as Black Monday, the LTCM crisis, the recent2007-2009 recession, etc., we nd that in 18 out o24 cases (75%) analysed, portolios which includedgold outperormed those which did not. In particular,in the period between October 07 and March 09,an asset allocation similar to a benchmark portolio,2which included an 8.5% allocation to gold, wasable to reduce the total loss in the portolio byalmost 5% relative to an equivalent portoliowithout gold. In other words, adding gold savedabout US$500,000 on a US$10mn investment.

1 Gold allocations within this range are consistent with the fndings o previous studies by the WGC. Importantly, investors who only have goldexposure in the orm o a commodity index tend to be under allocated. Golds typical weight in benchmark commodity indices, such as the S&PGoldman Sachs Commodity Index or the Dow-Jones UBS Commodity Index, is usually between 2% to 6%. Even a 10% allocation in one o theseindices implies a much smaller eective gold exposure o 0.2% to 0.6%.

2 We reer to a benchmark portolio as one which has a 50%-60% allocation to equities, 30%-40% to fxed income, and 5%-10% to alternative assets.


6/20


For more inormation, please contact:

Juan Carlos Artigas

Manager, Investment Research

[email protected]

Eily Ong

Manager, Investment Research

[email protected]

Johan Palmberg

Analyst, Investment Research

[email protected]

Louise Street


[email protected]

Nitin Tuteja


[email protected]

Marcus Grubb

Managing Director, Investment

[email protected]


7/20


Why hedging against tail risk matters

Most investors would agree that one o the primarypurposes o investment is to maximise returns,whether these are monetary or otherwise, andpreserve capital. However, there is a trade-o aninvestor makes with every investment: return versusrisk. In other words, risk is the price an investor hasto pay in his or her quest or higher returns. Thereis, however, no unique denition o risk. The mostobvious denition, and the one that many marketparticipants associate with, is volatility, i.e., howmuch uncertainty or variability there is surroundingthe expected return on an asset. There are, however,

other kinds o risks that can prove very important,especially in times o economic distress; or example,liquidity, credit, counterpar ty, market and event risk.

It is common or investors, in times o economicexpansion, to seek higher returns or their portoliosat the expense o taking on more risk, whether it isin the orm o higher volatility, lower liquidity, etc.Some academics debate whether this so-calledrisk appetite gradually changes over time. However,there are events that create structural shits inthe perception o risk and provide a betterunderstanding as to the extent o the damagethat risk causes when highly unlikely but extremelynegative events occur. The Great Recession whichstarted to unold by the end o 2007 and whoseeects we continue to eel, is one example o thesestructural changes. Ater experiencing substantiallosses in their portolios, both institutional andprivate investors alike have increased theirawareness o risk management. This is particularlytrue o long-term investors, such as pension unds,oundations and endowments, as well as individualssaving or retirement that need to preserve their capitalto meet uture claims. Partly, risk management

can be achieved with careul analysis and portoliodiversication, but investors need to dig deeperwhen it comes to protecting against systemic risk.It is also here that gold comes into play.

Gold is rst and oremost a portolio diversier.Gold is very liquid, with an estimated US$2.1tn in

bullion orm in the hands o investors, institutionaland private, as well as central banks, the IMF, etc.3 Inaddition, gold bullion has no credit or counterpartyrisk. Gold can also be shown to protect againstevents that are not necessarily requent (or likely) butwhich, when they occur, can substantially erode thecapital o an investors portolio in unexpected ways.These events are typically reerred to as tail risk, asthey produce observed returns that all in the tailo a distribution. In this study we concentrate onreturns that are more than two standard deviationsaway rom the mean.4

In Gold as a Strategic Assetand Gold as a TacticalHedge and Long-Term Strategic Asset, the WGChas shown how even moderate allocations to gold(2%-10%) can produce optimality in a portolio. Inother words, it helps increase the return per unit orisk in a portolio (i.e. achieve a higher inormationratio5). Here we show that gold does not only helpincrease expected (or average) risk-adjusted returns,it can also considerably mitigate the potential or lossin a portolio.

The rationale is relatively simple. Firstly, most portoliooptimisers assume that the returns rom an asset areclose to a normal distribution (i.e., they are symmetricand the majority o the returns 95% to be exact all within two standard deviations). In practice, thisis rarely the case. Many asset returns have skeweddistributions, commonly negatively skewed,6 as wellas heavy tails there are more observations thatoccur beyond two standard deviations than a normaldistribution would predict. Secondly, correlationsamong assets are not necessarily constant andwhile average correlations can be used to computethe optimal weights in a portolio, extreme conditions

can change how assets interact with one another inunexpected and typically unwanted ways.

3 Dempster, N. and J.C. Artigas (2010), An Investors Guide to the Gold Market, WGC.4 Depending on the likelihood o these occurrences (i.e. how ar into the tail o the distribution they lie), they are known as 2-sigma (2), 3-sigma (3)

or 6-sigma (6) events, where is the mathematical expression to denote standard deviation. While some defnitions put tail risk as 3-sigma events,in this study, we concentrate on 2-sigma events to acilitate the statistical techniques used

5 Inormation ratio is a measure o risk-adjusted returns. In passive investment strategies, it is usually defned as expected return o an asset or aportolio divided by its corresponding volatility.

