Investment Strategies for Gold in a Dutch Equity Portfolio
Bachelor Thesis Finance
Wouter Lakeman
10054340
Supervisor: Dr Razvan Vlahu
Bachelor Economics & Business, specialization Finance & Organization
Faculty of Economics and Business
University of Amsterdam
ABSTRACT
This research answers the question if gold is a safe haven for investors in the Dutch equity market and analyses the potential of gold in a Dutch equity portfolio. Using the historical returns from 1983 to 2015, this research provides evidence the gold prices increases on days of negative AEX returns, confirming the safe haven status. Adding a fixed 5% weight of gold to the equity portfolio or actively managing a hybrid portfolio with a 50% weight in gold after days of negative AEX-return, did however not outperform the all-equity portfolio in overall Sharpe-ratio.
Chapter 2 Motivation and literature review 2
Chapter 3 Methodology 6
Chapter 4 Data 8
Chapter 5 Hypotheses 9
Chapter 6 Empirical results 10
Chapter 7 Conclusions 16
Literature 17
Appendices 18
LIST OF FIGURES
Figure 1 Historical prices of gold, 1968-2015 2
Figure 2 Historical values AEX-index, 1983-2015 5
Figure 3 Correlation coefficients, 1983-2015 10
Figure 4 Annual portfolio return of the compared portfolios 12 Figure 5 Annualized portfolio volatility of the compared portfolios 13 Figure 6 Cumulative portfolio return of the compared portfolios 13 Figure 7 Overview excess Sharpe ratios in comparison to AEX-return 15
LIST OF TABLES
Table 1 Dataset 8
Table 2 Correlation coefficients on specified days of negative AEX returns 11
LIST OF APPENDICES
Appendix A Overview of portfolio performances 1983-2015 18
Appendix B Optimal risky portfolios 1983-2015 19
Appendix C Days with lowest AEX returns 20
This document is written by Wouter Lakeman, who declares to take full responsibility for the contents of this document. I declare that the text and the work presented in this document is original and that no sources other than those
mentioned in the text and its references have been used in creating it. The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.
Chapter 1 Introduction
Over the last decade, gold has gained in popularity for both investors and individuals. The price of one troy ounce gold, the common metric for gold, approximately 31 grams, has risen from 387 United States Dollars (hereinafter: USD) in 2006 to over a thousand USD in 2015, with its peak value of almost USD 2,000 in September 2011. Over the same time period, stock indices worldwide have seen dramatic decreases following the financial crisis of 2007-2008 and the global recession thereafter. This gives the suggestion that an investor had better put his money in gold, rather than in stocks, as it seems to hold his value in troubled economic times.
Since the Federal Reserve Bank of the Unites States, and the European Central Bank as well, has put its interest rate at almost 0%, individuals are looking for an alternative for their savings accounts, as commercial banks are offering very low interest rates on deposit accounts. This has led to an increased demand for stocks, which have been showing great returns over the past years. Especially index trading has become increasingly popular, which is a fund tracking the return of stock indices. With increasing interest in the stock market, retail investors are well aware of the popular investing rule to not put all your eggs into one basket. There are a lot of ways to diversify an investment portfolio and with the up going gold prices, it leads to the suggestion that adding exposure to gold price movements will properly diversify an equity portfolio. As the popularity of investing in alternative assets increases, and with the rising gold prices in times of negative market returns, it is interesting to investigate the investment opportunities of gold in the traditional equity portfolio.
This research investigates the potential of gold to serve as a safe place to allocate investments, when stock markets face negative returns, which gives gold the status as a safe haven. Furthermore, this research investigates its role in a mixed equity portfolio and proposes the question whether gold is a valuable addition to a Dutch equity portfolio. In this research, the AEX-index (hereinafter: AEX), a stock exchange index compromised of the 25 most traded Dutch stock, is used as a benchmark for a Dutch equity portfolio.
The first chapter gives an introduction to gold and its place in modern portfolio theory. The second chapter discusses the current literature on the gold prices and its use in investment portfolios. The third chapter describes the methodology on investigating the safe haven status of gold and introduce the portfolios that will be compared. This research investigates the properties of both assets, gold and the AEX, and have a look at the historical performance on both assets and will seek to find the correlation between them. The correlation of the two assets is a very important tool to find the diversification potential, which will be discussed using modern portfolio theory. Hereafter, the portfolio implications of adding gold to a portfolio of Dutch stocks are investigated. As the fundamentals of portfolio management are about risk and return, this paper rates the portfolio performance, measured by the return and standard deviation of the combined portfolio, using the Sharpe-ratio. Chapter four describes the 33 years of data, covering the period of 1983 to 2015, including all the major booms and busts of the Dutch stock market. Chapter five gives the hypotheses for this research and chapter six describes the empirical results and my main findings. In the final chapter the characteristics of gold and its potential in a Dutch equity portfolio are evaluated.
Chapter 2 Motivation and literature review
Gold has a long tradition in the financial system. Its use as a monetary standard dates back to the 6th century BC, when the first gold coins were struck in the area that is now part of Turkey. The former Dutch currency, the Dutch guilder, was originally based on a specified weight of fine gold and until the 1970’s the USD had a fixed exchange rate for a quantity of gold, with the official exchange rate of USD 35 per troy ounce (World Gold Council, 2006).
Nowadays, gold is mostly used as a stability asset for central banks. Besides its use in jewellery, and in dental and industrial applications, wealthy individuals, especially in Russia and India, are buying gold as a social symbol of wealth. Gold is often seen as an investment class that keeps its value. In times of troubled financial markets, equities may lose their value fast. Retail investors then begin to escape the financial market and put their money into a safe investment. Gold is then often referred to as a safe haven. (World Gold Council, 2006)
Since there has been free trade in gold, the gold price has had many fluctuations over time. Figure 1 shows the historical prices for gold from 1968 to 2015. In September 2001, the gold price was approximately USD 300 per ounce. Ten years later, the price for one ounce of gold was USD 1,900, providing a return of almost 600%, while going through the largest financial crisis since the 1930’s. It is often suggested that investors are buying gold in times of poor market returns, when they are looking for a safe investment. An asset which is expected to retain its value in periods of uncertainty and low returns is called a safe haven. (World Gold Council, 2006)
Figure 1: Historical prices of Gold in USD per troy ounce, 1968-2015
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Considering the historical prices, the price of gold was stable until the beginning of the 1970’s. This former stability was caused by the Gold Reserve Act, a law in the United States enacted in 1934, which banned the private possession of non-jewellery gold and forced individuals in the United States to sell their gold to the United States Treasury (World Gold Council, 2006). The gold price was then fixed for a specified amount of USD, providing the currency with stability. In 1973, United States citizens were again allowed to buy and hold gold, leading to an increased demand and up going gold price. The gold price has since then fluctuated between USD 35 per ounce to almost USD 2,000.
