Gold as a safe haven investment in a financial crisis

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Gold as a safe

haven investment

in a financial crisis

MASTER THESIS WITHIN: Finance NUMBER OF CREDITS: 15

PROGRAMME OF STUDY: International Financial Analysis

AUTHORS: Lea Rosskopf & Rebecka Rutersten JÖNKÖPING May 2020

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Acknowledgments

We would like to thank our tutor Michael Olsson, Ph.D. for his inputs and feedback throughout the whole writing process of this thesis. We would also like to thank Toni Duras, Ph.D., for his advice regarding our regressions. Finally, we want to express our appreciation for the good collab-oration with each other during the whole writing period.

_________________________ __________________________ Lea Rosskopf Rebecka Rutersten

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Master Thesis in International Financial Analysis

Title: Gold as a safe haven investment in a financial crisis

Authors: Lea Rosskopf and Rebecka Rutersten Tutor: Michael Olsson

Date: 2020-05-18

Key terms: gold, safe haven, crisis, financial markets, uncertainty, investor behavior

Abstract

Especially in the current times of financial instability and turmoil in connection to the outbreak of covid19, investors are seeking opportunities to protect their assets and their values. We are there-fore aiming to investigate whether gold is a safe haven investment during turmoil times, as well as compare its properties with the ones of silver and platinum. We also analyze if the findings are universal or limited to specific markets. This is why we search for patterns between developed and emerging markets. Our study is based on crisis theory and the concept of risk and volatility, the theory of gold, the Efficient Market Hypothesis, and the theory of investor behavior. The theory is followed by the presentation of some descriptive statistical measurements and correlation matri-ces, which should give an overview of the used data. After that, the methodology is presented, containing the Ordinary Least Squares regressions for a 20-year period from 2000 through 2019 with dummies for the specific years 2002, 2008, and 2013 with financial turmoil. The results show that gold does not generally act as a strong safe haven and, more often, as a weak safe haven. The only finding for gold having strong safe haven properties was for the Dow Jones in 2013. Further-more, the regressions showed that gold has significantly stronger safe haven properties compared to silver and platinum. We could not find any specific differences between developed and emerging markets. These findings can be used by investors looking for safe haven investment opportunities during turbulent times on the stock market.

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Figures

Figure 1: The CAPM with Different Saving and Borrowing Rates ... 17

Figure 2: Average market index and gold excess return comparison ... 43

Tables

Table 1: Annualized excess return ... 25

Table 2: Annualized standard deviation ... 26

Table 3: Sortino ratio ... 27

Table 4: Skewness ... 29

Table 5: Kurtosis ... 30

Table 6: Lower partial standard deviation (LPSD) ... 31

Table 7: Value at Risk (VaR) ... 32

Table 8: VaR (95) ... 32

Table 9: Expected Shortfall ... 33

Table 10: CVaR (95) ... 33

Table 11: Correlation matrix 30-years ... 34

Table 12: Correlation matrix 20-years ... 35

Table 13: Correlation matrix 2002 ... 36

Table 16: Regression output for gold ... 46

Table 17: Regression output for silver ... 48

Table 18: Regression output for platinum ... 48

Appendix

Table A1: Compilation of descriptive measures for 30- and 20-years………...59

Table A2: Test for serial correlation; DW test and BG Serial Correlation LM test.…....60

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1. Introduction

The opening chapter starts with an overview of the current crisis situation, followed by a review of previous recessions, bubbles, and financial crises. Thereafter the background of gold is presented, followed by the concept of gold viewed as a safe haven. Moreover, the problem discussion about how gold can be seen as a safe haven in case of financial turmoil is presented as well as the research question and the purpose. Lastly, the focus of the research and the overall disposition is presented.

1.1 Background

The financial market is currently suffering from one of the biggest crises ever, maybe even more significant than the crisis during World War II (Partington & Wearden, 2020). The outbreak of covid19 has spread worldwide, and as we are writing, the number of confirmed cases has just passed one million, and the number of deaths caused by the virus is over fifty-six thousand worldwide (World Health Organization, 2020). The outbreak of covid19 and the effect of governmental decisions related to preventing the spread of the virus has resulted in an extremely uncertain financial market. Several companies are facing bankruptcy or the tough decisions to lay off a high number of employees (Partington & Wearden, 2020). Even if we cannot say how this crisis is going to develop furtherly and what the result of it is going to be, we can look into previous historical events that are similar to the one of today to seek answers. During the last 30 years (1990 through 2019), the financial market has suffered multiple times from several recessions, bubbles, and financial crises where the market has been greatly affected. The dot-com bubble in the early 2000s (Valliere & Peterson, 2004), the global financial crisis in 2008 (Donici & Diaconu, 2010) and the European sovereign debt crisis in 2013 (Ardagna & Caselli, 2014) are some examples of when the market has histori-cally been extremely uncertain during the last 30 years (Obstfeld, Cho & Mason, 2012). Borio, Drehmann, and Xia (2018) indicate that the dot-com bubble of 2000 shows a great example of when a crash follows a large boom of the economy in the stock market. Reces-sions and booms in the economy are part of the natural global financial cycle. They are de-fined as a time when the market is facing a natural downward trend or a natural upward trend, respectively, uncorrelated with any additional events (Nowotny, Ritzberger-Grunwald

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& Backé, 2014). Borio, Drehmann, and Xia (2018) argue that the economy is typically suf-fering once the financial cycle peaks during a boom. When a boom occurs, it can lead to higher optimism and more positive economic records for businesses, but also to high levels of credit and asset price growth, which could be a clear warning sign for an upcoming finan-cial crisis. The consequences of a boom are, therefore, a subsequent recession where the economy suffers from high debt burdens, need for balance sheet repairs, and falling asset prices, which leads to a decreasing growth of the economy instead (Borio, Drehmann & Xia, 2018). If the boom is large enough, the following recession can be devastating and, in some cases, lead to a financial crisis (Borio, Drehmann & Xia, 2018).

A financial crisis is often occurring after a great boom. It is triggered by a financial institution that threatens the whole financial system by being unable to meet its obligations or continue its trade. Financial institutions, in this case, could be either banks or sovereign nations. What mainly characterizes a financial crisis is that it is like a domino effect; the failure of one nancial institution can have significant impacts on others and therefore affect the whole fi-nancial system. Defaults on debt, bankruptcies as well as bank runs may be possible conse-quences. Related shortages of liquidity through reduced credit transfers can lead to an addi-tional economic downturn as the spending and trust in financial assets decrease. De Bonis, Giustiniani, and Gomel (1999) used their “monetarist approach” to define a financial crisis as the effect of shortages related to money supply as a consequence of bank runs and there-fore reduced financial flows that have a negative influence on the economy. The current ongoing crisis of the pandemic of covid19 has already been predicted to have an even more substantial potential impact on the economy than any previously known crises have ever had before (Partington & Wearden, 2020). It is, therefore, more up-to-date than ever to investi-gate how investors can protect themselves from the risks of a potential financial crisis. Baur and Lucey (2010), Baur and McDermott (2010), and Reboredo (2013) investigated the difficulties of preserving wealth during financial crisis and discovered that historically gold could be used as a safe haven. Referring to a “safe haven” means that an asset is uncorrelated or negatively correlated to another asset or a portfolio, but especially in times of a crisis and extreme market conditions. Therefore, a safe haven asset protects an investor in these times as the price of the asset will increase while the value of other assets or the portfolio decreases (Baur and Lucey, 2010).

