Introduction

 In the financial world all investments carry some degree of risk. The practice of risk management allows investors to mitigate risk and alter exposures. Such practices include, but are not limited to, asset allocation, portfolio diversification and hedging. One of the most popular commodities traded is gold, which has been historically used as a hedge against inflation and the depreciation of the US dollar. Moreover, gold has been referred to as a safe haven for investors in the event of a potential financial crisis. In addition, gold is a highly liquid precious metal that has the most desirable properties of money: medium of exchange, measure of value and store of value. It is for these reasons that central banks and international financial institutions have substantial gold reserves. This paper empirically investigates the nonlinear Granger causality between the gold market and the United States, United Kingdom, Spain, and France stock indices from January 2005 to January 2019.

 According to Gokmenoglu and Fazlollahi (2015), the inter-relationship between financial and commodity markets proposes distinct challenges for investors, as the volatility of one market could affect the price index of the other market. Moreover, according to Baur (2012), despite the importance of gold as a hedge and a safe haven asset, an increase in volatility of gold may lead to negative consequences in financial markets, because an increase in the gold volatility can lead to effectiveness of gold as a safe haven diminishing, while lower gold volatility leads to higher effectiveness of gold as a safe haven. Therefore, an increase in gold volatility is foreseen as a trepidation to financial investors. It’s for the aforementioned that the paper estimates the inter-relationships between the financial and commodity markets.

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 The rest of the paper is structured as follows. The following section reviews relevant literature associated with the inter-connectedness of the gold market and aforementioned stock indices. Section 3 encapsulates the data that was examined, and methodology performed. Section 4 presents the empirical analysis of the performed methodology. Section 5 concludes the paper and presents the implications of the study.

Literature Review

Reference

Title

Variables

Countries Analyzed

Test Method

Results and Implications

Baur (2011)

Asymmetric Volatility in the Gold Market

Gold (US dollar, UK pound, Euro and Australian Dollar)

United States, United Kingdom, Switzerland and Australia

Glosten, Jaganathan and Runkle (1993)

The volatility of gold returns demonstrates an asymmetric reaction to positive and negative returns. Investors interpret positive gold price changes as a signal of future adverse conditions and uncertainty in other asset markets, which introduces higher volatility. The increased volatility in gold complements the negative correlation of gold and equity markets in periods of financial crisis and enhances the safe haven property of gold.

Baur et al., (2010)

Is Gold a Hedge or a Safe Haven? An Analysis of Stocks, Bonds and Gold

Gold, Stock Market and Bond Market

United States, United Kingdom and Germany

Baur and Lucey (2010)

Gold is a safe haven for stocks, but only functions as a safe haven for a limited time, around 15 trading days. In the longer run, when investors hold gold more than 15 trading days after an extreme negative shock lose money with their gold investment.

Choudhry et al., (2015)

Relationship Between Gold and Stock Markets During the Global

Financial Crisis: Evidence from Nonlinear Causality Tests

Gold, Stock Market and Interest Rates

United States, United Kingdom and Japan

Hiemstra and Jones (1994); Baek and Brock (1992)

Minimal evidence of Granger causality between gold returns and stock returns during the pre-crisis in all three countries studied. Therefore, gold was a safe haven during the pre-crisis period; however, the results are the opposite during the crisis period, where there is ample evidence of significant causality. As a result, there is evidence against the ability of gold to act as a safe haven during crisis. Results from the financial crisis period shows strong feedback among the variables for all three countries. The exception is Japan; there is no evidence of feedback from the stock and gold returns to interest rates. Both bivariate and multivariate tests show that gold lost its ability as a safe haven in the UK, the US, and Japan during the financial crisis. Therefore, using gold to hedge may not be feasible.

Gokmenoglu et al., (2015)

The Interactions among Gold, Oil, and Stock Market: Evidence from S&P500

Gold, Oil and Stock Market

Gold price, oil price, gold price volatility, oil price volatility and S&P 500

Unit root test, co-integration test, ARDL, and ECM

Oil and gold price volatilities have extensive impacts on economic and financial activities of the US. The gold price has the highest impact in the stock market.

Hood (2013)

Is Gold the Best Hedge and a Safe Haven Under Changing Stock Market

Volatility

Gold and S&P 500

Gold and S&P 500 returns and volatility, and Volatility Index

Baur and McDermott (2010)

Gold serves as a hedge and a weak safe haven for the US stock market. In period of extremely low or high volatility, gold does not have a negative correlation with the US stock market.