Many studies have investigated the driving factors of the gold price and its fluctuations. Sjaastad et al. (1996) find that floating exchange rates among the major currencies have been a major source of price instability in the gold market. Furthermore they found that appreciations of European currencies have a strong effect on the price of gold in other currencies. Sherman (1983) makes a gold pricing model and finds that an increase in global tension leads to an increased gold prices. Furthermore, he provides evidence of a negative relationship with the Euro to USD rate. He also provides evidence for a very significant positive relationship for economic growth, and a very significant positive relationship for excess liquidity, which he uses as a proxy for anticipated inflation. His findings on the negative relationship with economic growth and positive relation with global tension provides the suggestion that gold might be a stable asset in troubled economic times. Statistical analysis from Mills (2004) provides evidence that daily gold prices data follow a three-week persistence from shocks, which provides a suggestion for short-term investments in my portfolio research.
The fluctuations in the gold price, especially the positive returns in times of low stock market returns, raises the question if adding gold to a portfolio consisting of company stocks, will improve overall portfolio performance. This research investigates the possibilities for investing in gold in addition to investing in the stock market, combining the return and risk to evaluate the marginal portfolio performance of gold.
Since the issuance of stocks and the existence of stock markets, investors have thought of different ways of managing a portfolio of securities. The breakthrough that led to modern portfolio management was in the second half of the 20th century when Harry Markowitz published his article on portfolio selection in 1952. The fundamental insights about diversifying portfolio comes from the joint movement of the different underlying assets. Generally, the correlation between two assets provides a useful measure to rule out the idiosyncratic risk and therefore reducing the overall variance of returns. He elaborated this idea of stock diversification to the creation of the efficient frontier of risky assets. This frontier shows the efficient portfolio set which generates the highest possible return for any risk level. This insights will give the incentive to test to additional value of gold in an all-equity portfolio. Some years later Sharpe (1966) was the first to rate the performance of securities on a reward-to-variability ratio. This measure, later developed into the Sharpe-ratio, will be the other main component of my research.
A lot of research has been done about the potential of gold as a hedge instrument and a safe haven for different portfolios, mostly consisting investments in United States. The insights of these researches, provide an incentive to investigate the characteristics of gold with respect to the Dutch market. In the research of Reboredo (2013), the role of gold as a hedge or a safe haven is assessed against oil price movements. With the use of probability models he provides evidence that gold can act as a safe haven against oil price movements, but there
are no hedging opportunities as there is a positive dependence between the two assets. Ciner et al. (2013) investigate the relations of return between major asset classes from the United States and the United Kingdom, to examine the potential of stocks, bonds, gold, oil and exchange rates as hedge and safe havens. With respect to gold, they investigate the potential of gold as a safe haven for bonds, gold and currency in the United States and the United Kingdom. They define a safe haven in finance as an asset which is expected to retain its value in volatile market circumstances. Their research shows that gold can be regarded as a hedge for exchange rate fluctuations and to some extend as a safe haven for equities. Baur and McDermott (2010) test the hypothesis that gold represents a safe haven for major emerging and developing countries. They find evidence that gold can act as a safe haven for most major stock markets, including the United States, the United Kingdom, France, Italy and Germany, using correlation models and gold returns on days of extreme negative market returns. Joy (2011) uses a model of dynamic conditional relations of sixteen major dollar-paired exchange rates to investigate if gold acts as a hedge or a safe haven against the USD. His findings are that gold had behaved as a hedge for the USD, but proves to be a poor safe haven.
Besides the research about the main drivers for gold price and its characteristics, there are many articles that provide insights in portfolio characteristics of gold. In comparison with other commodities, Renshaw and Renshaw (1982) find a positive correlation between the quarterly changes in the gold price and in the U.S. Producer Price Index for crude oil. Ratner and Klein (2008) investigate portfolio implications of adding gold to a mixed equity portfolio, and find that gold is a relative poor investment compared with equity investments in the United States in the period 1975 to 2005. Their research find generally low or negative correlations with U.S. stock markets. Adding gold to the portfolio provides only small improvement in portfolio performance on specified periods of poor equity returns but for a long-term investment horizon there is no material benefit. Chua, Sick and Woodward (1990) investigate diversifying portfolios with gold mining and processing companies stocks in the 1970s and 1980s. They find that if the beta of market portfolio strongly increases, the beta for gold remains stable, suggesting meaningful portfolio diversification. However, their results show very low benefits of diversifying common stock portfolios with gold mining and processing companies stocks, for different investment horizons.
Although a lot of research has been done on the potential of gold as a safe haven, there is not much literature about the implication for the Dutch stock market. This research follows up on the research done by Baur and McDermott (2010) and Ratner and Klein (2008). This paper examines the use of gold as a safe haven by calculating the regression coefficient of Dutch AEX volatility with the gold price. This research investigates the potential of gold as a safe haven during the several financial crises from 1983 to 2015, including the greatest periods of negative stock returns following the burst of the dot-com bubble in 2000, and the global financial crisis in 2007-2008 following the American sub-prime mortgage crisis. As the stock market has recently become more attractive to investors, it is interesting to find diversification benefits in alternative assets, in case financial markets suffer from low returns. Besides that, a lot of traditional investors, who do not make use of derivatives, such as stock options and interest swaps, which are considered difficult to understand, make use of commodities as safe investments during troubled times.