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Gold has more or less always been part of the financial system, and its history goes back to ancient times, since when it has been known as one of the first payment methods ever used (Habashi, 2016; Baur & Lucey, 2010). In general, gold has an extensively long history, and for decades it has been used as a store of value, a unit of exchange, and as a main supplier for jewelry crafting (Bredin, Conlon & Potí, 2015). The target of the gold standard, mainly used in the 19th and the beginning of the 20th century, was to cover up currencies with gold reserves owned by governments and central banks. Even nowadays, governments keep vast gold reserves to be prepared for crisis times and to decrease the risk of currency fluctuations. Large gold reserves also ensure independence, as they could easily be used as a means of payment (Eichengreen and Flandreau, 1997). Gold has always been seen as a stable, eternal source of wealth and universal means of exchange (Baur & McDermott, 2010). Moreover, gold has been traded on the commodity market since 1971, when the U.S. government de-cided to suspend the ability to convert dollars to gold (Aggarwal & Soenen, 1988). Thereby, gold can since then be viewed as an investment asset as well (Solt & Swanson, 1981). As an investment, gold is characterized by some difficulties. One major issue is that the real intrinsic value of gold is difficult to be estimated as its value is not mainly related to the usage value for the society as most other commodities (Baur and McDermott, 2010) and is not recognized for its ability to pay an income like dividends (Aggarwal & Soenen, 1988; Abken, 1980). According to the Mineral Commodities Summaries 2019 of the U.S. Department of the Interior and the U.S. Geological Survey, gold is currently at most used for luxury items like jewelry (46 percent) and electronics (40 percent). Nine percent are used for official coins, and the rest is used for other purposes (U.S. Department of the Interior, 2019). Other char-acteristics are the relative inelasticity of supply (Baur and McDermott, 2010) as the mining and extraction from natural sources is difficult and time-consuming. According to the World Gold Council (2020), setting up a new mine can take decades after the source has been dis-covered. Another characteristic of gold is its counter-cyclical movements of the demand, which are related to the relationship of decreasing stock market prices along with increasing gold prices. These attributes lead to the theory that gold can act as a store of value or a safe haven in a time of uncertainty (Baur and McDermott, 2010).

To sum up, there are different market cycles as well as events like recessions, booms, and financial crises that influence the global economy differently (Borio, Drehmann & Xia, 2018). During the last 30 years, there has been financial turmoil mainly related to three events, the

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dot-com bubble in the early 2000s (Valliere & Peterson, 2004), the global financial crisis of 2008 (Donici & Diaconu, 2010; Allen, 2016) and the Greek government debt crisis with its peak from 2010 to around 2013 (Ardagna & Caselli, 2014) that affected the financial markets. Borio, Drehmann, and Xia (2018) argue that these events can be traced back to different market cycles like recessions, booms, and financial crises. Therefore, similar events could be repeated in the future. Consequently, it is in the best interest of any investor to know about how to preserve their wealth in turmoil times. As previous research mainly used data from before the last global financial crisis 2008 and, therefore, not included this severe financial crisis in the analysis, our investigation will contribute with a more recent study. It will also include the Greek government debt crisis, which was not yet covered by other studies. Thereby we will expand the knowledge within the field of gold investments and provide investors with a more reliable and current analysis of how to evaluate the security of an investment in gold.

The purpose is, therefore, to investigate if gold could be used as a safe haven during turmoil times. To be able to fulfill our purpose, we want to investigate further to what extent gold can be considered to be a safe haven during turmoil times. Our first and second research questions are, therefore, whether gold is a strong safe haven during turmoil times and if gold is a weak safe haven during turmoil times. We also want to investigate if gold has a unique safe haven capability in comparison with other metals. This is the reason we decided to com-pare the results of the analysis of gold with silver and platinum, as also done by Hood and Malik (2013). Our third research question is, thus, whether gold has stronger safe haven properties than the other precious metals, silver, and platinum, during turmoil times. In addition, we also want to investigate if gold is a safe haven during turmoil times, even in different markets. To investigate this matter further, we decided to compare different se-lected global indices from both emerging and developed markets with gold. To be able to distinguish between developed and emerging markets, we chose four indices that represent emerging as well as four indices representing developed markets to compare their develop-ment to the one of the gold prices. Our fourth research question is thus, whether gold is a safe haven for both developed and emerging markets. By comparing the results of the de-veloped and emerging markets, we strive to provide a better overview of how gold prices behave, not only limited to one market but from a global perspective.

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1.2 Focus of the research

We decided to cover a total time frame of 30-years and also focus specifically on three turmoil times, the years 2002, 2008, and 2013 to represent the timeframes of the financial crisis or turmoil times. Furthermore, we decided to focus on the comparison of gold with the pre-cious metals silver and platinum due to their common attributes with gold as they are all three precious metals traded in USD, measured in Troy ounces, and do not pay any divi-dends. Another reason for our choice is that we want to compare classical investment metals like gold and partly silver with the precious metal platinum, which is mainly used for indus-trial purposes (Hillier et al., 2006).

In line with Bauer and McDermott (2010), our study will also focus on a few carefully se-lected indices when conducting the analysis. We thereby only compare the prices of gold with the specifically chosen indices. When selecting the different indices, we decided to make a distinction between developed and emerging markets. As representatives for developed markets, the indices prices of the Dow Jones Industrial Average (DJI), the DAX Perfor-mance Index (DAX), the Financial Times Stock Exchange 100 Index (FTSE), and the S&P/TSX Composite Index (TSX) were used. Therefore, mainly the financial markets of the United States of America, Germany, Great Britain, and Canada are investigated. As a comparison, daily market prices were also retrieved for the emerging markets NIFTY50 (only from April 23, 1996, due to data availability) to represent India, the Brazil Bovespa Index (BOVESPA) for Brazil (only from January 16, 1990, due to data availability), the Hang Seng Index (HSI) for China and Korea Composite Stock Price Index (KOSPI) for South Korea.

1.3 Disposition

In the second chapter, we present the relevant theory for the study. The section starts with crisis theory and the concept of risk and volatility followed by the theory of gold and the Efficient Market Hypothesis (EMH). Thereafter, investor behavior related to gold invest-ments, the theory on portfolio selection and asset risk determination are presented. Lastly, we discuss the distinction between developed and emerging markets, followed by definitions of different statistical measurements used for the descriptive part of the study. In the third chapter, we present basic descriptive statistics. Firstly, we describe different measurements as excess returns, standard deviation, Sortino ratio, skewness, and kurtosis for every index as well as for silver, platinum, and gold. After that, we present the results of a more in-depth

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analysis of only the precious metals. Lastly, we present correlation matrices for different time periods. In the fourth chapter, we introduce the methods we used. First, we discuss the OLS model followed by additional tests, the Durbin-Watson test, and the Breusch-Godfrey Serial Correlation LM test as well as the used research model. Lastly, we present different alterna-tive approaches that could have been used as an alternaalterna-tive to the one we used. In the fifth chapter, the results are presented, and the findings for each research question are discussed and analyzed. In the sixth and last chapter, the final conclusions are followed by implications and the contributions of the research. The last part will give an overview of possible exten-sions of our study as well as suggestions for future research.