6 Negatively skewed distributions have more outliers due to negative than due to positive returns.


8/20


Unlike other assets, gold tends to exhibit lowervolatility on negative returns than it does on positive

returns (chart 1). At an annualised volatility o15.3% o weekly returns rom January 87 to July10, negative returns tended to be less volatile atan annual rate o 14.4% while positive returns hadhigher volatility o 16.2%. Whereas the S&P 500had an annualised volatility o 17.3%, over the sameperiod, in which negative returns varied at a rate o

19.2% and positive returns at 15.1%. In other words,based on historical perormance, gold is less likely

to all by more than 2 x 15.3% = 30.6% (2-sigma) ina year than it is to rise by more than the same return.This is contrary to what tends to happen with equities.The economics behind this phenomenon are, in part,due to what is commonly known as fight-to-quality.As negative news hits the market (especially theequity market) and risk-aversion increases, investorsusually retreat rom equity and other risky assets intoassets that tend to protect wealth, such as Treasuriesand gold.7

In risk management and portolio theory, it is not only

individual volatilities that matter; it is also how assetsinteract with each other, i.e., their correlation structure.Gold tends to have little correlation with many assetclasses, thus making it a strong candidate or portoliodiversication. More importantly, unlike other assetstypically considered diversiers, golds correlation toother assets tends to change in a way that benetsportolio returns. For example, while gold correlationto US equities is usually not statistically signicant,on average, historically it tends to decrease as USequities all and increase when they rise (chart 2).

This behaviour is more evident when one comparesthe correlation o equities to gold and commodities

Chart 2: 1-year rolling correlation between weekly returns on gold (US$/oz) and equities compared to the S&P500 Index level

Dec-00 Nov-01 Oct-02 Sep-03 Aug-04 Jul-05 Jun-06 May-07 Apr-08 Mar-09 Feb-10

1.0

0.8

0.6

0.4

0.2

0

-0.2

-0.4

-0.6

-0.8

-1.0

Correlation

1600

1500

1300

1400

800

900

1000

1100

1200

700

600

Index level

S&P 500 (RHS)1 year rolling correlation b/w gold (US$/oz) and S&P 500 (LHS)

Source: London Bullion Market Association, Standard & Poors, WGC

Chart 1: Annualised volatility o positive and negative weekly

returns or gold (US$/oz) and S&P 500; Jan 87-Jul 10

20

16

12

8

4

0

Negative returns Positive returns

%

S&P 500Gold (US$/oz)

Source: London Bullion Market Association, Bloomberg, WGC

7 For a more in depth analysis on negative economic news and gold, see Roach S.K. and M. Rossi (2009), The Eects o Economic News onCommodity Prices: Is Gold Just Another Commodity?, IMF Working Paper.


9/20


in periods when equity returns all by more thantwo standard deviations rom zero (chart 3). FromJanuary 87 to July 10, the average weekly-returncorrelation o the S&P 500 and the S&P GoldmanSachs Commodity Index was 0.13; while thiscorrelation increased slightly in periods in whichequity returns rose by more than 2 to 0.14, itincreased even more to 0.47 when equities altered.Put simply, in economic and nancial downturns,most industrial-based commodities and equities tendto ollow a similar pattern. On the other hand, historyshows that golds correlation to equities became

more negative during these same periods. BetweenJanuary 87 and July 10, the average correlationbetween gold and the S&P 500 stood at -0.17.In periods in which equity returns rose by more than2, the correlation turned positive to about 0.09, butwhen equities ell by more than 2, the correlationcoecient dropped to -0.17. This is, by no means, astrong negative correlation, but it serves to exempliythe benets that gold can oer when managing theoverall risk o a portolio.

The role o gold in reducing apotential loss

Intuitively, the characteristics that gold exhibits interms o its perormance, volatility and correlation toother assets should help reduce potential lossesin a portolio. In this paper we show how, using acommon measure or maximum expected loss in agiven period o time, gold can be used to managerisk more eectively and, ultimately, protect aninvestors capital against potential losses in negativeeconomic conditions. Specically, we use Value atRiskto achieve this observation. While the analysisis based on historical perormance and uture

uncertainty can aect the results, the data showsthat golds useulness in protecting against systemicrisk can be proven in multiple occasions.

In nancial markets, Value at Riskor VaR is used tocalculate the maximum loss expected (or worstcase scenario) on an investment, over a given timeperiod and given a specied degree o condence.8Beyond a more rigorous mathematical denition,conceptually, VaR is simply a way o measuring howmuch an investor could expect to lose in a givenportolio, in the case o an unlikely and sometimesinrequent, yet possible, event occurring.9 There aremany methods to estimate the VaR in a portolio;we use the empirical distribution o the returns toallow or skewness (asymmetry) and kurtosis (heavyor light tails) typically ound in nancial data.10 Inother words, we compute the maximum possibleloss or a given degree o condence using thehistorical distribution o returns or each asset.

In general, VaR tends to be a unction o volatility;the higher the variability, the more an investor maylose. However, the heaviness o the tails in thedistribution o returns will also have an eect. The

greater the number o unlikely events that allbeyond two or three standard deviations to the let ozero, the higher the value at risk.

Asset and period selection

As previously discussed, beyond individualmeasures o risk and return, portolio theory relieson the covariance/correlation structure o multipleassets. Thereore, we use a collection o assetsrepresentative o a typical investment portolio,namely: cash, US Treasury and corporate bonds,

international debt rom developed and emerging

8 http://www.investopedia.com/articles/04/092904.asp.9 In statistical terms, the VaR o a portolio, at a given confdence level between zero and one, is the minimum loss, such that the probability that any

other loss exceeds that value, is not greater than (1 ) during a period o time.10 Alternatively, one can compute the mean and standard deviation o a portolio, or a given set o weights, and estimate the corresponding critical value

based on the desired confdence level using the assumption that returns ollow a normal distribution. Another method involves Monte Carlo simulations;here multiple return samples are drawn rom the empirical distribution o a given portolio, to subsequently compute the expected critical value.