As described earlier, from 1983 to 2015 the price of gold has risen from USD 300 per troy ounce to almost USD 1,400 and is currently trading around USD 1,000. This gives a strong sense that when the financial
markets suffered from multiple crises, the price of gold was steadily increasing from 2002 to 2011. Therefore this research investigates the current status of gold as a safe haven for investor in the Dutch stock market, during the several periods of negative market returns from the 1980’s to 2015.
To benchmark the performance of gold to the Dutch stock market, this research will be based on the AEX. The AEX is a stock exchange index which consists of the 25 most traded Dutch stocks, selected each year, and the main indicator for the Dutch stock market. It was founded in 1983 as the EOE-index, named after the European Options Exchange, which was founded in Amsterdam. In 1994 the name changed to AEX. Lacking a sophisticated benchmark for the Dutch stock exchange before the founding of this index, and the increased popularity after its founding, this research takes 1983 as a starting point.
Since the 1980’s the Dutch economy has suffered from several small and big crises. In 2000, the dot-com bubble burst, which led to strong negative returns on international stock markets, with the Nasdaq, a U.S. stock market index for technological companies, losing up to 78% of its value. In the Netherlands, the AEX dived from a value of over 700 points to beneath 300 points in the period starting March 2000 until the summer of 2002 . The index recovered to a value of almost 600 points in 2007 but fell dramatically in the global financial crisis of 2007-2008 to an ultimate low of 199 points in March 2009. In the coming years, the index steadily recovered until 2010, but again suffered a period of negative returns. The final period of negative returns was following the Chinese stock market crash in 2015. Figure 2 provides an overview of the historical prices of the AEX from 1983 until the end of 2015.
Figure 2: Historical values for the AEX, 1983-2015
The research question of this paper is: How can an investor in the Dutch stock market use gold in his portfolio? First, this research will examine the historical returns for the Amsterdam Exchange Index (AEX) and for the Gold price in Euro. Then, the historical returns of gold are implemented in a portfolio mix, to examine the potential for gold in the investor’s portfolio in terms of return and risk.
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Chapter 3 Methodology
The first part of this research investigates the financial characteristics of gold and the AEX. To find potential evidence for the role as a safe haven, a regression analysis is performed with the dependent variable “Return on Gold”, and the explanatory variable “Return on AEX”, which is made from the return on the AEX,
which is compromised of the 25 most traded Dutch stocks. The final model that is used has the following form:
𝑟𝑒𝑡𝑢𝑟𝑛𝑔𝑜𝑙𝑑 = 𝛼 + 𝛽1∗ 𝑟𝑒𝑡𝑢𝑟𝑛𝐴𝐸𝑋+ 𝜀𝑖
As there might be different correlations over time, e.g. the relationship between gold and the index are positive in one year, but negative in another year, there is controlled for this by performing a rolling regression. As a trading year consists of approximately 260 trading days, a regression analysis is done on the first 260 trading days with the return of the AEX as independent variable and the return of gold as the dependent value. The first regression is on the period starting January 1st, 1983 until December 18th, 1983. The second regression is of 250 trading days starting January 2nd, 1983 until December 19th, 1983 and so on until the final regression of 250 trading days ending December 31st, 2015. This provides 8,349 regression coefficient, which are checked to be significantly differing from 0. As the volatility of the returns is not constant, this research is using the robust least squares. The correlation of the entire period is used in portfolio calculations.
To find evidence for the safe haven ability, this research is calculating the correlation coefficient during days of negative AEX-return. The definition of a safe haven in finance is an asset which is expected to remain its value during periods of negative market returns. If the correlation coefficient during periods of negative market returns is lower than zero, this provides therefore evidence if gold is a safe haven. Furthermore, the correlation coefficients are found during days of extreme negative market returns to strengthen the evidence.
After finding the correlation of gold and the AEX, this research uses portfolio theory on the potential of a portfolio consisting of gold and index-stocks. First, the portfolio of the two assets are revised and the historical returns are used to give a prediction of future returns. Combining these assets in a portfolio gives the following expected rate on return, based on historical returns:
𝐸(𝑟𝑝) = 𝑤𝑔𝑜𝑙𝑑∗ 𝑟𝑔𝑜𝑙𝑑+ 𝑤𝐴𝐸𝑋∗ 𝑟𝐴𝐸𝑋
Where 𝑟𝑝 represents the rate of return for the combined portfolio, 𝑤𝑔𝑜𝑙𝑑 and 𝑤𝐴𝐸𝑋 represent respectively the weights in the total portfolio for gold and AEX, and 𝑟𝑔𝑜𝑙𝑑 and 𝑟𝐴𝐸𝑋 are used as the historical
returns of respectively gold and the AEX over the period from 1983 to 2015.
While the returns of both assets will have a proportional weight in the total expected return for the portfolio, the variance is computed somewhat different. The variance of the assets themselves will come from their own returns, but when combining these assets, the risk are reduced due to diversification benefits. This happens because some of the gains, or losses, from one assets are reduced by the gains or losses from the other assets. This fundamental idea for portfolio diversification was originated by Markowitz (1952). Formally, the variance and standard deviation of this portfolio are:
This formula uses the same weights as those used for the expected portfolio return, the standard deviation of the daily returns for both asset and the correlation as found from the regression analysis. Taking the square root of the variance gives the standard deviation, which is computed annually, the most used measurement of risk in portfolio management.
As the historical returns of the AEX outperform gold in the long run, this research investigates the portfolio benefits of various weights in gold. This research considers the following portfolios;
Portfolio 1: An all equity portfolio, with 100% invested in AEX
Portfolio 2: A mixed buy-and-hold portfolio, with 95% invested in AEX and 5% in gold Portfolio 3: A mixed hybrid portfolio, actively managed every day, with the investment rule to invest 100% in the AEX if the AEX-returns of the previous day were positive, and invest 50% in AEX and 50% in gold if the AEX-returns of the previous day were negative.
This research does not take into account the transaction costs of buying and selling the gold shares on daily basis, as the bid-ask spread will vary throughout the period and other transaction fees, such as brokerage fees, vary for individual investors. This assumption may influence the portfolio performance and therefore should be considered when revising the results of this research.