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2. Literature Review

The second chapter covers the relevant theories and concepts. First, we discuss crisis theories and the concept of risk and volatility followed by the theory of gold and the Efficient Market Hypothesis. Furthermore, investor behavior related to gold investments, the theory of port-folio selection, and asset risk determination are presented, followed by the distinction be-tween developed and emerging markets.

2.1 Crisis theory and the concept of risk and volatility

Historically, recessions and booms have been a natural part of the financial cycle and are most likely going to continue with the same or similar patterns in the future (Borio, Drehmann & Xia, 2018). Although recessions and booms can be viewed as natural, the con-sequences of a too high boom or too deep recession can sometimes lead to a more severe condition in the economy, often referred to as financial crises (Nowotny, Ritzberger-Grun-wald & Backé, 2014; Borio, Drehmann & Xia, 2018). Three of the latest 20-years’ most sig-nificant examples of the consequences of a too high boom or too deep recession are the dot-com bubble in the early 2000s (Valliere & Peterson, 2004), the global financial crisis in 2008 (Obstfeld, Cho & Mason, 2012) and the Greek government debt crisis peaking from 2010 to around 2013 (Ardagna & Caselli, 2014).

The financial cycle is defined as when the market is facing a natural downward trend (reces-sion) or a natural upward trend (boom), respectively, uncorrelated with any additional events (Nowotny, Ritzberger-Grunwald & Backé, 2014). A boom leads to higher optimism and more positive economic records for businesses but also to high levels of credit and asset price growth, which might be a warning signal for an upcoming financial crisis (Borio, Drehmann, & Xia, 2018). After a boom, there is naturally a subsequent recession where the economy suffers from high debt burdens, falling asset prices, and the need for balance sheet adjustments. A recession, therefore, leads to a decreasing growth of the economy in contrast to a boom (Borio, Drehmann & Xia, 2018). In case of an extreme boom, the following re-cession is at risk to also be extreme (Borio, Drehmann & Xia, 2018).

The dot-com bubble of 2000 is an example of when an extreme boom also gets followed by a severe recession. During the dot-com bubble, the share prices of companies within the

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internet or computer sector increased rapidly as a result of high expectations and optimism within the market. The high expectations and great optimism about the new market resulted in more investors investing in the stock market, which resulted in a great boom for the econ-omy. The share prices were thus increasing rapidly to a new high until the prices reached the top and started to drop instead. As soon as the prices were decreasing, the chaos was una-voidable (Valliere & Peterson, 2004). Even though the crisis only hit one sector in the market (the internet sector), the desolation was complete. Several big companies were going bank-rupt at the same time as all investors were facing significant losses, which caused the whole economy to turn into a deep recession. During bubbles as the dot-com bubble, Valliere and Peterson (2004) argue that investors are more open to accepting risks, as they assume that the potential returns are even higher than the losses they could face. The investors are, there-fore, more tempted to invest larger amounts to compensate the losses (Valliere & Peterson, 2004).

Even though the dot-com bubble was devastating in many ways for the economy, it was harmless compared to what happened during the financial crisis of 2008. This crisis has been identified as the worst financial crisis since the crash of the stock market in 1929, also known as the great depression (Obstfeld, Cho & Mason, 2012), but that was before the outbreak of covid19 in 2020 was known (World Health Organization, 2020). However, in 2007 and 2008, the long going mortgage crisis in the United States that had already been growing for several years finally burst and resulted in panic all over the world (Obstfeld, Cho & Mason, 2012). The crisis was primarily triggered by the bankruptcy of Lehman Brothers, which was seen as one of the world’s biggest and most successful banks at the time (McDonald & Roinson, 2009). The big crash of the banks and financial institutions in the United States resulted in the necessity of implementing macroeconomic policies that have never been used before in both emerging and developed markets. These new macroeconomic policies resulted in huge budget deficits for most developed countries, as the policy interest rates fell to almost zero (Obstfeld, Cho & Mason, 2012). The damages from the financial crisis were significant and were leading to new questions about how financial crises are arising and the investigation about the reasons behind them. Evidence shows that financial distress is mainly occurring after a great boom and is usually triggered by a bankruptcy of a financial institution that could be either banks or sovereign nations. Such failures could cause a domino effect and influence the whole financial system with defaults on debt, bank runs, and bankruptcies as an outcome.

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transfers, which could lead to an additional decrease of the economy as the spending and trust in financial assets are decreasing (Hashimzade, Myles & Black, 2017).

After the global financial crisis of 2008, the economy of the EU had suffered from great negative shocks. The effect of the global financial crisis was particularly devastating for Greece, where the government had overestimated the country’s ability to repay the national debt for years. The trigger for the complete loss of confidence in Greece was approximately in October 2009 when an announcement was made from the recently elected new govern-ment. The new government then revealed that the previous government had stated the over-all budget deficits to be much lower than the actual deficits were. The budget deficits were, in fact, around twelve to thirteen percent of the GDP in contrast to the previously estimated six to eight percent of the GDP. As the debt/GDP also exhibited a high percentage of 115 percent, the country, therefore, also exceeded the EU parliaments requirements of a maxi-mum of debt/GDP rate of 60 percent. After the announcement in October 2009, it did not take long until the interest rates for Greece went straight up, and the government bonds that previously had the same ratings as other EU members such as Germany now went to an all-time low. This was the beginning of a long series of credit-rating downgrades (Ardagna & Caselli, 2014).

The credit downgrades led to an extremely uncertain and volatile time for Greece, and the EU as Greece could no longer pay off their debt. This resulted in a great crisis, not only in Greece but for all countries involved in the Euro-zone as the value of the Euro decreased. After several bailouts from the EU, Greece could finally start paying off its debt, and the regulations about governmental spending became stricter. As of today, Greece still has a vast amount of debt but lower than before, and new regulations are keeping the Greek govern-ment away from committing the same mistake again and are helping them to maintain a stable financial system (Acharya, Eisert, Fufinger & Hirsch, 2018).

As can be seen from the European sovereign debt crisis in 2013, for the stability of a financial system, the concept of risk and volatility plays an important role. For instance, Neumark, Tinsley, and Tosini (1991) found in their study about risk and volatility that the correlations between different countries’ stock market prices are increasing when the markets are experi-encing extreme volatility. They also found that when markets are facing more “normal” pe-riods, the correlations are decreasing. Neumark, Tinsley, and Tosini (1991) mean that one

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explanation for these asymmetrical correlation patterns could be transaction costs. In 1994 Lin and Ito (1994) discovered a remarkable rise of the hourly return correlation between the S&P 500 Index and the Tokyo Stock Exchange’s Nikkei 225 Index during the 1987 crash period. Specifically related to the gold market, Baur (2012) performed a study on the concept of risk and volatility. He used data from a 30-year period between the 19th_{of November}

1979, to the 18th_{of November 2009, to investigate the asymmetric volatility in the gold}

mar-ket. Bauer (2012) found that the volatility of gold returns differs between positive and nega-tive events and that the effect is significantly higher than for equity markets. The volatility of gold prices is also higher during positive shocks compared to negative shocks. This could be traced back to the safe haven properties of gold. Baur (2012) argues that increasing gold prices give investors the signal that there is generally higher volatility in the market and that a higher uncertainty could be expected for other assets. This uncertainty creates higher vol-atility of the gold price itself (Baur, 2012).

