Time-varying risk aversion and realized gold volatility

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Abstract

We study the in- and out-of-sample predictive value of time-varying risk aversion for realized volatility of gold returns via extended heterogeneous autoregressive realized volatility (HAR-RV) models. Our findings suggest that time-varying risk aversion possesses predictive value for gold volatility both in- and out-of-sample. Time-varying risk aversion is found to absorb the in-sample predictive power of n index of economic policy uncertainty at a short forecasting horizon. We also study the out-of-sample predictive power of time-varying risk aversion in the presence of realized higher-moments, jumps, gold returns, a leverage effect as well as an index of economic policy uncertainty in the forecasting model. In addition, we study the role of the shape of the loss function used to evaluate losses from forecast errors for the role of time-varying risk aversion as a predictor of realized volatility. Overall, our findings show that time-varying risk aversion often captures information useful for out-of-sample prediction of realized volatility not already contained in the other predictors.

Introduction

Recent research on global financial markets establishes a link between cycles in capital flows and the level of risk aversion (e.g. Rey, 2018), showing that risk aversion has significant explanatory power over equity-market comovements (e.g., Xu, 2017, Demirer et al., 2018). Clearly, capital flows across risky and relatively safer assets would be closely linked to the level of risk aversion in financial markets as utility maximizing investors assume investment positions based on their willingness to take on risks. To that end, given the role of gold as a traditional safe haven in which investors seek refuge during periods of financial market jitters, one can argue that the role of risk aversion as a driver of return dynamics in financial markets is not necessarily limited to equities, but also extends to the market for gold. Interestingly, however, despite the multitude of studies that explore the role of gold as a potential safe haven (e.g., Baur and Lucey, 2010, Lucey and Li, 2015), the influence of time-varying risk aversion on the volatility of gold-price movements is largely understudied, partially due to the challenges in controlling for the time variation in macroeconomic uncertainty to estimate the time variation in risk aversion. The main contribution of this paper is to examine the predictive power of risk aversion over gold volatility by utilizing a recently developed measure of time-varying risk aversion. By doing so, we provide new insight to the role of risk aversion in financial markets and volatility modeling in safe-haven assets.

Clearly, forecasting volatility of gold returns is of interest not only for investors in the pricing of related derivatives as well as hedging strategies for stock market-fluctuations (Poon & Granger, 2003), but also for policy makers given the evidence that commodities, in particular gold, possess predictive value over currency-market fluctuations (e.g., Chen and Rogoff, 2003, Cashin et al., 2004, Apergis, 2014), an issue that is particularly important for emerging economies that have high risk exposures with respect to currency fluctuations. Furthermore, given the evidence of significant volatility spillovers across gold and other commodities, particularly oil (e.g., Ewing & Malik, 2013), and that precious metals served as sources of information transmission during financial crises (Kang, McIver, & Yoon, 2017), exploring the predictive role of risk aversion over gold volatility can provide valuable insight to whether the time-variation in risk aversion is the underlying fundamental factor driving the spillover effects across asset classes, particularly during periods of high uncertainty. Although the literature offers a limited number of studies relating various uncertainty measures to gold-return dynamics (e.g., Jones and Sackley, 2016, Balcilar et al., 2016, Bouoiyour et al., 2018), these studies have not specifically examined the effect of the changes in the level of market risk aversion on safe-haven assets, particularly gold. To that end, the time-varying risk aversion measure recently developed by Bekaert, Engstrom, and Xu (2017) offers a valuable opening as it distinguishes the time variation in economic uncertainty (the amount of risk) from time variation in risk aversion (the price of risk), providing an unbiased representation for time-varying risk aversion in financial markets. To the best of our knowledge, ours is the first study to utilize this unbiased measure of risk aversion in the context of forecasting for safe-haven assets.

In recent studies, volatility is associated with a volatility risk premium, which can be regarded as the compensation that investors demand against unexpected market fluctuations beyond what can be computed based on the first moments of a price process (e.g. Li & Zinna, 2018). Furthermore, there is a well established literature on the so-called leverage effect which refers to the empirical evidence that establishes a link between asset returns and volatility (e.g. Christie, 1982). To that end, one can argue that the level of risk aversion that serves as a driver of a possible volatility risk premium embedded in the price of gold can be linked to expected volatility either from a risk-premium or a leverage-effect channel. As noted, gold has traditionally been considered an asset to preserve value, offering long-term stability and security in financial markets during volatile periods and against downside risks (Erb & Harvey, 2013). Given this, one can argue that return and volatility dynamics in gold can be affected in different ways depending on the effect of different types of investors. The first type of investors are those looking for a safe haven during periods of financial market jitters. The second type of investors sees gold as an investment just like other traditional assets (e.g., investors in mining firms). Clearly, during periods of turbulence in financial markets, there will be upward pressure on the price of gold, while during market booms the price of gold may (or may not) fall, depending on whether or not investors who consider gold as a traditional investment still see value in gold-related assets. When we consider gold related stocks whose prices generally move in tandem with the price of gold, a relatively small increase in gold price could lead to significant profits in some gold stocks, while a relatively small drop in gold prices could lead to significant losses in some gold stocks, especially in the case of firms with relatively weaker fundamentals and management structure. Therefore, depending on the market state and investors’ appetite for risk, gold and gold related assets can exhibit highly volatile patterns, closely related to the degree of risk appetite among investors, which can be captured by time-varying risk aversion. To that end, insofar that risk aversion has predictive power on gold volatility, our findings can provide useful insights to understanding how risk aversion relates to the time variation in gold market fluctuations, and thus, to the gold volatility risk premium. Furthermore, estimating volatility via quadratic variation, which is regarded as the best estimator of integrated (latent) volatility, our findings can also provide useful insights into gold-jump risk premium documented in the literature (see Todorov & Tauchen, 2011).