To compare the portfolio performance a variation of the reward-to-volatility ratio is used, as described by Sharpe (1962). Originally, the ratio is calculated by dividing the return over the standard deviation, but in recent times it is more usual to subtract the risk-free rate from the expected return. This is more intuitive, because if the ratio becomes negative, there is a higher return possible by investing at the risk-free rate, and the portfolio becomes instantly unattractive, as there is more risk, and also a lower return. This ratio is known as the Sharpe ratio and is calculated by:
𝑆𝑝=
𝑟̅𝑝− 𝑟𝑓
𝜎𝑝
With 𝑟𝑓 as the risk-free rate, which is obtained from the Dutch interbanking overnight rate, as discussed
by Damodaran (2008), a reference rate based on the average interest rate at which Dutch banks offer to lend money to other banks. This rate was until 1999 known as the AIBOR, which was set especially for banks from the Netherlands, and later replaced by the EURIBOR, a rate for which all banks within the Eurozone would lend other banks money. As this is an interest rate, solely used by large financial institutions to stall money with very low chances of default, this will serve as one of the best proxy available for a risk-free rate in the Netherlands.
Chapter 4 Data
The dataset consists of daily gold prices, from January 3rd, 1983, to December 31st, 2015, in USD per troy ounce, the equivalent of approximately 31 grams, as set by the London Bullion Market Association, which is the leading global gold price (World Gold Council, 2006) and the closing price of the AEX. The gold prices are converted to Euro prices, using the daily exchange rate of USDs to Euros, as this research looks from a Dutch perspective to the return on gold. The return on gold and the AEX is calculated by using the daily closing quote for the same period, calculating the daily returns with these. Exchange rates for the same period are the USD / Euro exchange rate, of which daily price changes are calculated. The exchange rate is used to calculate the daily gold price in Euro, as the AEX is also based on Euro prices of underlying Dutch share prices. All data is obtained from Datastream.
Observatons Mean Standard Error
Median Minimum Maximum
AEX 8 609 297,90 1,79 313,23 45,15 701,56 Gold (USD) 8 609 599,21 4,43 390,70 252,85 1.898,25 USD to EUR 8 609 1,19 0,00 1,22 0,70 1,60 Gold (EUR) 8 609 489,12 3,19 339,76 221,45 1.379,28 return GOLD 8 608 0,01% 0,01% 0,00% -10,32% 7,09% return AEX 8 608 0,04% 0,01% 0,03% -12,00% 11,83%
Table 1: This table presents the descriptive statistics for the data used in this research. The observations are daily closing
prices from January 3rd, 1983 to December 31st , 2015. Return is calculated by dividing the difference between subsequent daily closing prices by the previous former closing price. All data is collected from Datastream.
This specific period is chosen for different reasons. The starting period is set at 1983, when the first index based on Dutch trading stocks was introduced as the EOE-index. This name originated from the European Options Exchange, which was based in Amsterdam, and later changed to AEX, for the Amsterdam Exchange index. As dicussed earlier in this paper, lacking a sophisticated benchmark for the Dutch stock exchange before the founding of this index, and the increased popularity after its founding, this research takes 1983 as a starting point. In the period from 1983, many economic circumstances changed the prices for Dutch stocks. One of the largest stock market crashes was in April 2000, following the burst of the dotcom-bubble. There has not yet been done any research on the safe haven ability and portfolio implications of gold in the most recent years. Also, this research includes the recent stock market crash in China in the summer of 2015, as this may also had an impact on the AEX. Therefore, the data until the end of 2015 is included in this research.
Chapter 5 Hypotheses
This research tests strategies for investment portfolios with the combination of gold and Dutch stocks. If the performance of the mixed portfolio is better than the original all-equity portfolio, it is concluded that it is beneficial to hold gold in a stock portfolio. To investigate this potential, this research first performs statistical research on the properties of gold and then compiles the different portfolios.
In the first part of this research, the correlation between the return on gold and the return on the AEX is computed. The first hypothesis is that gold retains its value when the AEX has a strong negative return, indicating a safe haven. To investigate this hypothesis, the coefficient on the return of the AEX is checked if it is below zero; 𝛽1< 0, during periods of negative return. If the AEX has a period of negative returns, and the
coefficient in that period is below zero, there is an indication that gold can act as a safe haven. There are four periods of negative returns that are included in this research; all of the days of negative returns, the worst 10% of negative returns and the worst 5% and 1%. If the correlation coefficient during all these periods are below zero, it is concluded that gold can act as a safe haven.
The popular belief is that gold will act as a safe haven, therefore the null-hypothesis is that this safe haven status is confirmed. In the previously cited research there was evidence that gold could actually be a safe haven for major European and American stock markets. When looking at the data, there was a large increase in the value of gold from 2001 to 2009, and there were strong negative returns for the AEX. This may give an argument of the stable value of gold in comparison to the exchange index.
The alternative hypothesis , 𝛽1≥ 0, indicates either no significant relationship of gold and the index
(𝛽1= 0), in periods of negative return on the AEX, the return on gold is stable., or there is a positive
relationship of gold and the index (𝛽1> 0). Summarizing these hypotheses gives:
𝐻0: 𝛽1 < 0 , 𝑖𝑓 𝑟𝐴𝐸𝑋< 0
𝐻1: 𝛽1 ≥ 0 , 𝑖𝑓 𝑟𝐴𝐸𝑋< 0
The second hypothesis for this research is about the portfolio implications of adding gold to an all-equity portfolio. After finding the correlation coefficient, the three portfolios are computed to compare the additional value of gold. The portfolio performance measurement used is the Sharpe-ratio, and the different Sharpe ratios are compared for each portfolio. The null-hypothesis for this research is that gold does not significantly add value to the stock portfolio and the average Sharpe ratio of the first portfolio will be greater or equal to the Sharpe ratio of the mixed portfolios. The alternative hypothesis is that there is a benefit in adding gold to the equity portfolio.
𝐻0: 𝑆̅̅̅̅̅ > 𝑆𝑝1 ̅̅̅̅, 𝑆𝑝2 ̅̅̅̅̅ > 𝑆𝑝1 ̅̅̅̅ 𝑝3
Chapter 6 Empirical Results
A rolling regression is performed for a period of 260 days using Stata statistical software. There are 8609 trading days between January 1st, 1983 and December 31st, 2015, and therefore 8349 regression coefficients are collected for the alpha and the beta. The robust standard errors are used to find the upper and lower bound for the 95%-confidence interval by respectively adding and subtracting 1.96 times the standard error to the beta for each coefficient. Summary of the coefficients are displayed in figure 3.