Chart 3: Weekly-return correlation between equities, gold and

commodities when equities move by more than 2 standard

deviations; Jan 87-Jul 10

Correlation between S&P 500 and gold (US$/oz)

Correlation between S&P 500 and S&P GSCI

-0.5 -0.25 0 0.25 0.5

S&P 500 returnless than -2s

S&P 500 returnmore than +2s

Source: London Bullion Market Association, Bloomberg, WGC


10/20


markets, US and international equities, a commodityindex as well as gold as an asset class. Ideally, we

would use series going back as ar as 72, the yearby which the gold window had been closed and theyellow metal was allowed to foat reely. However, amodern investor typically holds many more assets ina portolio than those available in the 70s and early

80s, or or which data is unavailable or unreliable,such as high yield bonds, or emerging markets

sovereign debt and equities. Thus, the period underconsideration or this analysis spans rom January87 to July 10 or which most data series are available.Moreover, this period contains at least three businesscycles11 and includes multiple market crashes.12

Table 1: Perormance o selected assets in a model portolio; Jan 87-Jul 101

CAGR2 (%) Annualised

volatility3

(%) In. Ratio4

Weekly VaR (US$ 000s)5

Real Nominal 2.5% 1.0%

Gold (US$/oz) 1.8 4.7 15.3 0.31 451 590

JP Morgan 3-month T-Bill Index 2.1 5.0 1.0 5.05 - -

BarCap US Treasury Aggregate 4.0 7.0 4.8 1.46 130 166

BarCap Global ex US Treasury Aggregate 4.5 7.5 8.9 0.85 223 252

BarCap US Credit Index 4.6 7.6 5.2 1.48 138 175

BarCap US High Yield Index 5.3 8.3 8.2 1.01 209 338

JP Morgan EM Sovereign Debt Index6 10.2 13.0 12.8 1.02 358 566

MSCI US Equity Index 5.5 8.6 17.3 0.50 466 708

MSCI EAFE Equity Index 2.7 5.7 18.1 0.31 490 736

MSCI EM Equity Index 7.6 10.7 22.2 0.48 686 946

S&P Goldman Sachs Commodity Index 3.7 6.8 21.1 0.32 636 896

Note: Perormance based on total return indices except or gold in which spot price is used.

1) MSCI EM rom Dec 87 and JPMorgan EM sovereign debt index rom Dec 90; 2) compounded annual growth rate; 3) estimated using weekly returns;

4) ratio o nominal return and volatility, also known as avg. risk-adjusted return (a higher number indicates a better return per unit o risk);

5) Expected maximum loss during a week at a given conidence level (1-a) rom a US$10mn investment; 6) EMBI prior to Jan 00 and EMBI Global post

due to data availability.

Source: LBMA, JP Morgan, Barclays Capital, MSCI Barra, Standard & Poors, WGC

11 http://www.nber.org/cycles.html12 Not all data series are available going back to 72; however, we used the modifed likelihood ratio test o equality o covariances (also known as Box

test) to veriy the equivalence o the correlation structures o the available data series (namely, gold, commodities, US equities and US Treasuries) orthe longer time period. All tests were perormed at the 5% signifcance level, thus, we conclude that the analysis o this paper is robust and that theconclusions should hold using estimates over a longer time period.

Chart 4: Histograms o standardised weekly returns on gold and US equities

-4 -3 -2 -1 0 1 2 3 4

No. of standard deviations away from zero

Gold (US$/oz)

Cumulative 15.7%

0

5

10

15

20

25

30

%

-4 -3 -2 -1 0 1 2 3 4

No. of standard deviations away from zero

MSCI US Index

Cumulative 16.5%

0

5

10

15

20

25

30

%

Source: London Bullion Market Association, MSCI Barra, WGC


11/20


Table 1 shows the assets selected to construct themodel portolio, as well as their summary statistics

over the period, such as average return, volatility,inormation ratio (dened as nominal return dividedby volatility) and Value at Risk (VaR). While goldexhibits a lower inormation ratio than other assetslisted in the table, golds diversication propertiesmake it a valuable asset to hold in a portolio.Furthermore, the maximum expected loss in a givenweek rom a US$10mn investment in gold isUS$590,000 with 99% certainty (also called 1% VaR).In the case o the MSCI US Equity Index, the weekly1% VaR is US$708,000 even though its inormationratio is higher at 0.50. Moreover, the equivalent 1% VaR

or emerging markets (EM) sovereign debt isUS$566,000, only 4% lower than gold despite the actthat golds annualised volatility is 20% higher than EMdebt and its inormation ratio is considerably higher at1.02. Indeed, this is due to the act that EM debt,among many assets, has heavier tails than gold.

As inormative as the individual perormance statisticsare, a portolio is comprised o a collection o assets.In general, diversication allows an investor to obtaina desired (expected) return without taking as muchrisk as with an individual security. This principle isbased on the correlation structure o multiple assets,or the way they react to economic, nancial andgeopolitical news, and perhaps more relevant or ourdiscussion, their behaviour in times o unprecedentedand systemic risk.

