The role of gold as a component of Dutch equity-investing portfolios

The role of gold as a component of

Dutch equity-investing portfolios

2

Abstract

This research investigates the role of gold as a component of Dutch-equity investing portfolios for the period of 2007 until 2017. Specifically, the function of gold as a hedge and safe haven during downturns on the Dutch stock market is examined using regressions with dummy variables for lower quantiles and analyzing conditional correlations. The Amsterdam Exchange Index is used as a market proxy. Evidence is found that gold can function as a hedge and safe haven in the sample period of 2007 until 2017. A correlation analysis conditional on the lower percentiles showed values between -0.12 and -0.34, confirming the function of a hedge on average and the function of a safe haven for the lower percentiles. Therefor, holding a well-diversified portfolio of Dutch stocks and gold could increase returns on the portfolios of Dutch-equity investors. Sharpe Ratio maximization and Variance minimization concluded that the optimal weight of gold in a Dutch-equity investing portfolio is increasing in the lower percentiles, with a minimum of 76.15% and a maximum of 100% for the Sharpe Ratio maximization and likewise 29.46% and 59.69% for the Variance minimization. Statement of Originality

This document is written by Student Jesse de Bruijn who declares to take full responsibility for the contents of this document.

I declare that the text and the work presented in this document are 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.

3 CONTENTS 1. Introduction p. 4 2. Literature review p. 6 2.1 Gold as a hedge and safe haven p. 6 2.2 Gold as a component of portfolios p. 8 3. Research method p. 10 4. Data and descriptive statistics p. 13 4.1 Data p. 13 4.2 Descriptive statistics p. 13 5. Results p. 15 6. Conclusion and discussion p. 22 References

4

1. Introduction

Since the beginning of the financial crisis of 2007-2008, the gold price has shown an incredible growth. The price of one troy ounce of gold, a system used for weighing and pricing precious metals like gold, which is approximately 31 grams, has risen from 479 euros in January 2007 to over a thousand euros in 2018. More importantly, the gold price has shown an increase of more than 30% during the financial crisis while other assets, in particular AEX stock prices, decreased drastically. While on the other hand, after the financial crisis, the gold price experienced dramatic decreases in the year of 2013 of -31,6% (World Gold Council, 2018). Given the development of the price of gold during and after the financial crisis and the recent decline in the price of gold in 2013 while stock markets started to come up to new heights, the relationship between stock prices and the gold price during different circumstances is an interesting attention point for investors. The main investment-based goals of investors are maximizing expected returns and minimizing the risk of portfolios to increase utility. But choosing the right

5

components is usually a difficult task for investors, especially during extreme changes in the stock markets. While gold is quite volatile as an individual asset, its returns are generally independent of those on other stocks, and thereby fulfills the function of an hedge. If gold reduces losses due being uncorrelated or negatively correlated with other assets in times of financial crisis or market stress by more than a hedge, gold fulfills the function of a safe haven asset which is attractive for investors to cover losses (Baur and Lucey, 2010).

But is gold still an attractive component of an optimal diversified investment portfolio after the financial crisis, with the dramatic decline of 2013 in our minds? The recent financial crises and the corresponding strength of the gold price during these crises, highlights the sense of testing the resistancy of gold as an instrument to hedge portfolios from losses for possible upcoming crises. Therefor, the main question for this research with the sub questions respectively are as follows. Can gold function as a hedge and safe haven as a component of Dutch equity-investing portfolios?

- Is there a change in correlation pattern during and after downturns on the stock market?

- Does the optimal proportion of gold in a portfolio significantly change during and after downturns on the stock market?

The purpose of this thesis is to investigate whether gold can contribute to an optimal portfolio of a Dutch equity investor. Current literature, see Section 2, is mostly based on the U.S. stock market and the data used in the researches done in the past is mostly from before the financial crisis of 2007-2008, which is not very actual. Therefor, in this research, the function of gold as a hedge and a safe haven is tested to investigate the functions of gold during average periods and periods of financial crisis using data between 2007 and 2017, including the financial crisis of 2007-2008 and is based on the perspective of a Dutch-equity investor. The function of a hedge and a safe haven is tested using regressions with dummy variables for the lower percentiles and conditional correlations analysis. The results of this approach show negative coefficients for the entire period and the dummy variables, together with negative correlation coefficients. Therefor, the function of a hedge and safe haven can be confirmed. Furthermore, to construct an optimal portfolio, comprising Dutch stocks and

6

gold, the Markowitz’ Portfolio Variance Minimization model and the Sharpe Ratio maximization model are used, resulting in optimal values of gold increasing in the lower percentiles. The results of this research do have some implications. The overall AEX is used as a market proxy, ignoring diversification possibilities inside the market. Thereby, it does not take into account any additional cost of trading and storing (physical) gold.