Figure 3: correlation coefficients for regression analysis of return of AEX on return of gold
Observing the data, it can be noticed that both the assets have had great fluctuations in their prices. The AEX originally started at 100, the basis point of the index, but was later converted from Dutch Guilder-standards into Euro-Guilder-standards and therefore divided by the official exchange rate of 2,20371 Dutch Guilder per Euro. The starting point of our analysis is therefore 45,38, and the index had only one lower value, which was the second trading day, as it lost 0,5% of its value to 45.15. The peak value was in September 2000, reaching over 700 points, as the expectations for the internet raised stock prices to new heights.
The ability of safe haven is to remain positive returns, when other assets face negative returns. Therefore, the specific return on gold during periods of negative AEX-returns are checked. In total, there are 9 years of negative annual return on the AEX. In these years, the gold price faced 3 times an annual negative return, and remained positive returns in the other 6 years. Especially, in the three years with the largest negative returns, 2008 (-52%), 2002 (-32%) and 1987 (-32%), the gold price remained stable and increased with respectively 8%, 5% and 4%.
Specifying the data and take a closer look at monthly level it can be observe that in the 32 years of data there were 153 months of negative returns in the AEX. During these months, there were 81 times a positive
-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 19 84 19 84 19 85 19 86 19 87 19 88 19 89 19 90 19 91 19 92 19 93 19 94 19 95 19 96 19 97 19 98 19 99 20 00 20 01 20 02 20 03 20 04 20 05 20 06 20 07 20 08 20 09 20 10 20 11 20 12 20 13 20 14 20 15
Correlation coefficients
return on gold and 72 times a negative return. This implies that only in about half of the occurrences of negative monthly AEX-returns, gold has provided positive returns. The three months with the largest negative returns, October 1987 (-30%), July 2002 (-22%) and September 2008 (-19%) gave the respective returns on gold of -3%, -2% and +12%.
Looking at the daily returns, 3905 daily negative returns have been observed for the AEX in the total 32 years. On these days, the returns on gold were positive on 1872 days. On the days with three largest negative returns on the AEX, 19th of October 1987 (-12%), 26th of October 1987 (-9%) and 6th of October 2008 (-9%) the price of gold increased however with +2%, +0,2% and +5% respectively. In the bottom 1% of negative returns, the average return on gold was positive, at 0,14%. In the worst 5% of AEX-returns, the return on gold was also slightly positive at 0,14%. In the worst 10% of negative daily returns, the return on gold was also positive at just over 0,05%. This provides evidence that gold remains its value during extreme market conditions. An overview of the 20 trading days with most negative returns can be found in appendix C.
To check the potential as a safe haven, the correlation coefficient is computed of the return on AEX on the return of gold. If the coefficient is zero or negative, and the return in the AEX is negative, this means that when there is a decrease in share prices, the gold price had a positive movement and did not suffer from the same underlying decreasing factor. The role of gold as a safe haven can then be confirmed. If the yearly correlation coefficients of the returns is considered, it can be concluded that the overall correlation is on average a little above zero. The results are shown in the figure 3. There are some periods in which the yearly correlation is below zero, from 1989 to 1992, around the year 2002-2003 from 2008 to 2012 and in 2014. This gives an impression there might be negative correlation in periods of negative market returns.
To justify the role of a safe haven, this research looks to the correlation during periods of negative AEX returns. The results are presented in table 2 and prove that gold have kept its value in the past 33 years on days of negative AEX returns. Looking at all the days of negative AEX returns, 3914 in total, the correlation coefficient was negative at -0,05. When looking at the worst 10%, 5% and 1% days of negative returns, the correlation decreases further, with the lowest correlation of -0,7 at the 1% of worst negative AEX-return days. All these correlation are significantly lower than zero and therefore this research accepts the null-hypothesis, which confirms that gold is a safe haven for the AEX.
Table 2 Correlation coefficients on specified days of negative AEX returns.
* significant at 5%, ** significant at 1%
Negative AEX-return days Observations Av. Return AEX Av. Return Gold Correlation
All negative days 3,914 -0.39% -0.02% -0.050** lowest 10% 391 -3.31% 0.04% -0.153** lowest 5% 196 -4.20% 0.15% -0.170* lowest 1% 39 -6.50% 0.17% -0.692**
With this information, the portfolio implication of adding gold to an all-equity portfolio is investigated. For the years 1983-2015 the monthly returns on three portfolios are checked and the risk profiles as described by Markowitz (1952) are computed. The computed portfolios are as follows:
Portfolio 1: An all equity portfolio, with 100% invested in AEX
Portfolio 2: A mixed buy-and-hold portfolio, with 95% invested in AEX and 5% in gold
Portfolio 3: A mixed hybrid portfolio, actively managed every day, with the investment rule to invest 100% in the AEX if the AEX-returns of the previous day were positive, and
invest 50% in AEX and 50% in gold if the AEX-returns of the previous day were negative.
As the correlation between the return of both assets is negative in periods of negative AEX-returns, this gives insights there are diversification benefits possible. The performance of the different portfolios is shown in figures 5, 6 and 7 and in detail in appendix A.
Figure 5: Annualized portfolio volatility of the all-equity, buy-and-hold and day-trading portfolios
Figure 6: Cumulative performances of the all-equity, buy-and-hold and day-trading portfolios, starting with a EUR 1,000 investment in 1983
Looking at the empirical results of the three different portfolios, the cumulative performance of the day-trading portfolio gives the highest return over the entire 33-year period. Also the average volatility was around 2% lower than the other portfolios. However, the average Sharpe-ratio of this portfolio, which is 0.57, is not greater than for the all-equity portfolio, which is 0.58.