2.2 Theory of gold

Contrarily to the previously mentioned currently volatile gold prices, initially, the gold price was kept constant at around 20 USD per Troy ounce between 1833 and 1933. In the follow-ing period from 1934 through 1967, the price was increased but still fixed at 35 USD per Troy ounce by President Roosevelt. A couple of years after the gold price was not fixed anymore, in 1971, gold could finally be traded on the commodity market (Aggarwal & Soenen, 1988). Since then, the prices have been more volatile, and one major increase in the gold price could be spotted in 2008 during the financial crisis. While most metal prices dropped from 2008 to 2009 and mines even struggled to survive, gold’s behavior during that time was the opposite, and during the peak of the financial crisis of 2008, the price of gold rose about six percent. In comparison, key mineral prices and other financial assets fell by about 40 percent (Shafiee & Topal, 2010).

There are different forms of investing in gold, which are split into physical and paper forms of gold ownership (Agarwalla, Singh & Choudhury, 2018). The investment opportunities in paper-related or certificate forms of gold are sovereign gold bonds (SGBs), gold exchange traded funds (ETFs) as well as gold accounts. Another way is to invest in shares in the sector of gold mining (Agarwalla, Singh & Choudhury, 2018). The physical gold market is split into

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bars. The first two sections follow the regular business cycles and thereby depend on the consumers’ spending power (Baur and McDermott, 2010). However, according to Baur and McDermott (2010), the historical demand for gold follows counter-cyclical patterns, which means that the interest is rising in times of market turndowns, and therefore, the gold prices increase.

The reasons behind the different behavior of gold have been explained by Shafiee and Topal (2010), who identified short- and long-term reasons for gold price increases. On a short-term basis, Shafiee and Topal (2010) mean that one of the main factors for gold price increases is that during times of financial crisis and recessions, investors are looking for alternative in-vestments in uncorrelated and less risky markets or assets. Another short-term reason is that gold is bought to hedge currency risks as so the devaluation of the U.S. dollar with other currencies (Shafiee & Topal, 2010). Baur and McDermott (2010) explain this reason with the fact that gold is priced in U.S. dollars. If the dollar decreases in value, nominal gold prices tend to increase, which hedges the real value of gold (Baur & McDermott, 2010; Capie, Mills & Wood, 2005). Shafiee and Topal (2010) argue that the same hedge function is used to protect investors from inflation. In the long run, one reason for price increases is the de-creased mined amount, which is related to inde-creased mining costs and lower availabilities. Another long-term influencing factor is that investors keep holding gold in their portfolios to profit from its liquidity, especially in times of financial instability (Shafiee & Topal, 2010). The third reason for a price increase of gold is the easy accessibility and therefore increased interest in gold by investing in gold Exchange Traded Funds (ETFs) (Baur & McDermott, 2010; Shafiee & Topal, 2010).

Comparing the gold price behavior to the one of other precious metals, Hillier, Draper, and Faff (2006) state that all metal prices are influenced by various long- as well as short-term factors. In contrast to gold as well as silver, the supply and demand of platinum is mainly related to its usage in the industrial sector. Its price reflects the current status of the economy, and therefore, its price is expected to move along with the industrial demand of it. The mar-ket for silver is mainly split to an industrial demand, which makes up around 40 percent of the annual production amount and demand related to jewelry, which accounts for about 45 percent. Compared to gold, the demand share related to investments is smaller for silver, with only eleven percent of the total demand for silver. According to the fact that the primary source to retrieve silver is to get it as a by-product while searching gold, its prices are strongly

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related. Platinum’s demand for investment purposes makes up for only around ten percent of the total demand. As platinum in contrast to gold and silver is not held by central banks, its price is also not influenced by their behavior (Hillier et al., 2006).

Hood and Malik (2013) built a model on the comparison of gold and the other precious metals silver and platinum as safe haven assets. The volatility was represented by the volatility index (VIX), and the data was retrieved for U.S. stock markets. Within the timeframe of November 1995 through November 2010, gold acts as a weak safe haven for the U.S. stock market while the other metals do not. However, in market conditions with high or low vol-atility throughout the sample period, gold did not have a negative correlation with the U.S. stock market (Hood & Malik, 2013).

Historically, central banks and governments held gold reserves to secure their national cur-rencies and as a store of value. This was especially focused during the times of the gold standard during the 19th and parts of the 20th century (Eichengreen, 1992). Nowadays, the largest federal gold reserve is owned by the U.S. government, which had a book value of over eleven billion USD on January 31, 2020 (Bureau of the Fiscal Service, 2020). The quote "We have gold because we cannot trust governments." from the U.S. President Herbert Hoover in 1933 shows the confidence in the value of gold (CBC News, 2011). It was related to the Emergency Banking Act when all Americans were forced to exchange their gold re-serves of any kind into U.S. dollars (Eichengreen, 1992).

According to Baur and Lucey (2010), one of the reasons why gold has been viewed as a safe haven is mainly, that gold historically has been one of the first forms of money and is often used as a hedge against inflation. Baur & McDermott (2010) state that gold has always been seen as a stable, eternal source of wealth and universal means of exchange. Baur and Lucey (2010) prove that gold is a safe haven for stocks in the United Kingdom, Germany, and the United States in their analysis, which covered data from 1995 through 2005. The safe haven attribute cannot be used universally but in times of extremely negative market conditions. They also found out that during bullish markets, gold does not act as a safe haven investment. Additionally, they stated that gold is not a safe haven for bonds in any of the markets in their analysis (Baur & Lucey, 2010).

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Baur and McDermott (2010) performed a multi-country analysis and included 53 global stock markets to investigate if gold could act as a safe haven and put a particular focus on times of financial turmoil. They found out that gold can act as a safe haven for developed markets like major European markets and the U.S.A., but not in emerging markets like the BRIC countries as well as not for Australia and Canada. Their investigation covered 30 years from 1979 through 2009. In contrast to these findings, Baur and McDermott (2010) also state that extreme uncertainty defined by high volatility on the stock markets makes gold move in the same direction as other financial assets.

2.3 Efficient market hypothesis (EMH)

Fama (1970) published the first article about the efficient market hypothesis (EMH). The efficient market hypothesis says that financial markets are efficient if the available infor-mation is already part of the market price. It also states that no technical analysis or insider trading is capable of achieving extraordinarily high returns. The theory assumes that unin-formed investors will receive the same returns as inunin-formed ones as the market leaves no opportunities to profit from asymmetric information (Fama, 1998; Malkiel, 2003).