This thesis is organized as follows. The first section of the thesis is the introduction. Section 2 provides the literature review to further describe the purpose of the thesis with respect to the existing literature. Section 3 describes the research method and hypotheses. Section 4 provides the data and analyzes the descriptive statistics. Section 5 analyzes the regressions and empirical results. Section 6 includes the discussion and gives an overall conclusion of the results obtained.

2. Literature review

The results of scientific research done so far on the role of gold as a hedge or safe haven is mostly based on the dollar prices and the stock market of the United States. Numerous studies have explained the investment benefits of adding gold to portfolios of U.S. equities and many find that the right allocation improve the overall performance of the portfolios (i.e. Jaffe [1989] and Chua, Sick and Woodword [1990]).

2.1 Gold as a hedge and safe haven

Capie, Mills and Wood (2005) analyzed the role of gold as an exchange rate hedge against the dollar, using sterling-dollar and yen-dollar exchange rates, and concluded that gold indeed has been a hedge against the dollar for their weekly data used from 1974-2004. Capie, Mills and Wood (2005) concluded that gold has been a hedge because authorities cannot produce gold like authorities produce currencies. They also concluded that the strength of the negative relationship between the dollar and gold price has shifted over time, which makes the conclusions unpredictable for upcoming political proceedings.

Baur and Lucey (2010) found evidence that gold is a hedge against stocks on average and a short-lived safe haven in extreme stock market conditions in the United Kingdom, United States and Germany. The data of their research covers the time period

7

of November 1995 until November 2005. Baur and Lucey (2010) are the first in the literature to make a distinction between a hedge and a safe haven. They define that a hedge is an asset that is uncorrelated or negatively correlated with another asset or portfolio on average. On the other hand, they define a safe haven to be an asset that is uncorrelated or negatively correlated with another asset or portfolio in times of extreme negative stock market conditions. This research uses the definitions Baur and Lucey introduced in 2010.

Baur and McDermott (2010) test the hypothesis that gold can act as a safe haven against stocks of major emerging and developing countries for the period of 1979 until 2009. Their analysis shows that gold is both a hedge and safe haven for major European stock markets and the United States, but not for Australia, Canada, Japan, and large emerging countries such as the BRIC countries. They furthermore looked at the difference between daily, weekly and monthly data and found that the findings for the safe haven role of gold are the strongest for daily data. Therefore, Baur and McDermott (2010) suggest that gold can be seen as a panic buy during and after extreme negative market shocks. The results of Ghazali, Lean and Bahari (2013) are in line with the results of Baur and McDermott (2010). Ghazali et al. (2013) investigated the role of gold to hedge risks on average and the function of gold as a safe haven asset against losses in financial markets in Malaysia. The results are in line with the results of Baur and McDermott (2010) where gold functions as a hedge and safe haven for emerging markets like Malaysia, but the results are short-lived. Ghazali et al. (2013) suggest readjusting the portfolios by withdrawing from emerging markets to developed markets.

Ciner, Gurdgiev and Lucey (2013) use regressions with dummy variables for the lower quantiles to provide evidence on whether assets classes, including gold, can act as a safe haven for each other. For the hedge function of gold, Ciner et al. (2013) use conditional correlations. The findings of their study confirm that gold can act as a safe haven against exchange rates in both the U.S. and the U.K. using daily data between 1990 and 2010.

8

Beckmann, Berger and Czudaj (2015) investigate whether gold can act as a hedge or safe haven using a splitsed up regression model consisting of two extreme regimes. The first regime consists of periods in which stock returns are measured on average to test the hedge function of gold, while on the other hand the second regime accounts for periods of extreme market conditions consisting of high volatility of stock returns. The study includes data of 18 individual markets and covers a sample period from 1970 until 2012, using monthly data. The overall findings of their study confirm the importance of gold as an ingredient of a diversified portfolio. 2.2 Gold as a component of portfolios Jaffe (1989) created a portfolio consisting of gold proxies of the Toronto Stock Exchange and a mutual fund of South African gold-mining in combination with a market proxy consisting of S&P 500 stocks, long-term corporate bonds, long-term government bonds and Treasury bills. The combination of the gold proxies together with the hypothetical diversified portfolio resulted in an increase of average returns together with an increase of the standard deviations. However, the increase in average returns outperforms the increased standard deviations.

Chua et al. (1990) investigated whether adding gold proxies to a portfolio of U.S. common stocks in a timeframe of 1971-1988 leads to diversification benefits using the Capital Asset Pricing Model (hereafter CAPM) and the Markowitz mean-variance framework. The results confirm the diversification benefits of adding the gold proxies to the U.S. common stock portfolio for the entire period and subsample periods, both in short and long run.