Adding 5% of gold to the he buy-and-hold portfolio does lower volatility a little, but the return drops in almost every year. This research extended this analysis of the buy-and-hold portfolio, to calculate the optimal risky portfolio for each year. In seven years in the period 1983-2015 the Sharpe ratio is increased by adding gold to the stock market portfolio. In all other years the portfolio has a higher Sharpe ratio if it is 100% invested in the stock market. The years for which gold is an valuable addition in terms of risk-return payoff, are 1986, 1987, 1992, 1994, 2000, 2007, 2010 and 2014. However in four of these seven years, the return of this portfolio did not exceed the risk-free rate, and one would be better off putting his money into more secure investment, such as bank savings deposits. Therefore, the only years in which adding gold to a stock market portfolio was more beneficial was in the years 2007, 2010 and 2014. The optimal weights for investment in gold in these years are respectively 100%, 67% and 69%. These weights are computed by maximizing the Sharpe ratio for each year, and solving for the weights, thereby giving the optimal risky portfolios. An overview of optimal risky portfolio can be found in appendix B.
There is therefore enough evidence to state that adding a fixed weight of gold to a portfolio based on the Dutch stock market has no additional value. The only instances in which their might be evidence for diversification benefits are under extreme market circumstances. Actively managing the portfolio and making the investment rule to put a 50% portfolio weight in gold after a day of negative return on the AEX, there are benefits from the diversification ability. The annual volatility dropped by an average of 2% each year and the cumulative results for the 33 year period from 1983 to 2015 were also better in terms of return. The actively managed portfolio would have led to 11.3 times the initial investment and the all-equity portfolio would have led to 9.3 times the initial investment. Also the actively managed portfolio has a maximum volatility of 30% in the 33 year period, whereas the all-equity portfolio had a maximum volatility of 41%. These results do include the assumption that no transaction costs are paid when buying and selling the weight in gold on daily basis.
However the average Sharpe ratio does not improve and is the highest for the all-equity portfolio at 0.58, followed by the buy-and-hold portfolio with 0.57 and the actively managed portfolio has the lowest average Sharpe ratio, 0.56. Therefore, this research concludes that the Sharpe-ratio has not improved in the period from 1983-2015 by adding gold to the portfolio. Therefore, this research accepts the null-hypothesis and rejects the hypothesis that gold has a proved additional value in a stock portfolio for the investor who is pursuing the highest Sharpe ratio. Investor looking to lower the volatility of their equity portfolio, could however include gold in specific periods of negative market returns, but have to take into account the transaction costs of buying and selling gold.
Specifying for each year, there are some years in which adding gold proved to be of additional value. The buy-and-hold portfolio outperformed the all-equity portfolio in 16 of the 33 years, by a small excess in Sharpe-ratio but independent from the return on the AEX. Figure 6 and appendix A shows the outperformance of the two alternative portfolios with the original all-equity portfolio in comparison for the return of the AEX.
Figure 7: Overview of excess Sharpe ratio for both portfolios in comparison to return of AEX
The day trading portfolio shows a different pattern when compared to the all-equity portfolio. There are in total 14 years in which the day trading portfolio outperforms the return on the AEX. The years in which the all-equity portfolio has a better Sharpe ratio are during years in which the AEX had positive returns and in most of the years in which the day trading had the most extreme excess Sharpe ratio, the AEX faced negative returns. When checking for independence it can be shown that the outperformance of the day trading portfolio was dependent on the return of the AEX. The overall Sharpe ratio of the all-equity portfolio may be higher than for the other portfolios, the alternative portfolios with the addition of gold did outperform the original portfolio in periods of negative AEX return. It may therefore be a suggestion for an investor who is expecting negative market returns, however it should not be included in the investor’s portfolio at all time. Transaction costs for the day trading portfolio are not included in the portfolio performance. Individual investors will have to take into account their personal transaction costs and bid-ask spread to review the possibilities of adding gold on their portfolio performance. -80% -60% -40% -20% 0% 20% 40% 60% 80% -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 1 9 8 3 1 9 8 4 1 9 8 5 1 9 8 6 1 9 8 7 1 9 8 8 1 9 8 9 1 9 9 0 1 9 9 1 1 9 9 2 1 9 9 3 1 9 9 4 1 9 9 5 1 9 9 6 1 9 9 7 1 9 9 8 1 9 9 9 2 0 0 0 2 0 0 1 2 0 0 2 2 0 0 3 2 0 0 4 2 0 0 5 2 0 0 6 2 0 0 7 2 0 0 8 2 0 0 9 2 0 1 0 2 0 1 1 2 0 1 2 2 0 1 3 2 0 1 4 2 0 1 5
Performance Alternative Portfolios vs Return AEX
Chapter 7 Conclusions
This research investigates the potential role of gold as an investment asset. Over the last 30 years the Dutch stock market has had many small and large fluctuations which negatively affected the return for investors. To protect themselves from exposure to negative market shocks, investors can diversify their portfolio with other investment assets, preferably assets that tend to move in the opposite directions, when the primary assets face negative returns. This concept of diversification was elaborated by Markowitz and led to the rise of modern portfolio theory. The fundamental rational is that investors can remove the idiosyncratic risk of an asset, industry or country by adding assets from other investment classes.
This research consults the existing literature on gold price movements to find an explanation for the diversification potential of adding gold to an existing equity portfolio. The main findings from previous research are that an increase in expected inflation, insecurity of financial markets and fluctuating exchange rates were the main sources of the movement in the gold price. This leads to the suggestion that gold can keep its value when equity markets are in troubled times, as the fluctuations are one of the driving factors of rising gold prices.
For the empirical research, the daily gold prices and AEX values for the period from 1983 to 2015 are observed. Using the daily returns, the diversifying potential is examined by regressing the index returns on the gold price returns, and found that the correlation between the returns of both assets tend to be above zero on average. In times of negative returns, the return on the gold price is overall positive and the correlation coefficient is significantly below zero. Therefore this research concludes that the safe haven ability of gold is confirmed. Especially in times of extreme shocks on the Dutch stock market, there are overall positive returns of holding gold. This is confirmed by the significant positive returns on gold, during the 1%, 5% and 10% of largest negative returns on the AEX.