Since 1970, there has been a lot of researchers within the field questioning the EMH. One of the first to question the EMH was Grossman and Stiglitz (1980) that proved that full information efficiency is impossible as information is only available at a certain cost. This would go along with the hypothesis that all invested resources in the analysis of the stock market would end up with no benefits for investors. In reality, there needs to be compensa-tion as an incentive for the research (Grossmann & Stiglitz, 1980). Malkiel (2003) also raises some doubts about fully efficient markets as not all market participants can be concluded to act rationally. If the market would directly reflect all information, then there would be no motivation for experts to investigate their opportunities, and this discrepancy gets even more significant with more technical possibilities. On the other hand, Malkiel (2003) also argues that bubbles like the dot-com bubble were just short-term inefficiencies and do usually only remain for a short period (Malkiel, 2003). Sewell (2011) also states that a “full” reflection of all available information in the market is an unrealistic assumption. Therefore, he concludes that no market could ever fulfill the efficiency criterion. On the other hand, he also admits that the basic idea of the EMH is right (Sewell, 2011). In line with the previously mentioned statements, Dieupart-Ruel, Grauffel, Le Roy, and Vacheret (2013), also state that the

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Efficient Market Hypothesis (EMH) is challenged, especially since the last financial crisis of 2007 and 2008 where financial assets’ prices seem to move apart from the principles of EMH. When asset prices are no longer connected to their real value, the factor of investor behavior is a possible explanation (Dieupart-Ruel et al., 2013). Shiller (2003) also stated that the effi-cient market hypothesis can lead to wrong assumptions of special stock market phenomena like bubbles and claims that especially the field of behavioral finance and theories about investor behavior could help explain.

2.4 Investor behavior related to gold investments

Investor behavior is defined as approaches to explain how certain investors behave and how they select, hold, and trade their portfolios (Barberis & Thaler, 2003). According to Baker and Ricciardi (2014), investor behavior is a combination of psychological factors as well as investments under individual and market influences. Understanding the impact of related decision-making is crucial for investors to make the right decisions (Baker & Ricciardi, 2014). Some of the most common biases are representativeness, the familiarity bias, worry, anchor-ing, and the trend-chasing bias. The phenomenon of representativeness is based on an in-vestor’s belief that stocks which recently increased in price will further rise, while others that decreased are left out from investment considerations. The familiarity bias is related to an investor’s choice of familiar investments contrarily to rational diversification. The preference for holding familiar assets is called local bias and often goes along with the home bias, which is related to buying domestic securities. Another bias is worrying, which increases the per-ceived risk of investors and, as a result, lowers the level of risk tolerance. Anchoring is related to a particular piece of information, which is used as a reference point for all judgments, even though it might not be a rational reference. The last-mentioned bias is the trend-chasing bias, which influences investors to trust historical returns as a means to predict future returns even though there is no reliable future indicator in historical performances (Baker & Ricciardi, 2014).

In contrast to behavioral finance theories, Fama (1998) argues for especially two main points that can be criticized. One is that underreaction and overreaction of investors are equally probable, which would indicate that, unusually high returns before special stock market events are as equal to remain that way as to reverse afterward. The second point is that the

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methodology of the investigation has a strong influence on the identification of anomalies, which tend to vanish with adjustments to the research technique (Fama, 1998).

Using the Grossmann-Stiglitz approach, Dieupart-Ruel et al. (2013) found that the value of gold is influenced by human behavior. They identified three types of agents on the market and split them concerning their rationality and information levels. The first group is called Rational Informed Agents (RIA), which is considering the basic principles and has strong indicators of how the gold price will develop in the future. The second class is called Irra-tional Informed Agents (IIA), which are more biased concerning their decisions and future expectations. Non-Informed Agents (NIA) are the third group, and they are mainly making their investment decisions by observing and anticipating the market movements. Therefore, the biases of class two (IIA) are also included in the third group (NIA). While during 2004 through 2008, the volatility of the gold price as well as the identified bias of investors was weak, it was above the expected rational price and had higher volatility than it could have been expected from a rational perspective. The reason was the effect of the crisis, and the safe haven believes of biased investors who reacted with an increased interest in gold with one year of delay to the crisis. The authors mention that central banks’ gold acquisitions can also be an influencing factor which was not evaluated in the model (Dieupart-Ruel et al., 2013).

Baur and McDermott (2012) performed a study on investor behavior under uncertainty re-lated to safe haven assets comparing gold and U.S. government bonds. The theoretical frame-work was based on the Ellsberg rule from 1961 to investigate which investment preferences investors have with different degrees of uncertainty. Baur and McDermott (2012) found that investors buy gold in times of substantial uncertainty on the market. The comparison with U.S. government bonds shows that if the market signals are extreme but clear, the govern-ment bonds are the preferred investgovern-ment asset. Bonds and gold are both safe havens after severe market shocks but only on a short-term basis for gold. Baur and McDermott (2012) show that emotions and psychological factors influence investors’ decisions. During times of strong uncertainty, investors tend to look for tangible and historically proven assets what makes gold so attractive. The next significant investment risk could, therefore, be to under-estimate the risk of investing in safe haven assets and that bubbles of such assets could result in high losses for investors. It could have been this effect that caused a decline in market

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confidence and decreased the trustability of financial markets during the last financial crisis in 2007 and 2008 (Baur & McDermott, 2012).

2.5 Theory on portfolio selection

According to Berk and DeMarzo (2020), the risk preference and allocation of assets within a portfolio are determining factors for investors when constructing their individual portfolio. Often, the risk-free rate is assumed to be the same whether an investor is saving or borrow-ing, but in reality, the risk-free rate can differ weather the investor is saving or borrowing. Investors generally receive a lower rate when they save than if they are borrowing. For in-stance, short-term margin loans from a broker usually have a higher rate compared to Treas-ury securities. As can be seen in figure 1, the rate of saving or lending (𝑟𝑆) is thereby lower than the rate for borrowing (𝑟𝐵). However, even if the rates are different and a more risk-averse investor, therefore, would choose to save for the lower rate (𝑟_𝑆) and another investor might be an aggressive investor who might borrow funds at the higher rate (𝑟𝐵), the two investors would still have efficient portfolios, just containing different diversification levels based on their individual risk preference. This is because each rate has a corresponding tan-gent portfolio (determined as 𝑇𝑠 and 𝑇𝑏 in figure 1).

However, a more accurate and useful tool created by CAPM is the Security Market Line (SML) which depends only on the market portfolio being a tangent for some interest rate 𝑟∗_{between 𝑟}

𝑆 and 𝑟𝐵. The rate 𝑟∗ depends on the number of savers and borrowers in the economy, but even without this information one can conclude that 𝑟∗_{must be within a} narrow range as saving and borrowing rates (𝑟_𝑆 & 𝑟_𝐵), which tend to be close to each other. Therefore, the formula (1) for the SML still approximately holds and can be used for esti-mating reasonable expected returns:

𝐸(𝑅𝑖) = 𝑟∗_{+ 𝛽}

𝑖(𝐸(𝑅𝑚) − 𝑟∗). (1)

A similar conclusion can be drawn for which risk-free rate to use. For instance, to find the optimal portfolio, the investor needs to find the tangent line by using the risk-free rate that corresponds with the investment horizon of the investor. The risk-free rate varies together