Demidova-Menzel and Heidorn (2007) explain the role of gold on portfolio investment from the perspective of the U.S. and European investors during different periods between 1974- 2006, just before the financial crisis. Their research shows the benefits of adding gold to the U.S. dollar and Euro investment portfolios when the return of gold is of considerable size due to a low correlation with the other assets. They thereby concluded that this is not true when the return on gold is near zero, despite the low correlation.

9

Ratner and Klein (2008) evaluated in their study the performance of gold in a sample from 1975 until 2005. They compared the stand-alone performance of gold with the U.S. total stock market. Their results show relatively low or negative correlations between gold and the U.S. stock market, but concluded that adding gold to the portfolio results in only small improvement in portfolio performance in periods of negative market returns but for a long-term investment horizon there is no overall benefit of adding gold to the mixed portfolio.

In 2011 a small pension fund from The Netherlands called “Pensioenfonds Vereenigde Glasfabrieken” was brought to court by De Nederlandsche Bank (DNB), or the Dutch central bank. The case covered the asset allocation of the Dutch pension fund. The pension fund had invested up to 13% of the total portfolio in 2009 in gold in order to protect itself from financial downturns. The Dutch central bank was convinced that the investment strategy of the pension fund involved too much risk due to the relatively low gold price (see Figure 1), while the DNB holds 44% of its reserves in gold (Middelkoop, 2016). Was the DNB right in its choice to prohibit Pensioenfonds Vereenigde Glasfabrieken to keep a certain percentage of gold in its portfolio, or was the DNB also convinced that gold could have a special function in a portfolio and therefor kept 44% of its reserves in gold?

This research contributes to the current literature in several ways. The studies mentioned above show that the correlation between the gold’s return and the asset’s return in the portfolio remains low throughout the time period, implying the existence of diversification benefits to the portfolios in case. However, the studies mentioned above are mostly based on the U.S. stock market and thus do the conclusions not have to be similar for the Dutch stock market. Next to this, the studies done outside the U.S. market like Baur & Lucey (2010) and Baur & McDermott (2010) use dollar-denominated prices for gold, while this study uses the domestic (Dutch) prices of gold. Thereby the conclusions of the benefits of gold do not tell us the optimal proportion of gold to add in a portfolio for Dutch equity investors and in the timeframe after the financial crisis of 2007-2008.

10 Table 1: Overview literature 3. Research method In order to answer the research question the following hypotheses are tested: - The return on gold is negatively correlated with the returns on the AEX over the entire period, confirming the hedge function of gold using Equations (1) and (3)

- The return on gold is negatively correlated with the returns on the AEX during times of financial stress, confirming the safe haven function of gold using Equations (1) and (3)

- The optimal weights of gold in a Dutch equity-investing portfolio is significantly higher in times of financial stress compared to the entire period using Equations (5), (6) and (7)

Market Study Sample _period Countries Research method Main results

Stock market Chua, Sick and Woodword (1990) 1971-1988 US Sub-sampled regression Diversification benefits Foreign exchange market Capie, Mills and Wood (2005)

1974-2004 US ARDL model Hedge for foreign _{exchange market} Stock

market Klein (2008) Ratner and 1975-2005 US Portfolio analysis

Short term benefits of adding gold to a the studied portfolios Stock and bond market Baur and Lucey (2010) 1995-2005 Germany US, UK, Regression with dummy variables for lower quantiles Hedge and safe haven for stocks, no hedge and safe haven for bonds Stock market Baur and McDermott (2010) 1979-2009 G7, BRIC countries, Australia, Switzerland Regression with dummy variables for lower quantiles Weak safe haven for emerging markets and strong safe haven for developed markets Stock market Ghazali, Lean and Bahari (2013) 2001-2013 Malaysia Regression with dummy variables for lower quantiles Short-lived hedge and safe haven for stocks Foreign exchange market, oil market Ciner, Gurdgiev and Lucey (2013) 1990-2010 US, UK DCC-GARCH model, regression with dummy variables for lower quantiles for stocks Hedge & safe haven for foreign exchange market and bonds, no safe haven for stocks Stock market Beckmann, Berger and Czudaj (2015) 1970-2012 18 countries (G7, emerging markets) SVAR-GARCH model Hedge for foreign exchange market

11

I expect that gold is an important component of an optimal portfolio of a Dutch equity investor, as I believe one of the most important contributions of gold to a portfolio is its ability to maintain value during financial crises due to its negative correlation with Dutch stocks. This phenomenon is described as a safe haven function by Baur and Lucey (2010). Thereby, the euro is one of the most important alternatives to the U.S. dollar among fiat currencies and the price of gold is often tied to the U.S. dollar and thus the conclusion should embrace the conclusions of the studies mentioned above. The time period after the financial crisis of 2008 should not contradict the conclusions because the gold price pursued to rise on average.