Golds reaction to external actors such as nancialand economic conditions tends to benet investors

and, in particular, helps them manage risk moreeectively. Charts 5 and 6 show the correlation ogold to the assets relevant or our analysis. Duringthe January 87 to July 10 period, chart 5 shows theaverage correlation between weekly returns or goldand returns or all the other assets. In general, goldtends to have low correlations to most assetsincluding other commodities. For example, thecorrelation o gold to US equities was -0.07 duringthat period and 0.27 to commodities, as representedby the S&P Goldman Sachs Commodity Index (S&PGSCI). The highest correlation to gold among the

selected assets is with global Treasuries excludingthe US at 0.35. Chart 6 shows the weekly-returncorrelation between gold and other assets in periodsin which equity returns all by more than two standarddeviations, our proxy or an unlikely risky event.13

Unsurprisingly, most correlations all. Moreimportantly, the correlation to many risky assets,such as corporate debt and developed marketequities, turns negative, and golds low correlation toother commodities at 0.05 becomes statisticallyinsignicant. Unexpectedly, perhaps, the correlationto emerging markets sovereign debt increases to0.30 rom 0.13.

Chart 5: Correlation o weekly returns between gold

(US$/oz) and selected asset classes (US$);

Jan 87-Jul 10*

JPM 3-month T-bill Index

JPM US Treasury Index

BarCap Global Tsy Agg ex USBarCap US Credit

BarCap US High Yield

JPM EM sovereign debt

MSCI US

MSCI EAFE

MSCI EM

S&P GSCI

Gold (US$/oz)

1.00.750.50.250-0.25-0.5

Chart 6: Conditional correlation o weekly returns between

gold (US$/oz) and selected asset classes (US$) in periods

when US equity returns drop by more than two standard

deviations; Jan 87-Jul 10*

JPM 3-month T-bill Index

JPM US Treasury Index

BarCap Global Tsy Agg ex US

BarCap US Credit


JPM EM sovereign debt

MSCI US

MSCI EAFE

MSCI EM

S&P GSCI

Gold (US$/oz)

1.00.750.50.250-0.25-0.5

*Except or MSCI EM index (Dec 87-Jul 10) and JPMorgan EM sovereign debt index (Dec 90-Jul 10) due to data availability.

Source: London Bullion Market Association, Barclays Capital, JP Morgan

13 There are 30 such occurrences between Jan 87 and Jul 10.


12/20


0

Finding optimal portolios

In previous studies, the WGC has demonstrated thatadding gold to a portolio tends to increase risk-adjusted returns, in many cases expanding theecient rontier.14 In other words, by adding gold,an investor can obtain a desired expected returnwhile incurring less risk than an equivalent portoliowithout gold. We now nd that those portolios whichinclude gold are not only optimal in the sense oproducing better risk-adjusted returns, but that theyalso tend to reduce the potential loss in a portolio,i.e., they decrease the Value at Risk.

To nd the optimal weights employed to constructdierent sample portolios, we use ResampledEciency (RE) optimisation developed by Michaudand Michaud.15 We concentrate on two alternativescenarios. For each scenario, we apply projectedlong-term real returns, consistent with previousresearch notes, to remove a potential period bias.We then use the volatility and correlation estimates

based on weekly returns rom January 87 toJuly 10. In the rst scenario, we use average

correlations or the whole period as inputs orthe optimiser. This scenario produces portoliosdesigned to maximise expected returns over thelong run. For the second scenario, we use thecorrelation structure observed in periods o higherrisk, or when US equities ell by more than twostandard deviations, as explained in the previoussection. This scenario creates portolios constructedto maximise expected returns by taking advantageo asset interactions observed during periods ohigher risk. A summary o the projected returns andvolatilities used during portolio optimisation can be

ound in table 6 in the Appendix.

Portolio optimisation produces a myriad o dierentcombinations that orm the ecient rontier. Whileeach asset allocation that alls upon this rontier isconsidered optimal, or simplicity, we choose tocompare a nite number o portolios. For eachscenario, we nd optimal asset allocations with and

Table 2: Summary statistics and asset weight allocation or each o the selected portolios

Scenario 1: average correlation1 Scenario 2: high risk correlation3

Max. In. Ratio* Benchmark


w/o gold with gold w/o gold with gold w/o gold with gold w/o gold with gold

Expected annual return (%) 3.4 3.3 7.0 7.0 3.2 3.1 6.9 6.9

Annualised volatility (%) 3.4 3.3 11.8 11.8 2.4 2.3 11.9 11.7

Inormation ratio2 1.002 1.002 0.589 0.591 1.301 1.342 0.583 0.586

Portolio weights

Gold (US$/oz) - 3% - 6% - 4% - 9%

JP Morgan 3-month T-Bill Index 29% 30% 0% 0% 30% 34% 0% 0%

BarCap US Treasury Aggregate 36% 35% 8% 7% 37% 33% 15% 14%

BarCap Global ex US Treasury Agg 7% 6% 7% 7% 9% 7% 10% 9%

BarCap US Credit Index 3% 2% 2% 2% 0% 0% 1% 1%

BarCap US High Yield Index 11% 11% 5% 7% 17% 18% 7% 8%

JP Morgan EM Sovereign Debt 3% 3% 10% 8% 4% 3% 6% 5%

MSCI US Equity Index 4% 4% 19% 17% 0% 0% 21% 19%

MSCI EAFE Equity Index 2% 2% 15% 14% 0% 0% 9% 9%

MSCI EM Equity Index 3% 3% 25% 26% 2% 1% 25% 24%

S&P Goldman Sachs Commodity Index 2% 1% 8% 7% 0% 0% 5% 3%

1) Correlation estimation using all weekly returns rom Jan 87 to Jul 10; 2) expected return divided by volatility, also known as avg. risk-adjusted return

(a higher number indicates a better return per unit o risk); 3) correlation estimation using only weekly returns in which the MSCI equity index ell by more

than 2 std. deviations over the same period.