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have the same horizon, then the corresponding risk-free rate to the horizon will also be the SML. If investors have different horizons but still have the same expectations about the investment, then equation (1) will hold for some 𝑟∗_{on the current yield curve. The rate 𝑟}∗_is then dependent on the share of investors within each investment horizon. Since there are several possible efficient portfolios, some investors may invest more or less in gold depend-ing on what risk preference the investor has. In other words, the share of invested capital in gold will be different for different individual investors as all investors have different risk preferences and, therefore, diversification allocation within their portfolio (Berk & DeMarzo, 2020). 𝑇_𝐵 & Borrowing Market Portfolio 𝑇𝐵 Efficient Frontier of Risky investments 𝑇_𝑆 rb r* rs 𝑇_𝑆 & Saving

Volatility (Standard Deviation) Figure 1: The CAPM with Different Saving and Borrowing Rates

2.6 Asset risk determination

The systematic or market risk is a measure for the risk which cannot be erased by diversifi-cation based on co-movement of prices and the total risk of the economy. Investments in different asset categories can help to reduce this systematic risk. One of the main models which encounters market risk is the capital asset pricing model (CAPM)

𝐸(𝑅𝑖) = 𝑟∗+ 𝛽𝑖(𝐸(𝑅𝑚) − 𝑟∗) (2)

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where 𝐸 (𝑅𝑖) is the expected return of an investment, 𝑟∗ is the risk-free rate of interest; 𝛽𝑖 is the beta of the investment, which represents the relationship between the investment i’s return and the market return reduced by the risk-free rate. Lastly, 𝐸(𝑅𝑚) represents the expected return of the market. The focus on beta is especially crucial as it reflects the sensi-tivity of the observed asset in comparison to the market movement. A beta value of one leads to the assumption that the asset moves along with the market. When beta is larger than one, the asset moves stronger compared to the market. A positive beta value, which is lower than one, indicates that the movement of the asset is lower than the market movement. A negative beta is a sign of the asset moving in the opposite direction of the market (Baker & Filbeck, 2015).

Based on the literature review, the three first hypotheses are:

Hypothesis 1: Gold has a negative beta coefficient with the market during financial turmoil. In other words, gold is a strong, safe haven.

Hypothesis 2: Gold has a zero-beta coefficient with the market during financial turmoil. In other words, gold is a weak safe haven.

Hypothesis 3: Gold has a stronger negative or closer to zero beta coefficient with the market during financial turmoil compared to silver and platinum.

2.7 Distinction of developed and emerging markets

Emerging markets could be mainly found in some regions of the Asia-Pacific region, the Middle East and Africa, as well as in Latin America, while developed markets are rather markets in Europe, the U.S. as well as Australia and Japan (Zarantonello, Jedidi, & Schmitt, 2013). According to Harvey (1995), international investors can expect higher returns from investments in emerging markets. Recent studies state that the previously classified emerging markets are approaching and are increasingly merging with developed markets in the latest years and that therefore the distinction gets less necessary (Singh & Kaur, 2015). Neumark, Tinsley, and Tosini (1991) argue that emerging markets often tend to have more substantial price declines at the same time as they also have a longer time to recover than the developed

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emerging markets’ returns more than the ones of developed markets. By the end of the last millennium, emerging markets’ political situation got less risky while the stability of devel-oped markets tended to decrease. Forecasts about future political risks could influence the return expectations, especially for emerging markets. In case of a further shift of the political risks, the difference between emerging and developed markets may pale out or could even reverse (Diamonte et al., 1996). In contrast, according to the findings of Patel & Sarkar (1998), the stock market crises in the emerging markets differ a lot from the crises in the developed markets. Patel and Sarkar’s (1998) study indicates that during the period from 1970 to 1997, the magnitude of the crises in terms of a price decline and duration has become less severe for developed markets but not for those in emerging stock markets (Patel & Sarkar, 1998).

This leads us to the fourth and last hypothesis:

Hypothesis 4: Gold has a negative or a zero-beta coefficient with both developed and emerging markets during financial turmoil. In other words, gold is a weak or strong, safe haven for both developed and emerging markets during turmoil times on the stock market.

2.8 Additional statistical measurements for risk and return

The following measurements are used for data description and are intended to give a better understanding of the different mechanics of the measurements. Firstly, the more commonly used measures such as excess return, standard deviation, Sortino ratio, skewness and kurtosis will be presented. Thereafter, the definitions of the measurements used for further analysis with gold compared to other metals, such as lower partial standard deviation (LPSD), the value at risk (VaR), and the expected shortfall (ES), are added.

Excess return, also called risk premia, are defined as the reward which investors are expected to receive for taking a particular risk when investing in assets. The excess return thereby reflects if a specific asset or index under- or outperforms the returns of a risk-free asset. For this purpose, the risk-free rate is subtracted from the actual rate of return. The mean excess return is the average of all excess returns for the specific timeframe throughout all observa-tions. (Bodie, Kane & Marcus, 2014).

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The standard deviation is a measure of risk, defined as the square root of the variance. A high value of the standard deviation indicates a distribution which is rather spread from the mean. The higher volatility that goes along with it is associated with uncertainty and risk, and therefore, investors usually ask for a higher return to be willing to accept the risk (Bodie, Kane & Marcus, 2014).

The Sortino ratio is also a measure of total risk and return and is an adjusted version of the Sharpe ratio. The difference is that only negative excess returns are considered, therefore the actual returns which are below the risk-free rate. Therefore, instead of taking the total risk into account, only the actual downside risk (downside deviation) is considered, which gener-ates a more accurate picture. The excess return is divided by the downside deviation instead of the total standard deviation (Bodie, Kane & Marcus, 2014).

Skewness is used in statistics to estimate the degree of distortion or asymmetry of the excess returns compared to the normal distribution. Therefore, the skewness of a symmetrical dis-tribution should be zero. To evaluate the skewness, we calculated the ratio of the average cube deviations from the average to the cubed standard deviation. Distributions can be either negatively or positively skewed. A negatively skewed distribution indicates that the left side of the distribution has a fatter or longer tail. This goes along with a risk for investors as the standard deviation will underestimate the risk. In contrast, positive skewness is found, when the tail on the right side of the distribution is fatter or longer, and the mean and median is larger than the mode. These cases tend towards an overestimated risk of the distribution related to extreme positive deviations, which increases the estimated volatility (Bodie, Kane & Marcus, 2014).

Kurtosis is as skewness used to measure the distribution of the selected data compared to a normal distribution, especially to measure outliers. It estimates the tails of the distribution and describes the extreme values of the tails. In a normal distribution, the kurtosis is zero (k-3). Any higher kurtosis is an indicator of fatter tails than for a normal distribution. Kurtosis is calculated by using the deviations from the mean raised by the power of four and divide them by the fourth power of the standard deviation. Three is subtracted from this term as the expected kurtosis of a normal distribution is three (Bodie, Kane & Marcus, 2014).

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The lower partial standard deviation (LPSD) is a development of the previously mentioned measure standard deviation. Instead of calculating the “total risk”, the downside partial standard deviation is only measuring the standard deviation of the returns that are under the target rate (the risk-free rate). Apart from that, LPSD is calculated the same way as the stand-ard deviation. The measure is, therefore, reflecting only the risk of having “bad” returns that are below the required rate (Bodie, Kane & Marcus, 2014).