This research investigates the attractiveness of gold in a Dutch equity portfolio as a safe investment during the financial crisis when stock markets face negative returns, which gives gold the potential of serving as a safe haven, but also the potential of gold serving as a hedge after the financial crisis.

According to the Capital Asset Pricing Model (CAPM) there are two types of risk, namely idiosyncratic risk, which can be diversified due correlation, and systematic risk. If the correlation of gold with the portfolio is relatively low, gold reduces the amount of idiosyncratic risk in the portfolio. Therefore, the correlation of gold and other assets from the Dutch market are examined for the period during and after the financial crisis of 2008.

First, the returns on gold and the Dutch stocks in the period of and after the financial crisis are calculated, followed by an analysis of the relationship between these asset classes by percentiles (10%, 5% and 1%) of stock returns to see if the results differ from the average during periods of crisis. After this, we look at the correlations sorted by the different percentiles to see whether gold correlates with the Dutch stocks during periods of extreme stock declines and thereby to see whether gold can function as a hedge or a safe haven using equations (1) and (2).

12

𝑟_{gold,t = α + 𝛽1}𝑟_AEX,t + 𝜀_{𝑡 (1)}

𝑟_{gold,t = α + 𝛽1}𝑟_AEX,t + 𝛽₂inflationt + 𝛽₃bondyield_t +𝜀_𝑡 (2) 𝑟_{gold,t = α + γ1(𝑟AEX,tp10)} + γ_{2(𝑟AEX,tp5)+ γ3(𝑟AEX,tp1)+ 𝜀𝑡} (3) 𝑟_{gold,t = α + γ1(𝑟AEX,tp10)} + γ_{2(𝑟AEX,tp5)+ γ3(𝑟AEX,tp1)+ γ4inflationt +γ5bondyieldt +𝜀𝑡 (4)} Equation (1) estimates the relationship between gold and the market index returns. Equation (2) estimates the relationship between the returns on gold and the market index returns including inflation and bond yield as control variables to check for robustness. Equation (3) represents the 10th_{, 5}th _{and 1}st _{percentile dummies (p10, p5 and} p1) along with their interaction terms with the market index. The dummy variables are equal to 1 if the stock market exceeds the percentiles and 0 otherwise. To test whether gold is a hedge, all dummy variables should be equal to 0 and gold has to be uncorrelated or negatively correlated with the stock market on average. If one of the dummy variables is equal to 1 and gold is uncorrelated or negatively correlated with the market, gold is a safe haven for that specific percentile or market decline. Equation (4) represents the 10th_{, 5}th _{and 1}st _{percentile dummies (p10, p5 and p1) along with their} interaction terms with the market index, including inflation and bond yield as control variables to check for robustness.

To construct the “optimal” portfolio, comprising of Dutch stocks and gold, the Markowitz’ Portfolio Variance Minimization model is used, using Equations (5) and (6), and the Sharpe Ratio Maximization measurement is used, using Equation (7). 𝑤_!"#$!"# ₌ !!"#! !!"#(!!"#$,!!"#) !_!"#$! !!_!"#! !!!"#(!!"#$,!!"#) (5) 𝑤_!"#!"# _{= 1 − 𝑤} !"#$!"# (6)

Where σ2AEX is the variance of the AEX, σ2gold is the variance of gold, cov(rgold,rAEX) is the covariance between the return on the AEX and the return on gold and wgold and wAEX stand for the optimal portfolio weights while minimizing the variance of the portfolio of gold and the AEX, respectively. Sharpe (1966) was the first to measure the

13 performance of portfolios with a reward-to-volatility measurement, what later resulted in the Sharpe ratio (Equation (7)): max 𝑆ℎ𝑎𝑟𝑝𝑒 𝑟𝑎𝑡𝑖𝑜 = ! !! !!! !! (7)

Where E(rp) stands for the expected return of the portfolio, rf represents the risk-free rate of the average 10 year Dutch Government bond yield and σp stands for the standard deviation of the portfolio. 4. Data and descriptive statistics 4.1 Data The sample period used in this research to study the relationship between gold and Dutch stocks ranges from January 2007 to December 2017, which includes times of financial crisis until present, leading to a sample of 2871 observations of daily data. The daily gold price data has been provided by the World Gold Council (WGC) and is denominated in Euros per troy ounce gold. The Amsterdam Exchange Index (hereafter: AEX) is used as a proxy of the Dutch stock market. The risk free rate represents the average of a 10-year government bond yield from the Netherlands in the same sample period. This research does not take into account the transaction costs of buying and selling the gold shares on daily basis or the storage costs of gold when investing in gold. Furthermore, this research does not take diversification possibilities inside the AEX into account. These assumptions may influence the results of the research and therefore should be considered when revising the results presented in this research.