Lacking the ability to precisely time the market, this research looks at the portfolio implications of adding gold to an existing equity portfolio, replicating a buy-and-hold decision and an actively managed day trading portfolio. To evaluate the additional value of gold in a portfolio, three portfolios are replicated: an all-equity portfolio with 100% invested in the AEX, a mixed portfolio with 95% invested in the AEX and 5% in gold, and a day trading portfolio with 100% in the AEX after a day of positive AEX returns and 50% in the AEX and 50% in gold after a day of negative AEX returns. Both alternative portfolios did not significantly outperform the all-equity portfolio. There are in total seven years in which a partial investment in gold would have a beneficial effect to the equity portfolio, however returns and Sharpe ratios cannot be significantly greater with a fixed weight in gold.
The actively managed portfolio did outperform the AEX in terms of volatility and in terms of cumulative return in the 33-year period. Especially during the last decade returns were higher and volatility was lower. However, there was no significant outperformance in terms of Sharpe-ratio compared to the all-equity portfolio and transaction costs are not included. This research therefore concludes that there are no benefits in adding a fixed weight of gold to a stock portfolio, and a 50-50 weight in gold and AEX after a day with negative AEX-returns is not significantly outperforming. However, if the investors has the ability to time the market effectively, he can have benefit from the safe haven status of gold.
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Appendices
Appendix A: overview of results for portfolios 1983-2015. The NLIBOR gives the Dutch inter banking offering rate, the
Sharpe+ columns give the excess in Sharpe ratio for both portfolios in comparison to the all-equity portfolio. The last three columns give the 33-year cumulative return, starting with an investment of EUR 1,000 in 1983.
N L IBO R Y ea r Ra te Re turn St d. D ev Sha rp e Re turn St d. D ev Sha rp e Sha rp e+ Re turn St d. D ev Sha rp e Sha rp e+ AE B& H DT 1983 5.6% 61.3% 17.3% 3.22 58.4% 16.7% 3.16 0.06 - 43.9% 15.9% 2.41 0.81 - 1,613.49 1,584.00 1,439.33 1984 6.1% 17.1% 20.5% 0.53 15.9% 19.6% 0.50 0.03 - 18.7% 17.9% 0.70 0.17 1,889.60 1,836.34 1,708.59 1985 6.4% 41.7% 12.9% 2.75 38.9% 12.2% 2.67 0.08 - 34.5% 11.7% 2.40 0.34 - 2,677.39 2,551.05 2,298.08 1986 5.7% -5.6% 18.3% 0.62 - -5.4% 17.5% 0.64 - 0.02 - -9.2% 14.9% 1.00 - 0.38 - 2,527.32 2,412.19 2,086.51 1987 5.4% -32.1% 35.6% 1.05 - -30.3% 33.8% 1.05 - 0.00 - -29.1% 28.0% 1.23 - 0.18 - 1,715.95 1,681.38 1,480.18 1988 4.8% 53.5% 20.2% 2.41 50.5% 19.3% 2.37 0.04 - 34.4% 17.5% 1.69 0.72 - 2,633.98 2,530.98 1,989.23 1989 7.4% 14.3% 15.2% 0.45 13.3% 14.4% 0.41 0.05 - 22.3% 11.8% 1.26 0.81 3,009.92 2,866.50 2,432.43 1990 8.7% -23.9% 17.8% 1.82 - -23.4% 16.8% 1.91 - 0.09 - -7.8% 13.8% 1.19 - 0.63 2,291.98 2,197.14 2,242.12 1991 9.3% 20.9% 14.2% 0.81 19.5% 13.1% 0.78 0.04 - 9.6% 12.1% 0.03 0.79 - 2,770.38 2,625.10 2,457.43 1992 9.5% 3.2% 12.2% 0.52 - 3.3% 11.9% 0.52 - 0.00 12.1% 11.7% 0.22 0.74 2,858.31 2,712.84 2,754.57 1993 7.2% 47.1% 11.2% 3.57 46.2% 10.7% 3.64 0.07 44.9% 11.0% 3.43 0.14 - 4,203.61 3,966.77 3,991.99 1994 5.3% -0.8% 13.3% 0.46 - -1.3% 12.7% 0.52 - 0.06 - 3.7% 11.6% 0.14 - 0.32 4,171.66 3,915.90 4,141.34 1995 4.5% 16.3% 9.3% 1.27 15.2% 9.1% 1.19 0.09 - 21.6% 9.0% 1.91 0.63 4,853.24 4,512.48 5,036.14 1996 3.3% 33.6% 11.7% 2.58 31.9% 11.2% 2.55 0.03 - 21.2% 9.7% 1.85 0.73 - 6,482.15 5,951.37 6,105.50 1997 3.3% 40.9% 23.6% 1.59 38.5% 22.5% 1.56 0.03 - 32.1% 19.6% 1.47 0.13 - 9,136.40 8,240.13 8,064.04 1998 3.5% 29.8% 28.5% 0.92 28.0% 27.1% 0.90 0.02 - 33.9% 21.5% 1.41 0.49 11,863.38 10,545.44 10,794.04 1999 3.0% 25.5% 20.2% 1.11 25.0% 19.5% 1.13 0.02 34.1% 17.6% 1.77 0.66 14,884.09 13,185.78 14,471.14 2000 4.5% -5.6% 18.7% 0.54 - -5.3% 17.9% 0.54 - 0.00 - -9.3% 16.4% 0.84 - 0.30 - 14,050.24 12,493.44 13,126.11 2001 4.2% -20.5% 26.4% 0.93 - -19.1% 25.1% 0.93 - 0.01 -8.6% 