The value at risk is used to measure the loss that mainly goes along with remarkably high negative returns (Bodie, Kane & Marcus, 2014). The analysis is based on a five percent Value at Risk (VaR), which means that 95 percent of the returns exceed the VaR, and the remain-ing five percent are below. So VaR could be explained by the best rate of return, only lookremain-ing at the five percent future scenarios in the worst case (Bodie, Kane & Marcus, 2014). This measure can be used for normal distributions.

The expected shortfall is an enhancement of VaR. While VaR only looks at the highest re-turn within the five percent range, the estimated shortfall (ES) uses a more realistic view to determine the possible losses. ES is calculated as the average loss with the assumption that the loss is greater than the 95th_{percentile of the distribution of the loss. The expected}

short-fall is usually more likely to be higher than the VaR. ES assumes that the excess returns are normally distributed (Bodie, Kane & Marcus, 2014).

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3. Data

This chapter is initiated with a short description of the data selection process and motivation to why this data was selected. Thereafter, fundamental descriptive statistical measures are presented for gold, silver, and platinum. Furthermore, some extra measures are presented to analyze the different metals further. Lastly, we discuss some different correlation matrices for the different time periods.

The used data set consists of both daily closing market prices of the three metals/commod-ities gold, silver, and platinum and the daily market prices of eight different global indices. All data has been retrieved with the timeframe of January 1, 1990, through December 31, 2019, from the Thomson Reuters DataStream. When selecting the different indices, we de-cided to make a distinction between developed and emerging markets. As representatives for developed markets, the indices prices of the Dow Jones Industrial Average (DJI), the DAX Performance Index (DAX), the Financial Times Stock Exchange 100 Index (FTSE), and the S&P/TSX Composite Index (TSX) were used. Therefore, mainly the financial markets of the United States of America, Germany, Great Britain, and Canada are investigated. As a comparison, daily market prices were also retrieved for the emerging markets NIFTY50 (only from April 23, 1996, due to data availability) to represent India, the Brazil Bovespa Index for Brazil (BOVESPA) (only from January 16, 1990, due to data availability), the Hang Seng Index for China (HSI) and Korea Composite Stock Price Index (KOSPI) for South Korea. All index data was retrieved in the respective local currencies of the indices, but to make the data comparable, we converted all indices prices into USD by downloading the correspond-ing exchange rates in the form of the spot prices for the same period also from Thomson Reuters. By converting the daily closing prices of the indices, any effects related to exchange rates are avoided. Previous studies on gold as a safe haven, as Baur and Mc Dermott (2010), as well as Baur and Lucey (2010), used this fundamental currency adjustment for their studies. The 30-year period was chosen because we want to cover a period which is expected to be rather stable in the first ten years, meaning from 1990 through 1999 that could be compared to a phase with more financial turmoil from 2000 through 2019 and especially with the dot-com-bubble in 2000 and the global financial crisis of 2007 and 2008 afterward followed by the Greece sovereign bond crisis in 2013. We thus compared the results for a 30-year as well as the 20-year period with selected years with financial turmoil, namely 2002, 2008, and 2013.

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The data set of each asset consists of 7,826 daily observations, with exceptions for NIFTY50 and Brazil Bovespa Index, according to shorter data availability. To assess the performance of all assets accordingly, the daily excess returns instead of the simple returns are used for further analysis. The data for the risk-free rate on a daily basis for the specified timeframe was retrieved from the Kenneth R. French webpage by selecting the Fama/French Five-Factor daily data list. The risk-free rate can be defined as the rate of return that could be expected for investing money in risk-free assets such as the bank, money market funds, or T-bills (Bodie, Kane & Marcus, 2014). Any missing data for specific dates was completed with the monthly average of the respective month. According to the data description, the risk-free-rates are based on return data for the one-month Treasury bill rate, which French retrieved from Ibbotson Associates. To get an annualized rate of return, we multiplied the daily excess returns by 261 days. This number was calculated by the average annual data points. The daily standard deviations of the excess returns were thus multiplied by the square root of 261 to annualize the numbers for gold as well as for the indices.

3.1 Descriptive statistics

Descriptive statistics can be defined as the part of statistics that describes the essential statis-tical characteristics of the data set. The target is to give an overview of the presented data set (Clapham & Nicholson, 2014). To get a better overview and understanding of the collected material, we have, therefore, conducted some descriptive statistics on the different indices and commodities used for this research. An overview of all the measures can be found in table A1 in the appendix.

3.1.1 Annualized excess return

On a 30-year basis, we found that gold has the lowest annualized mean excess return of 2.89 percent compared to all other indices except for FTSE with 1.91 percent and KOSPI of 2.80 percent. Table1 shows that the values for the indices vary between 1.91 percent (FTSE) and 34.62 percent (BOVESPA), which further confirms that the excess return of gold is rather low. Remarkably, there is a clear distinction between emerging and developed markets as all the developed markets have a lower annualized mean excess return than the emerging mar-kets except for KOSPI, which has a lower excess return than most indices of the developed markets. In general, one can see that gold does not seem to be a profitable investment throughout different market cycles on a long-term basis from a return perspective. However,

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when comparing gold to the other metals, platinum has an even lower annualized excess return than gold with 1.78 percent, and silver has the highest returns of 5.03 percent. This indicates that even if gold has a lower return than most of the other indices, gold does not have the lowest annualized excess return compared to the other metals.

When analyzing the annualized excess return over a 20-year time period instead of 30 years, we found several interesting differences in the results. Gold had a higher excess return of 8.11 percent (compared to the previous 2.89 percent), which is higher than all indices in the developed markets. As can be seen in table 1, the annualized excess returns over a 20-year period are generally lower for all the indices in developed markets with an exception for TSX, which had the same excess return as for the 30-year analysis (3.77 percent). For the emerging markets, the picture is somewhat split as two of the indices (NIFTY50 & KOSPI) have a higher excess return of 9.29 percent and 5.44 percent compared to the 30-year period. The other two indices (BOVESPA & HSI) have a lower excess return of 11.42 percent and 3.37 percent compared to the 30-year analysis. According to the results, gold has an annualized excess return that is the third largest of all indices. The indices with the most substantial excess returns are still BOVESPA with 11.42 percent and NIFTY50 with 9.29 percent. How-ever, comparing the new excess return of gold with the other metals does not give any indi-cation of a big change more than a generally higher excess return for all three metals. Silver is thereby still the metal with the highest excess return of 8.59 percent, followed by gold with 8.11 percent and lastly platinum with an excess return of 4.83 percent.

The picture of gold throughout the selected turmoil times is quite torn apart.In 2002, when most indices had a negative mean excess return, except NIFTY50 and KOSPI, gold had a positive excess return of 21.01 percent, which is only excelled by platinum with 22.48 per-cent. In 2008, gold had the only positive mean excess return of all metals as well as the indices, which all had negative double figures on the average throughout this year. For 2013 the numbers show the opposite picture. Gold had a negative excess return of minus 30.50 percent while all indices except NIFTY50 and BOVESPA had positive mean excess returns. Silver and platinum followed gold with negative excess returns in 2013, while the numbers for silver were even lower than for gold with minus 37.52 percent.