4.2 Descriptive statistics

Table 2 presents the descriptive statistics of the AEX prices, Gold prices, the Returns on AEX and the returns on Gold for the entire sample period of January 2007 until December 2018. The columns in Table 2 include the number of observations, the mean, standard deviation and the minimum and maximum values of each variable. As represented in the Table, the average daily return on gold is higher for the entire period (0.0003415) than the average daily return on the AEX (0.000126). Concerning the standard deviation of the returns on Gold and the returns on the AEX, Gold shows a

14

lower standard deviation (0.0109437) than the AEX (0.0136316). The last three columns describe the 10th_{, 5}th _{and 1}st _{percentiles of the AEX, gold, returns on AEX and} returns on gold. All three percentiles of the returns of the AEX show lower values than the percentiles of the returns on gold. In addition, the quantiles of the returns on gold and the returns on the AEX are plotted against each other in Figure 2. Figure 2 shows evidence that especially the lower bound quantiles and higher bound quantiles differ. The difference between quantiles in the lower and upper bound indicates that the distributions of the returns on gold and the returns on the AEX differ for extreme market conditions.

Table 2: Descriptive statistics of AEX, gold, returns on gold and returns on AEX

N Mean Std. Dev. Min Max p1 p5 p10

AEX 2871 397.5104 86.0848 199.25 561.9 225.55 256.69 291.39 Gold 2871 950.0246 246.3587 468.5398 1384.735 483.865 502.2541 564.4084 AEXDailyReturns 2870 0.000126 0.0136316 -0.0914482 0.1054834 -0.04 -0.0209322 -0.0139129 GoldDailyReturns 2870 0.0003415 0.0109437 -0.0905635 0.0815318 -0.0283 -0.0162717 -0.011273 Figure 2: Quantile-Quantile plot

Table 3 presents the descriptive statistics of the 10th_{, 5}th _{and 1}st _{percentiles of the} returns of the AEX with the corresponding gold returns regarding to the dates. For all percentiles, represented by Table 2, the mean observations of gold returns are higher than the returns on the AEX. In the bottom 10% of negative returns on the AEX, the average return on gold was positive at 0.3521%. In the worst 5% of AEX-returns, the average return on gold was 0.48493%. In the worst 1% of negative daily returns, the average return on gold was 0.095447%. This provides evidence that gold remains its

15

value during extreme market conditions. Besides the higher average return, gold shows higher standard deviations relatively to the AEX in all percentiles.

Table 3: Descriptive statistics of the 10th, 5th and 1st percentiles

Variable N Mean Max Min Std. Dev.

Gold10th 287 0.003521 0.0815318 -0.0420936 0.0162525 AEX10th 287 -0.024986 -0.0139129 -0.0914482 0.0126903 Gold5th 144 0.0048493 0.0815318 -0.0420936 0.0194244 AEX5th 144 -0.0329174 -0.0209322 -0.0914482 0.0138185 Gold1st 29 0.0095447 0.0815318 -0.0400634 0.027203 AEX1st 29 -0.0552186 -0.0399892 -0.0914482 0.0151143 5. Results

In this section the first and second hypotheses are examined. The function of gold whether gold can be used as a hedge and a safe haven against Dutch stocks is investigated. A hedge is an asset that is uncorrelated or negatively correlated with another asset or portfolio on average. On the other hand, a safe haven is an asset that is uncorrelated or negatively correlated with another asset or portfolio in times of extreme negative stock market conditions (Baur and Lucey, 2010). If there are negative coefficients found of stocks over the entire sample period from 2007 until 2017, this means that investors can depend on gold investment to hedge themselves from the losses in the Dutch stock market.

16

Figure 3 shows the rolling 30-day correlation between the returns on the AEX and the returns on gold ranging from January 1st _{2007 until December 31}st _{2017. There} are 2872 observations in this period, resulting in 2842 correlation coefficients. Observing the data, the AEX faced 1364 negative days of returns of the total 2872 days. During these negative days on the AEX, gold faced 650 negative days of returns. Especially on the worst 30 days of the AEX (average of -5.4% daily return), gold faced a positive average return of 1.01%.