* Portolio selection based on allocations that achieved the maximum inormation ratio available. Portolio selection based on allocations that resembled benchmark portolio o 55% equities, 40% ixed income, and 5% alternative assets, with similar

expected returns.


14 Dempster, N. and J.C. Artigas (2009), Gold as a Tactical Hedge and Long-Term Strategic Asset, WGC, among others. For a comprehensive list oour publications, go to http://www.gold.org.

15 Michaud, R. and R. Michaud (2008) Efciency Asset Management: a practical guide to stock and portolio optimization and asset allocation,2nd edition, Oxord Press, New York.


13/20


without gold. We then choose: 1) the portoliowith the maximum risk-adjusted return; and 2) a

portolio with a similar composition to a typicalbenchmark allocation (50%-60% equities, 30%-40%xed income and 5%-10% alternative assets), suchthat the portolio with and without gold during theoptimisation have similar expected returns. Thereore,we compare a total o eight portolios.

Table 3 shows the expected return, volatility andinormation ratio or each portolio, as well as theweight assigned to each asset. On one hand, theselected portolios with maximum inormation ratiosproduced more conservative asset allocations,

with heavy weights in cash and xed income.16 Onthe other hand, optimal benchmark-like portoliosweighted xed income assets evenly among variousclasses when average correlations were used,while increasing exposure to cash and Treasuriesin the high risk scenario, as one would expect.Finally, allocations to gold ranged rom 3% to 9%,consistently with ndings in previous analysis.Considering that golds correlations to other assetsgenerally dropped in the high risk correlationscenario, it is not surprising that this scenario hadthe largest weight or gold at about 9%. Moreinterestingly, gold, unlike the commodity index, had

positive (and statistically signicant) allocations notonly in the selected portolios but throughout the

whole ecient rontier.

Reducing expected losses in a portolioby using gold

Relatively small allocations to gold can be shownto help investors reduce potential losses withoutsubstantially sacricing expected return. Using theempirical distribution o all asset returns romJanuary 87 to July 10, we compute average returns,volatilities and VaRs or each o the selectedportolios. We consistently nd that including gold in

a portolio delivers similar expected returns withlower volatilities, while reducing weekly VaR bybetween 0.1% and 18.5%. For example, usingaverage correlation estimates, adding gold to theportolio mix reduces the weekly 2.5% VaR by 6.9%or a maximum inormation ratio allocation and by18.5% when using a high risk portolio allocation.Similarly, using a benchmark-like portolio, includinggold reduces the weekly expected loss by between2.8% and 5.8% at a 97.5% condence level (2.5%VaR). Only in the benchmark-like portolio usingaverage correlation estimates, the weekly 1% VaR issimilar in both cases.

Table 3: Weekly Value at Risk (VaR) on a US$10mn investment or selected portolios with and without including gold;

Jan 87-Jul 10

Scenario 1: average correlation1 Scenario 2: high risk correlation2

Max. In. Ratio* Benchmark Max. In. Ratio* Benchmark

w/o gold with gold w/o gold with gold w/o gold with gold w/o gold with gold

Gold weight - 3% - 6% - 4% - 9%

Expected annual return (%) 6.6 6.5 8.1 8.0 6.6 6.5 7.9 7.7

Annualised volatility (%) 3.2 3.1 12.1 11.7 2.9 2.6 11.0 10.4

Inormation ratio3 2.06 2.13 0.67 0.68 2.31 2.50 0.72 0.74

2.5% VaR (US$ 000) 76 71 348 338 69 58 318 301

Gain (loss) by including goldin US$ 000 and %

US$ 000 4.9 9.6 10.7 17.5

% 6.9% 2.8% 18.5% 5.8%

1.0% VaR (US$ 000) 108 96 478 477 95 83 443 429

Gain (loss) by including goldin US$ 000 and %

US$ 000 12.2 0.5 12.2 14.0

% 12.7% 0.1% 14.7% 3.3%

1) Correlation estimation using all weekly returns rom Jan 87 to Jul 10; 2) correlation estimation using only weekly returns in which the MSCI equity

index ell by more than 2 std. deviations over the same period; 3) expected return divided by volatility, also known as avg. risk-adjusted return (a higher

number indicates a better return per unit o risk).

* Portolio selection based on allocations that achieved the maximum inormation ratio available. Portolio selection based on allocations that resembled benchmark portolio o 55% equities, 40% ixed income, and 5% alternative assets, with

similar expected returns;


16 Traditionally, a conservative portolio is one with little exposure to equities (domestic or international) and other alternative assets. These portoliostypically concentrate on cash and other fxed income assets. Conversely, an aggressive portolio places more weight to equities and alternativeinvestments.


14/20


2

The golden touch: managing risk inperiods o fnancial stress

We have established that, in general, there is a goodcase to be made or adding gold to a portolio.Indeed, expected losses tend to diminish withoutnecessarily sacricing return. We now show that, inmost periods o nancial stress, portolios whichinclude gold tend to perorm better (by either postinggains or reducing losses) than those without.To achieve this, we look back to periods, starting inJanuary 87, in which nancial markets experiencedan unexpected and negative shock that aectedmore than one asset class. We concentrate on six

such events: 1) the market crash around October87, also known as Black Monday, looking at the

perormance between August 25 and December 12o that year; 2) the Long-term Capital Management(LTCM) crisis, between July 20 and August 26,1998; 3) the Dot-com bubble burst in the periodsurrounding the dramatic drop in the NASDAQ index,between March 10, 2000 and April 4,17 2001; 4)September 11 terrorist attack, in the period betweenAugust 24 and September 21, 2001; 5) 2002 marketdownturn, as stocks ell sharply between March andJuly 2002; and 6) the nancial crisis o 2007-2009,also known as the Great Recession, betweenOctober 12, 2007 and March 6, 2009.