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Table 1: Annualized excess return

Asset 30 Years (%) 20 Years (%) 2002 (%) 2008 (%) 2013 (%)

Gold 2.89 8.11 21.01 8.94 -30.50 Silver 5.03 8.59 2.96 -17.62 -37.52 Platinum 1.78 4.83 22.48 -44.52 -10.24 DJI (U.S.A) 6.41 4.44 -16.80 -35.63 24.03 DAX (GER) 6.29 5.37 -36.01 -48.55 28.67 FTSE (U.K.) 1.91 0.04 -16.42 -60.97 16.57 TSX (CAN) 3.77 3.77 -14.06 -55.33 3.29 NIFTY50 (IND) 8.28 9.29 4.45 -80.65 -2.80 BOVESPA (BZL) 34.62 11.42 -50.14 -54.52 -27.30 HSI (P.R.C.) 7.91 3.37 -19.97 -53.92 3.96 KOSPI (SKO) 2.80 5.44 3.30 -69.81 3.47

3.1.2 Annualized standard deviation

For 30 years, the annualized standard deviation of the excess returns of gold is 15.75 percent, which is lower than for all the indices. However, the low standard deviation goes along with the low excess return. As one can see in table 2, the annualized standard deviations for the indices range from 16.68 percent (DJI) to 75.33 percent (BOVESPA). For this measure of risk, the picture for developed and emerging markets is well defined, as all standard devia-tions for the indices of developed markets are smaller than the ones for emerging markets. Therefore, the higher volatility of indices of emerging markets generally goes along with a higher mean excess return except for KOSPI, which has the second-lowest excess return of all indices compared to the second-highest standard deviation. These findings indicate that gold has a lower total risk than all the indices, which goes along the lines of the comparison of the metals where gold also has the lowest annualized standard deviation. Silver has the highest annualized standard deviation of 27.03 percent, which is almost twice as much as the annualized standard deviation of gold of 15.94 percent. Platinum also has a relatively high standard deviation of 21.52 percent.

Over a 20-year period, the annualized standard deviation of gold is 17.25 percent, which is slightly higher than the previous 15.75 percent from the 30-year analysis. The result could be interpreted as that gold seems to be riskier during the 20-year time period than the 30-year period. Interestingly this statement seems to be true for all the developed markets as well, as all the indices also have a higher standard deviation when only looking at a 20-year period. However, gold is still the alternative with the lowest standard deviation. A further interesting finding is that the results for the developed markets are the opposite as for the emerging

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markets where all the indices are decreasing for the 20-years period compared to the result for the 30-years analysis. This suggests that the emerging markets and the developed markets are moving closer together, and the differences between the two are no longer as big as for the 30-year analysis. When comparing the standard deviation of gold with the other metals, there are once again no vast differences in the results of the 30-year and 20-year analysis except that the values of the 20-year analysis are slightly higher.

Throughout 2002 and 2008, gold had the lowest standard deviation of all assets of the com-parison with 13.19 and 31.61 percent. In 2013, in contrast, the standard deviation of gold was rather high, with 21.55 percent, while the indices ranged between 3.96 (HSI) and 27.49 percent (BOVESPA). Silver had a higher annualized standard deviation than gold with 33.14 percent, while platinum’s standard deviation was the lowest standard deviation of the pre-cious metals with 17.67 percent (see table 2).

Table 2: Annualized standard deviation

Asset 30 Years (%) 20 Years (%) 2002 (%) 2008 (%) 2013 (%)

Gold 15.75 17.25 13.19 31.61 21.55 Silver 27.03 29.10 18.37 50.88 33.14 Platinum 21.52 22.79 17.75 44.75 17.67 DJI (U.S.A) 16.68 17.81 25.54 37.88 10.17 DAX (GER) 23.80 25.21 37.77 43.97 17.53 FTSE (U.K.) 19.90 21.42 25.69 45.88 13.27 TSX (CAN) 19.04 21.34 18.21 47.69 12.28 NIFTY50 (IND) 26.12 26.02 16.93 48.92 26.79 BOVESPA (BZL) 75.33 38.61 50.57 73.62 27.49 HSI (P.R.C.) 24.59 22.98 19.19 50.66 3.96 KOSPI (SKO) 29.73 25.95 31.86 51.14 15.96 3.1.3 Sortino ratio

During a 30-year period, the Sortino ratio of gold is 26.01 percent, which is high compared to the indices, which range from 13.38 percent (KOSPI) to 78.84 percent (BOVESPA). Only the Sortino ratios of KOSPI (13.38 percent) and FTSE (13.48 percent) are below the value for gold (see table 3). When only considering the downside deviations, gold still has a com-parably low trade-off of risk and return compared to most indices. However, compared to silver (25.93 percent) and platinum (11.52 percent), gold has the highest Sortino ratio. The Sortino ratios over a 20-year period show an interesting deviation from the previously

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men-the highest number of all indices and metals. The indices are ranging from 0.27 percent (FTSE) to 51.46 percent (NIFTY50). It is remarkable how low the Sortino ratio from FTSE of 0.27 percent is compared to the 30-year analysis, where it was 13.48 percent. Beyond this significant change, there is no clear pattern or relationship to the 30-year analysis or between the developed and emerging markets that could be detected. Compared to silver and num, gold still has the highest Sortino ratio, followed by silver with 40.92 percent and plati-num with 29.50 percent. However, compared to the 30-year analysis, the gap between gold and silver has now expanded to be 26.28 percent compared to the previously 0.08 percent. As to be seen in table 3, the Sortino ratios for 2002, 2008, as well as 2013 are exceptionally low or even negative compared to the numbers for the 30-year period. While the Sortino ratio for gold was 2.46 percent in 2002, it decreased to 0.41 percent in 2008 and minus 1.73 percent in 2013. In 2002 and 2008, gold’s Sortino ratio was higher than the values of all precious metals and all indices while it had the lowest value in 2013, also lower than all Sortino ratios of the indices. 2008 drew a clear picture when gold showed the only positive value for the Sortino ratio of all assets in the comparison and, therefore, the only positive risk-adjusted return.

Table 3: Sortino ratio

Asset 30 Years (%) 20 Years (%) 2002 (%) 2008 (%) 2013 (%)

Gold 26.01 67.20 2.46 0.41 -1.73 Silver 25.93 40.92 0.21 -0.49 -1.46 Platinum 11.52 29.50 2.14 -1.28 -0.80 DJI (U.S.A) 54.31 35.12 -0.97 -1.31 3.65 DAX (GER) 37.35 30.17 -1.32 -1.54 2.36 FTSE (U.K.) 13.48 0.27 -0.88 -1.83 1.85 TSX (CAN) 27.06 49.91 -1.07 -1.52 0.36 NIFTY50 (IND) 45.18 51.46 0.38 -2.18 -0.15 BOVESPA (BZL) 78.84 42.23 -1.34 -1.05 -1.40 HSI (P.R.C.) 46.30 20.78 -1.47 -1.50 0.04 KOSPI (SKO) 13.38 28.94 0.15 -1.86 0.31 3.1.4 Skewness

For the timeframe of 30 years, the skewness of gold is positive, with a value of 0.06. As can be seen in table 4, almost all the indices are positively skewed with values ranging from 0.01 for DAX and the extreme value of 6.41 for BOVESPA with an exception for DJI (-0.03) and TSX (-0.57) which have negative skewness. This indicates that the previously mentioned values of standard deviation, therefore, might be over valuated and thus overestimating the