Table 4 shows regressions of the AEX on Gold for the entire period and the 10th_, 5th _{and 1}st _{percentiles, respectively. The output based on Equation (1) in colomn [1]} gives the regression results of the daily gold returns on the daily AEX returns. The coefficient on the daily AEX returns is negative (-0.0949365) and statistically significant at the 1% significance level. This implicates that when the AEX goes down with 1 percentage point, gold increases with 0.0949365 percentage point. The output based on Equation (3) in colomn [3] gives the regression results of the daily gold returns on the 10th_{, 5}th _{and 1}st _{percentiles dummies of the daily AEX returns. To avoid issues of} multicollinearity, due to duplicated data in the percentiles, the corresponding gold returns are regressed separately on each percentile of the AEX. The coefficient on the 1st percentile dummy is negative (-0.6058166) and is statistically significant at the 10% significance level. This implicates that when the AEX goes down with 1 percentage point, gold increases with 0.6058166 percentage point in the 1st _{percentile of the AEX.} The coefficient on the 5th _{percentile dummy is negative (-0.3456155) and is statistically} significant at the 1% significance level. This implicates that when the AEX goes down with 1 percentage point, gold increases with 0.3456155 percentage point in the 5th percentile of the AEX. The coefficient on the 10th _{percentile dummy is negative} (-0.2766517) and is statistically significant at the 1% significance level. This implicates that when the AEX goes down with 1 percentage point, gold increases with 0.2766517 percentage point in the 10th _{percentile of the AEX.}

17 Table 4: Regressions of returns on gold on returns on AEX Dependent variable: GoldDailyReturns [1] [2] (Equation 1) (Equation 3) ΔAEXDailyReturns -0.0949365*** (-0.0148857) Δ<1st percentile -0.6058166* AEXDailyReturns (0.3261648) Δ<5th percentile -0.3456155*** AEXDailyReturns (-0.114341) Δ<10th percentile -0.2766517*** AEXDailyReturns (0.0740716) Number of observations: 2870 R-Squared: 0.0140 Notes: standard errors in parentheses; *p<0.10, **p<0.05, ***p<0.01 To check for the robustness of the variables, Table 5 shows the regression of the returns on gold on the returns on the AEX, with inflation and bond yield added as control variables for the entire period (colomn 1) and the 10th_{, 5}th _{and 1}st _percentiles (colomn 2). The data used in the regression is based on daily data provided from Datastream. The 10-year Dutch government bond functions as the bond yield, and the Dutch CPI rate functions as the inflation rate. The results provided in colomn 1 show a negative (-0.0396116) and insignificant coefficient of inflation. The coefficient of the bond yield is positive (0.0238631) and significant at the 10% significance level. However, the coefficient of the AEX in this regression is still negative (-0.0945476) and still significant at the 1% significance level. This coefficient is only 0.0003889 smaller than the coefficient of the AEX without the control variables. The regression of the percentiles with the control variables added is showed in colomn 2. To avoid issues of multicollinearity, due to duplicated data in the percentiles, the corresponding gold returns are regressed separately on each percentile of the AEX. For the 1st _percentile, the coefficient of inflation is positive (1.098286) and the coefficient of the bond yield is negative (-0.6937921), both coefficients insignificant. The coefficient of the AEX in the 1st _{percentile is still negative (-0.8254285), significant at the 5% significance level and} differs 0.2196119. For the 5th _{percentile, the coefficient of inflation is positive} (0.1395398) and the coefficient of the bond yield is negative (-0.1025545), both

18

coefficients insignificant. The coefficient of the AEX in the 5th _{percentile is still negative} (-0.3772421), significant at the 1% significance level and differs 0.0316266 with the coefficient from Equation 3. For the 10th _{percentile, the coefficient of inflation is positive} (0.2715187) and the coefficient of the bond yield is negative (-0.0341493), both coefficients insignificant. The coefficient of the AEX in the 10th _{percentile is still negative} (-0.2908355), significant at the 1% significance level and differs 0.0141838 with the coefficient from Equation 3.

19 Table 5: Regressions of returns on gold on returns on AEX, inflation and bond yield Dependent variable: GoldDailyReturns [1] [2] (Equation 2) (Equation 4) Entire Period Δ AEXDailyReturns -0.0945476*** (0.0148927) Δ Inflation -0.0396116 (0.0423125) Δ Bond Yield <1st percentile 0.0238631* (0.0143975) Δ AEXDailyReturns -0.8254285** (0.3487118) Δ Inflation Δ Bond Yield 1.098286 (1.047361) -0.6937921 (0.5061495) <5th percentile Δ AEXDailyReturns -0.3772421*** (0.1204651) Δ Inflation Δ Bond Yield 0.1395398 (0.3349635) -0.1025545 (0.1221683) <10th percentile Δ AEXDailyReturns -0.2908355*** (0.0760079) Δ Inflation Δ Bond Yield 0.2715187 (0.2016015) -0.0341493 (0.0701202) Number of observations: 2870 R-Squared: 0.0152 Notes: standard errors in parentheses; *p<0.10, **p<0.05, ***p<0.01 Table 6 shows the correlation coefficients of the daily return on the AEX on the daily return of gold. The Table represents the entire period, the 10th_{, 5}th _{and 1}st percentiles using Equations (1) and (2), respectively. If the coefficients are zero or negative and the return on the AEX is negative, which is true for all percentiles of Table