The Data and Methodology

3.1  The Data

 The four stock market indices examined are the S&P 500 (US), FTSE 100 (UK), IBEX 35 (Spain) and CAC 40 (France). All of the stock market indices have been converted into US dollars, respective of the exchange rate on the given day. Gold prices are based on the US dollar per troy ounce. The data regarding the aforementioned was retrieved from Thomson Reuters Datastream. The frequency is daily with a range of fifteen years from January 2005 to January 2019, covering 3,654 variables.

3.2  Multivariate Nonlinear Granger Causality

 Returns for gold and all four market indices are found by taking the first differences of their respective markets. As a result, the unit root is removed when the logs of each variable are differenced. Indubitably, the nature of financial data generally has the presence of heteroscedasticity, which presents an inconsistency in the estimated volatility as a result of conditional volatility. Therefore, an ARCH model is employed to identify the degree to which the heteroscedastic disturbances effect the time series. The Lagrange Multiplier across all five tests is significant, positive and smaller than unity, entailing that volatility is not turbulent and that there is volatility clustering. Ultimately, the following GARCH (1,1) model is implemented for each market to take into account conditional volatility when estimating the gold and stock market volatility:
σt2=α0+α1αt–12+β1+σt–12

As was the Lagrange Multiplier, the GARCH effect is significant and positive indicating continuous volatility. While GARCH (1,1) takes into account the conditional volatility, it can’t account for leveraging effects.

 Vector Autoregression (VAR) enables one to realize interdependencies amongst dependent variables. A postestimation syntax enables one to find the lag-order selection statistics for each respective dependent variable. The optimal number of lags is chosen using a maximum lag-order of twenty and based on the HQIC selection criteria, as its more efficient with a larger number of observations (Pollmann 2015). The determined lag length was 15, 13, 2 and 6 for the US, UK, Spain and France, respectively. However, it must be noted that when using VAR, one is assuming that returns are normally distributed, which isn’t normally the situation as financial returns are more often skewed.

Empirical Analysis

 Tables 1-4 presents the multivariate nonlinear Granger causality results between gold and stock market returns. Granger causality results alone will only provide the presence of a relationship between dependent variables in the system of equations. It is with impulse-response functions that we can analyze the direction of a shock in a given moment for a specified number of periods. Figure 1 presents the relationship between stock market index returns and conditional volatility. During the 2007 financial crisis it can be seen that volatility and return faced large amounts of turbulence. In addition, during 2016 the UK, Spain and France saw another sharp rise in volatility and returns, which could potentially be attributed to political events such as the Brexit Referendum or the US presidential election.

4.1  Gold Returns and Stock Market Returns

 This section presents nonlinear Granger causality between gold returns and stock market returns. At the 1% significance level, there is bidirectional causality for the US and UK. There is bidirectional causality for Spain at the 5% significance level from gold returns to stock returns and 1% significance level from stock returns to gold returns. France presents unidirectional causality from returns on gold to stock market returns. There is a strong feedback effect in the US, UK and Spain. According to the impulse response function, a shock in gold returns has no effect on the returns of stock market indices. Therefore, this would be a suitable hedge as there is no response.

4.2  Gold Returns and Stock Market Volatility

 This section presents nonlinear Granger causality between gold returns and stock market volatility. At the 1% significance level, there is bidirectional causality for the US, UK and France. Spain demonstrates unidirectional causality from gold returns to stock market volatility at the 5% significance level. France presents bidirectional causality at the 5% level. According to the impulse response function, a shock in gold returns has no effect on the volatility of the stock market indices. On that account, this would be a suitable hedge as well due to the lack of a response.

4.3  Stock Market Returns and Gold Volatility

 This section presents nonlinear Granger causality between stock market returns and gold volatility. For the US and UK there is unidirectional causality at the 1% significance level from stock market returns to gold volatility. At the 10% significance level there is unidirectional causality from gold volatility to stock market returns for Spain. France presents bidirectional causality at the %5 significance level. Once again, the impulse response functions have demonstrated that a shock in any stock market index returns has no effect on the volatility of gold. Indubitably, this would be a good opportunity to hedge.