20.1% 0.64 - 0.30 11,167.47 10,101.57 12,000.18 2002 3.3% -36.3% 37.9% 1.04 - -34.2% 36.0% 1.04 - 0.00 -22.9% 27.4% 0.95 - 0.09 7,111.72 6,642.72 9,255.43 2003 2.3% 4.6% 33.2% 0.07 4.4% 31.5% 0.07 0.00 - -8.2% 25.7% 0.41 - 0.48 - 7,440.50 6,938.22 8,492.49 2004 2.1% 4.2% 14.8% 0.14 3.9% 14.1% 0.13 0.01 - -1.2% 12.6% 0.26 - 0.40 - 7,754.74 7,210.99 8,391.29 2005 2.2% 25.2% 10.3% 2.23 25.6% 9.8% 2.38 0.15 25.7% 8.6% 2.73 0.50 9,707.36 9,056.75 10,549.98 2006 3.1% 12.4% 13.7% 0.68 12.4% 13.3% 0.69 0.01 7.6% 13.7% 0.33 0.35 - 10,915.38 10,176.06 11,356.47 2007 4.3% 4.1% 16.1% 0.01 - 4.9% 15.4% 0.04 0.05 1.9% 13.8% 0.17 - 0.16 - 11,365.58 10,670.72 11,571.30 2008 4.6% -52.3% 40.7% 1.40 - -49.3% 38.5% 1.40 - 0.00 -46.8% 30.1% 1.71 - 0.31 - 5,419.57 5,412.47 6,151.72 2009 1.1% 36.3% 30.9% 1.14 35.7% 29.2% 1.18 0.05 27.7% 22.7% 1.17 0.03 7,389.38 7,344.01 7,856.43 2010 0.8% 7.3% 20.4% 0.32 8.9% 19.4% 0.42 0.10 19.5% 16.1% 1.16 0.85 7,929.93 7,997.16 9,389.68 2011 1.4% -12.0% 22.1% 0.61 - -10.6% 20.8% 0.58 - 0.03 -3.5% 18.3% 0.27 - 0.34 6,981.49 7,145.80 9,063.11 2012 0.5% 8.2% 17.9% 0.43 8.0% 17.1% 0.43 0.01 10.4% 13.7% 0.73 0.30 7,552.01 7,714.68 10,010.10 2013 0.2% 17.2% 12.5% 1.37 14.9% 11.9% 1.23 0.13 - -1.4% 12.0% 0.14 - 1.50 - 8,853.90 8,860.54 9,870.11 2014 0.2% 5.6% 13.1% 0.41 6.0% 12.4% 0.46 0.05 -0.5% 10.4% 0.06 - 0.48 - 9,353.68 9,388.17 9,825.06 2015 0.0% 4.1% 21.2% 0.19 3.9% 20.2% 0.19 0.00 - 14.7% 17.6% 0.84 0.65 9,736.01 9,749.81 11,273.11 av er age 0.58 0.57 0.01 - 0.56 0.02 - 33 ye ar c u mu lati ve p er for ma n ce A ll-e qu ity P or tfol io Bu y-a n d-h ol d P or tfol io D ay tr ad in g P or tfol io
Appendix B: optimal risky buy-and-hold portfolios 1983-2015
Year Weight AEX Weight Gold Return Std. Dev. Sharpe
1983 100% 0% 61,3% 17,3% 3,22 1984 100% 0% 17,1% 20,5% 0,53 1985 100% 0% 41,7% 12,9% 2,75 1986 32% 68% -3,4% 27,0% - 0,34 1987 0% 100% 4,0% 14,7% - 0,09 1988 100% 0% 53,5% 20,2% 2,41 1989 100% 0% 14,3% 15,2% 0,45 1990 100% 0% -23,9% 17,8% - 1,82 1991 100% 0% 20,9% 14,2% 0,81 1992 28% 72% 5,6% 40,4% - 0,10 1993 100% 0% 47,1% 11,2% 3,57 1994 82% 18% -2,7% 21,5% - 0,37 1995 100% 0% 16,3% 9,3% 1,27 1996 100% 0% 33,6% 11,7% 2,58 1997 100% 0% 40,9% 23,6% 1,59 1998 100% 0% 29,8% 28,5% 0,92 1999 100% 0% 25,5% 20,2% 1,11 2000 3% 97% 1,2% 19,2% - 0,17 2001 100% 0% -20,5% 26,4% - 0,93 2002 100% 0% -36,3% 37,9% - 1,04 2003 100% 0% 4,6% 33,2% 0,07 2004 100% 0% 4,2% 14,8% 0,14 2005 100% 0% 25,2% 10,3% 2,23 2006 100% 0% 12,4% 13,7% 0,68 2007 0% 100% 18,9% 13,6% 1,07 2008 100% 0% -52,3% 40,7% - 1,40 2009 100% 0% 36,3% 30,9% 0,63 2010 33% 67% 28,4% 11,3% 2,44 2011 100% 0% -12,0% 22,1% - 0,61 2012 100% 0% 8,2% 17,9% 0,43 2013 100% 0% 17,2% 12,5% 1,37 2014 31% 69% 9,9% 9,8% 1,00 2015 100% 0% 4,1% 21,2% 0,19
Appendix C: Days with lowest 1% negative returns for AEX from 1983 to 2015, with corresponding gold returns
Date Return AEX Return Gold
October 19, 1987 -12.00% 2.26% October 26, 1987 -9.27% 0.24% October 6, 2008 -9.14% 5.07% September 29, 2008 -8.75% 2.23% October 10, 2008 -8.48% 0.86% October 8, 2008 -7.68% 3.43% October 15, 2008 -7.56% 1.36% September 14, 2001 -7.25% 1.04% October 22, 1987 -7.24% 1.06% November 9, 1987 -7.13% -0.29% September 11, 2001 -6.95% 5.19% July 22, 2002 -6.92% 0.83% November 30, 1987 -6.84% 2.14% December 1, 2008 -6.75% -4.09% November 6, 2008 -6.74% 1.05% October 16, 1989 -6.57% -0.24% M arch 24, 2003 -6.38% -1.99% January 21, 2008 -6.14% 1.00% September 30, 2002 -6.14% -0.13% January 12, 1987 -5.95% 0.31% October 28, 1987 -5.95% -0.23% September 21, 1998 -5.93% -0.16% August 1, 2002 -5.93% -0.34% October 20, 1987 -5.92% -1.72% July 15, 2002 -5.88% -0.43% October 16, 2008 -5.69% -4.67% December 28, 1987 -5.44% 0.00% January 13, 1999 -5.40% -2.40% February 24, 2003 -5.38% 1.53% November 3, 1987 -5.34% -0.75% October 22, 2008 -5.30% -1.20% October 2, 1998 -5.29% -0.19% August 24, 2015 -5.24% -2.09% M arch 5, 2009 -5.20% 0.08% M arch 31, 2003 -5.18% 0.27% January 14, 2009 -5.15% -1.22% September 20, 2001 -5.14% -0.26% September 10, 1998 -5.14% 0.32% April 27, 1998 -5.04% -1.05%