20

6. The correlation coefficient of gold return and the AEX return for the entire period is negative (-0.1183) and statistically significant at the 1% significance level. The correlation coefficient of the gold return and the AEX return in the lower 10% quantile is negative (-0.2160) and statistically significant at the 1% significance level. The correlation coefficient of the gold return and the AEX return in the lower 5% quantile is negative (-0.2459) and statistically significant at the 1% significance level. The correlation coefficient of the gold return and the AEX return in the lower 1% quantile is negative (-0.3366) and statistically significant at the 10% significance level. 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, increasing in the strength of the financial downturn in the returns on the AEX. Baur and Lucey (2010) confirm the hedge and safe haven property of gold in these cases of negative shocks in the market and positive movements of gold at the same time. Table 6: Conditional correlation analysis AEX return entire period Gold return -0.1183*** AEX return <10th percentile Gold return -0.2160*** AEX return <5th percentile Gold return -0.2459*** AEX return <1st percentile Gold return -0.3366* Notes: *p<0.10, **p<0.05, ***p<0.01 Tables 7 and 8 show the results of the Sharpe ratio maximization and variance minimization for the entire period and the 10th_{, 5}th _{and 1}st _{percentiles, respectively.} From the results of the Sharpe ratio maximization (Table 7), it can be concluded that the optimal fraction of gold in the portfolio during times of financial downturns on the AEX (represented by the percentiles) is 1, and thus it is optimal to store your entire budget in gold. When storing your entire budget in gold, the expected returns rise in the lower percentiles with a minimum expected return of 128.52% in the 10th _{percentile and a} maximum expected return of 348.38% in the 1st _{percentile. On average, the optimal} weight of gold in the portfolio is 76.15% resulting in an expected return of 10.59%. From the results of the Variance minimization (Table 8), it can be concluded that the optimal weight of gold decreases per percentile, with a maximum weight of 59,9% for the entire period and a minimum weight of 29,5% for the 1st _{percentile. This means that}

21 the variance of gold in the lowest percentiles of the returns on the AEX is more volatile and the weights of gold must decrease to minimize variance. From Table 8 can be also concluded that the expected returns are negative with a maximum expected return of 9,29% for the entire period and a minimum return of -1319,11% for the 1st _percentile. One of the main investment-based goals of investors is maximizing expected return. Based on the results from Table 8, the investor gets more expected return when investing in the risk-free asset. Therefore, minimum variance portfolios based on the percentiles with a constraint of the expected return to be equal or higher than the risk-free rate of 0,269% are created (Table 9). To increase the expected return of the portfolios, the weights of gold increased to a certain level where the expected return equals the risk-free rate.

Table 7: Results Sharpe Ratio maximization

_{E(rp) SDp rf Sharpe ratio wg waex}

Entire period 10,59% 16,39% 0,269% 0,629585042 0,761520616 0,238479384 <10th Percentile 128,52% 31,00% 0,269% 4,137501234 1 0 <5th Percentile 177,00% 36,98% 0,269% 4,778878878 1 0 <1st Percentile 348,38% 51,07% 0,269% 6,816729478 1 0 Table 8: Results portfolio variance minimization Table 9: Results portfolio variance minimization with constraint [E(rp)>=rf ]

_{E(rp) SDp rf Variance wg waex}

Entire period 9,29% 15,33% 0,269% 2,35% 0,59689506 0,403104932 <10th Percentile 0,27% 26,69% 0,269% 7,12% 0,87674650 0,123253505 <5th Percentile 0,27% 31,58% 0,269% 9,97% 0,87179519 0,128204816 <1st Percentile 0,27% 42,32% 0,269% 17,91% 0,85273591 0,147264083

E(rp) SDp rf Variance wg waex

Entire period 9,29% 15,33% 0,269% 2,35% 0,596895065 0,403104932 <10th Percentile -496,03% 16,94% 0,269% 2,87% 0,399763293 0,600236709 <5th Percentile -695,67% 18,72% 0,269% 3,50% 0,366935755 0,633064246 <1st Percentile -1319,11% 20,60% 0,269% 4,24% 0,294591108 0,705408893

22

6. Conclusion and discussion

This research investigated the role of gold in a portfolio of a Dutch equity investor. First, this research investigated whether gold can function as a hedge for negative returns on the Dutch stock market on average, or works as a safe haven asset against negative returns in times of extreme negative market conditions. Next to this, to construct an optimal portfolio, comprising Dutch stocks and gold, the Markowitz’ Portfolio Variance Minimization model and the Sharpe Ratio maximization model are used.