Table 4: Observed gain (loss) on a US$10mn investment or selected portolios with and without including gold during various

tail-risk events

Portolio using average correlation1


Portolio gain (loss)

in US$ 000Dierence

in US$ 000

Dierence

in %


in US$ 000Dierence

in US$ 000

Dierence

in %w/o gold with gold w/o gold with gold

Black Monday Aug 97 - Dec 87 88 111 22 25% -1,046 -868 178 17%

LTCM crisis Jul 98 - Aug 98 -194 -181 12 6% -1,258 -1,222 36 3%

Dot-com bubble Mar 00 - Apr 01 528 496 -32 -6% -1,420 -1,506 -86 -6%

9/11 Aug 01 - Sep 01 -184 -149 35 19% -1,174 -1,083 91 8%

02 downturn Mar 02 - Jul 02 151 171 20 13% -534 -463 71 13%

Great Recession Oct 07 - Mar 09 -211 -79 132 63% -4,049 -3,719 330 8%

Gold weight - 3% - 6%

Annualised return (%) Jan 87 - Jul 10 6.6 6.5 8.1 8.0

Portolio using high risk correlation2



in US$ 000Dierence

in US$ 000

Dierence

in %


in US$ 000Dierence

in US$ 000

Dierence


Black Monday Aug 97 - Dec 87 293 285 -9 -3% -893 -721 172 19%

LTCM crisis Jul 98 - Aug 98 -160 -138 22 14% -1,084 -1,028 55 5%

Dot-com bubble Mar 00 - Apr 01 684 624 -59 -9% -1,296 -1,363 -67 -5%

9/11 Aug 01 - Sep 01 -63 -34 30 47% -1,055 -934 121 12%

02 downturn Mar 02 - Jul 02 242 232 -10 -4% -467 -385 81 17%

Great Recession Oct 07 - Mar 09 148 225 77 52% -3,481 -3,014 467 13%


Annualised return (%) Jan 87 - Jul 10 6.6 6.5 7.9 7.7


index ell by more than 2 std. deviations over the same period.

* Portolio selection based on allocations that achieved the maximum inormation ratio available. Portolio selection based on allocations that resembled benchmark portolio o 55% equities, 40% ixed income, and 5% alternative assets,

with similar expected returns.


17It is arguable that the eects o the Dot-com extended longer; however, we only consider this 1-year portion, given the slight recovery in the marketsater that as we had to accommodate 9/11 as a dierent event.


15/20


Table 4 summarises gains (losses) experienced byselected portolios during the periods under

consideration. In general, we nd that, except or theDot-com bubble, portolios which included goldared much better, as they increased the return overperiod. In some instances, this implied that addinggold to the mix produced higher positive returns,while in others, it reduced the losses. For example,investors would have either gained or savedbetween US$22,000 and US$178,000 or US$10mninvested during Black Monday by including3% to 6% in gold, in portolios whose assetallocations were determined by using averagecorrelations. Similarly, they would have saved

between US$35,000 and US$91,000 during 9/11and between US$132,000 and US$330,000 duringthe recent nancial crisis o 2007-2009. They wouldhave lost, however, between US$32,000 andUS$86,000 during the Dot-com bubble. A possibleexplanation is that the Dot-com bubble was heavilyconcentrated towards one particular sector o theeconomy; hence, the added benets o gold as adiversier to the selected portolios may have beenlessened.

Portolios constructed using allocations based onhigh risk correlations, tended to outperorm thoseusing average correlations (except or the LTCMcrisis). This is not surprising given that they wereoptimised or similar situations, and while they werenot immune rom losses, these portolio allocationswould have saved considerable amounts orinvestors. This was especially the case assuming abenchmark-like portolio. By adding allocations togold o about 9%, or example, investors wouldhave reduced their losses by almost US$500,000(on a US$10mn investment) during the GreatRecession. This is equivalent to savings o around13% between the loss in the portolio with gold and

the one without.Moreover, long-run average returns or the portolioswith and without gold were similar. In other words,average gains remained consistent, but extremelosses were, in most occasions, reduced. Thus, goldnot only helps to manage risk or expected ortheoretical losses, but in multiple occasions it wasshown to reduce the observed loss o an investmentwhile keeping a similar average return prole.

Out-o-sample considerations: past andpresent

A clear constraint o this analysis is that the portoliosused to show the properties o gold as a tail-riskhedge were constructed using inormation that maynot have been available to investors prior to theevents occurrence. In other words, we are using anin-sample approach to compute returns, volatilitiesand expected losses. This does not invalidate theanalysis, but it does raise the question o whetherselecting a portolio allocation using only inormationavailable during a specic period o time, will stilldeliver similar results (i.e. i adding gold to the portolio

mix allows investors to manage risk more eectively)or events that happen outside o that period.

The answer is that it does. Gold can be shown toreduce losses even in out-o-sample analysis ormost cases. We estimate average correlations andvolatilities using weekly returns between January 87and June 07, excluding the most recent period.Subsequently, we nd optimal portolios using thesame methodology as beore: with and without goldwe select the portolio with the maximum inormationratio, as well as a portolio with allocations similar toa typical benchmark portolio or a total o ourportolios.18 We concentrate on ve dierent periods:1) the early 70s recession between December 72and September 74; 2) the Iran-Iraq war in the late70s and early 80s rom January to March 1980;3) the 80s recession between July 81 and August82; 4) the Great Recession, between October 07and March 09; and, nally, 5) the European sovereigndebt crisis, between November 09 and June 10.