Conclusions & Implications

 The use of nonlinear dynamic models provides one with the opportunity to analyze feedback effects amongst different asset classes. There are 3,654 observations, spanning from January 2005 to January 2019 based on a daily frequency. The S&P 500 (US), FTSE 100 (UK), IBEX 35 (Spain), and CAC 40 (France) indices were analyzed and constitute the world’s largest economies. All of our data was converted into US dollars with the exchange rate on the respective date. Gold returns were based in US dollars per troy ounce.

 The multivariate nonlinear results present strong evidence of bidirectional Granger causality between gold returns and stock market returns in the US, UK and Spain. In regard to France, there is unidirectional causality from stock returns to gold returns. Moreover, there is a presence of strong bidirectional causality between gold returns and stock market volatility in the US, UK and France. Spain presents a unidirectional causality from gold volatility to stock market returns. In addition, the US, UK and Spain present unidirectional causality from gold volatility to stock market returns. On the other hand, France presents bidirectional causality. There is sufficient evidence in the Granger causality and impulse response functions in favor of gold being a safe hedge and long-term investment as the variables examined have minimal correlation.

References

Baur, Dirk G., Asymmetric Volatility in the Gold Market (January 1, 2011).

Baur, Dirk G. and Lucey, Brian M. (2010). Is Gold a Hedge or a Safe Haven? An Analysis of Stocks, Bonds and Gold. Financial Review, Vol. 45, Issue 2, pp. 217-229.

Choudhry, T., Hassan, S. & Shabi, S. (2015). Relationship between gold and stock markets during the global financial crisis: Evidence from nonlinear causality tests. International Review of Financial Analysis, 41, 247-256.

Gokmenoglu, Korhan & Fazlollahi, Negar. (2015). The Interactions among Gold, Oil, and Stock Market: Evidence from S&P500. Procedia Economics and Finance. 25. pp. 478-488.

Matthew Hood, Farooq Malik. (2013). Is gold the best hedge and a safe haven under changing stock market volatility? Review of Financial Economics, Volume 22, Issue 2, Pages 47-52,

Pollmann, M. (2015). Are You Sure You Are Using the Correct Model? Model Selection and Averaging of Impulse Responses.

Table 1

Multivariate nonlinear Granger causality

United States

X  Y

Return on S&P 500

Volatility on S&P 500

Return on Gold

Volatility on Gold

Return on S&P 500

–

485.3 ***

52.85 ***

43.266 ***

Volatility of S&P 500

103.43 ***

–

49.068 ***

169.89 ***

Return on Gold

52.245 ***

66.646 ***

–

179.42 ***

Volatility on Gold

17.784

151.65 ***

32.336 ***

–

Note:

***, **, * denote significance levels at 1%, 5% and 10% respectively

Table 2

Multivariate nonlinear Granger causality

United Kingdom

X  Y

Return on FTSE 100

Volatility on FTSE 100

Return on Gold

Volatility on Gold

Return on FTSE 100

–

324.4 ***

40.03 ***

31.366 ***

Volatility of FTSE 100

68.332 ***

–

59.41 ***

72.891 ***

Return on Gold

48.705 ***

68.122 ***

–

168.96 ***

Volatility on Gold

19.058

106.76 ***

29.516 ***

–

Note:

***, **, * denote significance levels at 1%, 5% and 10% respectively

Table 3

Multivariate nonlinear Granger causality

Spain

X  Y

Return on IBEX 35

Volatility on IBEX 35

Return on Gold

Volatility on Gold

Return on IBEX 35

–

46.848 ***

11.333 ***

3.9922

Volatility of IBEX 35

1.762

–

1.3034

7.4152 **

Return on Gold

6.4091 **

5.7782 **

–

113.28 ***

Volatility on Gold

5.5165 *

15.343 ***

.01802

–

Note:

***, **, * denote significance levels at 1%, 5% and 10% respectively

Table 4

Multivariate nonlinear Granger causality

France

X  Y

Return on CAC 40

Volatility on CAC 40

Return on Gold

Volatility on Gold

Return on CAC 40

–

207.1 ***

10.047

14.359 **

Volatility of CAC 40

9.7137

–

23.44 ***

20.186 ***

Return on Gold

11.703 **

26.497 ***

–

109.27 ***

Volatility on Gold

12.008 **

60.748 ***

2.9274 

–

 Note:

***, **, * denote significance levels at 1%, 5% and 10% respectively

Figure 1 Daily stock market indices return and volatility

Figure 2 Daily gold returns and stock market volatility