In order to conclude the results, this section refers back to the research questions in the introduction section of this research. The main question is whether gold can function as a hedge and safe haven as a component of Dutch equity-investing portfolios. The results of the linear regression and the regression with dummy variables for the lower quantiles show negative coefficients. For the entire period the coefficient is -0.0949365, for the 10th _{percentile -0.2766517, for the 5}th _{percentile -0.3456155 and} for the 1st _{percentile -0.6058166. This highlights the existence of a negative}

co-movement of the returns on gold with the returns on the AEX. The first sub question to the main question is whether there is a change in correlation pattern during and after downturns on the stock market. The conditional correlation analysis shows negative and decreasing coefficients when the percentiles drop. From 0.1183, to 0.2160, to -0.2459, to -0.3366 for the entire period and the 10th, 5th and 1st percentiles, respectively. The second sub question to the main question is whether the optimal proportion of gold in a portfolio of Dutch stocks changes during and after downturns on the stock market. From the Minimum Variance model and the Sharpe ratio results can be concluded that the optimal weight of gold increases when the percentiles drop. The results from the Sharpe ratio maximization model show the optimal weights, which is 76,2% in gold and 23,8% in the AEX for the entire period and the entire capital in gold for the 10th_{, 5}th _{and 1}st _{percentiles. While on the other hand, the results of the Variance}

Minimization model provide lower optimal weights for gold, which decrease when the percentiles drop to the lower 1%. The results of the Variance Minimization model with the constraint of the average portfolio return to be at least equal to the risk-free rate provide higher and increasing optimal weights of gold when the percentiles drop to the lower 1% due to the higher average return on gold.

23

There are some limitations and suggestions for further research. This research does not take into account the transaction costs of buying and selling the gold on daily basis or the storage costs of gold when investing in gold. Furthermore, this research does not take diversification possibilities inside the AEX into account. These assumptions may influence the results of the research and therefore should be considered when revising the results presented in this research.

24

References

Baur, D. G., Lucey, B. M. “Is Gold a Hedge or a Safe Haven? An Analysis of Stocks, Bonds, and Gold”, 2010, The Financial Review, Eastern Finance Association;

Baur, D. G., McDermott, T. K. J. “Is Gold a Safe Haven? International Evidence”, 2010, Journal of Banking and Finance, vol. 34, issue 8;

Beckmann J, Berger T, Czudaj R. 2015. Does gold act as a hedge or a safe haven for stocks? A smooth transition approach. Economic Modelling 48: 16-24;

Capie, F., Mills, T. C., Wood, G. “Gold as a Hedge Against the Dollar”, 2005, Journal of International Financial Markets, Institution and Money, vol. 15, issue 4;

Chua, J., Sick, G., Woodword, R. “Diversifying with Gold Stocks”, 1990, Financial Analysts Journal, Vol. 46;

Ciner, C., Gurdgiev, C., Lucey, B. M., 2013, Hedges and safe havens: An examination of stocks, bonds, gold, oil and exchange rates. International Review of Financial Analysis 29: 202–11;

Demidova-Menzel, N., Heidorn, T., 2007, Gold in the Investment Portfolio, Frankfurt School of Finance and Management;

Ghazali, M.F., Lean, H.H., Bahari, Z. 2013. Is Gold a Hedge or a safe haven? an empirical evidence of Gold and stocks in Malaysia. Int. J. Bus. Soc. 14(3), 428-443;

Jaffe. Jeffrey F. "Gold and Gold Stocks as Investments for institutional Portfolios." Financial Analysts Journal, 49 (1989);

Middelkoop, W. (2016). The big reset: gold wars and the financial endgame. Amsterdam, Nederland: Amsterdam University Press;

Ratner, M., & Klein, S. (2008). The Portfolio Implications of Gold Investment. Journal of Investing, 17(1), 78-87;

25

Reservebeheer. (n.d.). Retrieved from

https://www.dnb.nl/rente-eninflatie/050_reservebeheer/index.jsp#;

Sharpe, W. “Mutual Fund Performance”, 1966, Journal of Business, Vol. 39, pp. 119-138;

World Gold Council. (2018). Gold price chart. Retrieved May 20, 2018 from https://www.gold.org/data/gold-price