In all, seven out o ten times, adding gold to theportolio mix helped either reduce losses or increasegains during those market events (table 5). For

example, during the early 70s recession, includinga 2.3% allocation to gold in a conservative portolioincreased gains by US$502,000 on a US$10mninvestment; a 4.6% gold allocation in a moreaggressive portolio, increased gains by US$552,000on a similar investment. The portolios which includedgold did not are as well during the early 80s crisisand 82 recession because the price o gold movedup rapidly during 1980 just to drop sharply thereater,but it had a much more positive impact during therecent global and European crises.

18 In this case, we do not estimate correlations based only on high-risk events given that there are ew such observations during that period, makingthe estimates less reliable.


16/20


Conclusion

Gold is rst and oremost a consistent portoliodiversier. Moreover, we nd that gold e ectively helpsmanage risk in a portolio, not only by means oincreasing risk-adjusted returns, but also by reducingexpected losses incurred in extreme circumstances.Such tail-risk events, while unlikely, can be seen tohave a damaging eect on an investors capital.On one hand, short- and medium-term holders,individual and institutional alike, can take advantageo golds unique correlation to other assets to achievebetter returns during times o turmoil. This is especiallytrue given that golds correlation tends to change in away that benets investors who hold it within theirportolios. On the other hand, by including gold in

their portolios,19 long-term holders, such as retirementsavings accounts, pension plans, endowments andother institutional investors, can manage risk withoutnecessarily sacricing much sough-ater returns.

Our analysis suggests that even relatively smallallocations to gold, ranging rom 2.3% to 9.0%, canhave a positive impact on the structure o a portolio.We nd that, on average, such allocations can reducethe Value at Risk (VaR) o a portolio, while maintaininga similar return prole to equivalent portolios whichdo not include gold. For the eight portolios analysed

using data rom January 87 to July 10, adding gold

reduced the 1% and 2.5% VaR by between 0.1%and 18.5%. Moreover, we ound that por tolios whichincluded gold outperormed those which did notin 18 out o 24 occasions (75%) when doing anin-sample analysis, and in seven out o ten (70%) inout-o-sample tests. A summary can be ound intable 7 in the Appendix.

We also note that investors who hold gold only in theorm o a commodity index are likely to be under-allocated.20 There is a strong case or gold to beallocated as an asset class on its own merits. It ispart commodity, part luxury consumption good andpart nancial asset and, as such, its price does notalways behave like other asset classes and especiallyother commodities.

Finally, while most o this analysis concentrates onrisk in the orm o tail-risk and volatility, gold has otherunique characteristics that make it very useul inperiods o nancial distress. For example, the goldmarket is highly liquid and many gold bullioninvestments have neither credit nor counterparty risk.

19 Concretely, average gold correlations to most other assets held in a portolio tend to be small; more importantly, correlation to equities, corporatedebt and even other commodities tends to all in economic downturns.

20 Golds weight in typical benchmark commodity indices, such as the S&P Goldman Sachs Commodity Index or the Dow-Jones UBS CommodityIndex, tends to be small, usually between 2% to 6%. Even i an investor holds a 10% allocation in one o these indices, their eective gold exposureis between 0.2% and 0.6%.

Table 5: Observed gain (loss) on a US$10mn investment or selected portolios with and without including gold during various

out o sample tail-risk events prior to 87 and post 07

Portolio using average correlation1

Max. In. Ratio2 Benchmark3


during various nancial

downturns in US$ 000Dierence in

US$ 000

Dierence

in %


during various nancial

downturns in US$ 000Dierence in

US$ 000

Dierence


Early 70s recession Dec 72 - Sep 74 505 1,210 705 140% -295 1,068 1,363 462%

Iran-Iraq war Jan 80 - Mar 80 -534 -635 -101 -19% -995 -1,158 -163 -16%

80s recession Jul 81 - Aug 82 2,018 1,917 -101 -5% 33 33 1 2%

Great Recession Oct 07 - Mar 09 99 272 173 175% -3,619 -3,193 426 12%

European sovereign debt crisisNov 09 - Jun 10 62 81 19 31% -454 -373 81 18%


Annualised return (%) Jan 87 - Jun 07 6.7 6.6 8.1 8.0

1) Correlation estimation using all weekly returns rom Jan 87 to Jul 10; 2) portolio selection based on allocations that achieved the maximum

inormation ratio available; 3) portolio selection based on allocations that resembled benchmark portolio o 55% equities, 40% ixed income, and 5%

alternative assets, with similar expected returns.



17/20


Chart 7: Historical distribution o weekly returns or selected assets; Jan 87-Jul 10*

Histograms o standardised monthly returns

%

0

10

20

30

-4 -3 -2 -1 0 1 2 3 4No. of standard deviations away from zero

Gold (US$/oz)

%

0

10

20

30


JPM 3-month T-bill Index%

0

10

20

30


%

0

10

20

30


JPM US Treasury Index BarCap Global Tsy Agg ex US%

0

10

20

30

-4 -3 -2 -1 0 1 2 3 4

No. of standard deviations away from zeroMSCI US

%

0

10

20

30

-4 -3 -2 -1 0 1 2 3 4

No. of standard deviations away from zeroMSCI EAFE

%

0

10

20

30


MSCI EM

%

0

10

20

30


BarCap US Credit%

0

10

20

40

30



%

0

10

20

30

40


JPM EMBI Global%

0

10

20

30


S&P GSCI

%

0

10

20

30


DJ UBS Comdty Index

*Except or MSCI EM index (Dec 87-Jul 10) and JPMorgan EM sovereign debt index (Dec 90-Jul 10) due to data availability.


Appendix


18/20


Table 7: Summary o tail-risk events in which a portolio containing gold observed a gain (+) or a loss (-) relative to a similar

portolio without gold

Portolio using average correlation1 Portolio using high risk cor relation2

Max. In. Ratio* Benchmark Max. In. Ratio* Benchmark

Gold weight 3% 6% 4% 9%

Portolio gains (+) or losses (-) during various nancial downturns in sample

Black Monday Aug 97 - Dec 87 + + - +

LTCM crisis Jul 98 - Aug 98 + + + +

Dot-com bubble Mar 00 - Apr 01 - - - -

9/11 Aug 01 - Sep 01 + + + +

02 downturn Mar 02 - Jul 02 + + - +

Great Recession Oct 07 - Mar 09 + + + +

Gold weight 3% 6%

Portolio gains (+) or losses (-) during various nancial downturns out o sample

Early 70s recession Dec 72 - Sep 74 + +

Iran-Iraq war Jan 80 - Mar 80 - -

80s recession Jul 81 - Aug 82 - +

Great Recession Oct 07 - Mar 09 + +

European sovereign debt crisis Nov 09 - Jun 10 + +


index ell by more than 2 std. deviations over the same period;

* Portolio selection based on allocations that achieved the maximum inormation ratio available. Portolio selection based on allocations that resembled benchmark portolio o 55% equities, 40% ixed income, and 5% alternative assets,

with similar expected returns.


Table 6: Projected returns and volatilities used during por tolio optimisation

Return (%) Standard Deviation (%) Inormation Ratio1

Gold (US$/oz) 2.0 15.3 0.13

JP Morgan 3-month T-Bill Index 0.0 1.0 0.00

BarCap US Treasury Aggregate 4.0 4.8 0.84

BarCap Global ex US Treasury Aggregate 4.0 8.9 0.45

BarCap US Credit Index 4.0 5.2 0.77

BarCap US High Yield Index 5.0 8.2 0.61

JP Morgan EM Sovereign Debt Index 6.0 12.8 0.47

MSCI US Equity Index 8.0 17.3 0.46

MSCI EAFE Equity Index 8.0 18.1 0.44

MSCI EM Equity Index 10.0 22.2 0.45

S&P Goldman Sachs Commodity Index 2.0 21.1 0.09

1) Ratio o return and volatility, also known as avg. risk-adjusted return (a higher number indicates a better return per unit o risk).

Source: WGC


19/20

Disclaimers

This report is published by the World Gold Council (WGC), 10 Old Bailey,London EC4M 7NG, United Kingdom. Copyright 2010.All rights reserved. This report is the property o WGC and is protected byU.S. and international laws o copyright, trademark and other intellectualproperty laws. This report is provided solely or general inormation andeducational purposes. The inormation in this report is based uponinormation generally available to the public rom sources believed to bereliable. WGC does not undertake to update or advise o changes to theinormation in this report. Expression o opinion are those o the author andare subject to change without notice. The inormation in this report isprovided as an as is basis. WGC makes no express or impliedrepresentation or warranty o any kind concerning the inormation in thisreport, including, without limitation, (i) any representation or warranty omerchantability or tness or a particular purpose or use, or (ii) anyrepresentation or warranty as to accuracy, completeness, reliability ortimeliness. Without limiting any o the oregoing, in no event will WGC or itsaliates be liable or any decision made or action taken in reliance on theinormation in this report and, in any event, WGC and its aliates shall notbe liable or any consequential, special, punitive, incidental, indirect or

similar damages arising rom, related or connected with this report, even inotied o the possibility o such damages.

No part o this report may be copied, reproduced, republished, sold,distributed, transmitted, circulated, modied, displayed or otherwise usedor any purpose whatsoever, including, without limitation, as a basis orpreparing derivative works, without the prior written authorisation o WGC.To request such authorisation, contact [email protected]. In no event mayWGC trademarks, artwork or other proprietary elements in this report bereproduced separately rom the textual content associated with them; useo these may be requested rom [email protected]. This report is not, andshould not be construed as, an oer to buy or sell, or as a solicitation o anoer to buy or sell, gold, any gold related products or any other products,securities or investments. This report does not, and should not be construedas acting to, sponsor, advocate, endorse or promote gold, any gold relatedproducts or any other products, securities or investments.

This report does not purport to make any recommendations or provide anyinvestment or other advice with respect to the purchase, sale or other

disposition o gold, any gold related products or any other products,securities or investments, including, without limitation, any advice to theeect that any gold related transaction is appropriate or any investmentobjective or nancial situat ion o a prospective investor. A decision to investin gold, any gold related products or any other products, securities orinvestments should not be made in reliance on any o the statements in thisreport. Beore making any investment decision, prospective investorsshould seek advice rom their nancial advisers, take into account theirindividual nancial needs and circumstances and careully consider therisks associated with such investment decision.

Printed on recycled paper with FSC certifcation.


20/20

World Gold Council

10 Old BaileyLondon

EC4M 7NG

United Kingdom

Tel +44 (0)20 7826 4700

Fax +44 (0)20 7826 4799

Email [email protected]

www.gold.org

wgc - gold - hedging against tail risks

Documents