In our empirical analysis, we focus on the realized volatility of gold returns that we compute from intraday data. The use of intraday data allows us to control for higher moments including the realized skewness and kurtosis that have been shown to have predictive power in forecasting models in a number of different contexts including gold (Mei et al., 2017, Bonato et al., 2018, Gkillas et al., 2018). We also control for an index of economic policy uncertainty in our models, allowing us to separately examine the impact of uncertainty and changes in risk aversion on realized volatility. This distinction is particularly important as risk aversion can fluctuate due to changes in wealth, background risk, and emotions that alter risk appetite (Guiso, Sapienza, & Zingales, 2018). To that end, given the unbiased nature of the risk-aversion measure we utilize in our tests, distinguishing the time variation in economic uncertainty from the time variation in risk aversion, our study provides new insight to the drivers of realized volatility of gold returns. We employ the heterogeneous autoregressive realized volatility (HAR-RV) model developed by Corsi (2009) to model and forecast the realized volatility of gold returns as this widely-studied model accounts for several stylized facts such as fat tails and the long-memory property of financial-market volatility, despite the simplicity offered by the model. By doing so, we extend the HAR-RV model to study the in- and out-of-sample predictive value of risk aversion, after controlling for various alternative predictors including realized higher-moments, realized jumps, gold returns, a leverage term as well as an index of economic policy uncertainty.

Our findings show that time-varying risk aversion possesses predictive value for realized gold volatility both in- and out-of-sample. While realized skewness stands out as a significant in-sample predictors for realized volatility, risk aversion has significant in-sample predictive value and is found to absorb the predictive power of economic policy uncertainty if investors predict realized volatility at a short forecasting horizon. Out-of-sample results show that the inclusion of risk aversion in the HAR-RV model yields better results for various model configurations in terms of forecast accuracy relative to alternative models that include realized higher-moments, jumps, gold returns, a leverage term, and economic policy uncertainty. We systematically document how the relative forecast accuracy of the HAR-RV-cum-risk-aversion model relates to the length of the forecast horizon and the loss function (absolute versus squared error loss, asymmetric loss) used to evaluate forecast errors.-Moreover, considering that the prices of risky assets drop as investors demand greater compensation for risk when risk aversion is high, one can argue that the volatility impact on gold would be in the positive direction, captured by good realized volatility (computed from positive returns), while the opposite holds during good times. For this reason, we differentiate between “good” and “bad” realized volatility, allowing us to explore possible asymmetric effects of risk aversion on gold volatility. Overall, our findings show that time-varying risk aversion contains information useful for out-of-sample forecasting of (“good” and “bad”) realized volatility over and above the information already embedded in other widely-studied predictors like higher-order moments, jumps, and an index of economic policy uncertainty, the latter measured by the economic policy uncertainty index developed by Baker, Bloom and Davis (2016).

We present in Section 2 a brief review of the different strands of studies on gold. We describe in Section 3 the methods that we use in our empirical analysis. We present our data in Section 4, summarize our empirical results Section 5, and conclude in Section 6.

Section snippets

Literature review

Given the potential safe-haven and hedging properties of gold investments, a growing number of studies has undertaken significant efforts to model and forecast return volatility in the gold market. One strand of research focuses on macroeconomic determinants of gold returns and volatility. For example, Tulley and Lucey (2007) estimate an asymmetric power GARCH model on monthly data and show that fluctuations in the value of the dollar have an impact on gold returns whereas major macroeconomic

Methods

We follow Andersen, Dobrev, and Schaumburg (2012) who propose median realized variance (MRV) as a jump-robust estimator of integrated variance, computed using intraday data. MRVt is considerably less biased than other measures of realized volatility in the presence of jumps and/or market-microstructure noise. It is given by MRVt:

Data

We use intraday data on gold to construct daily measures of standard realized volatility, the corresponding good and bad variants, realized skewness, and realized kurtosis. Gold futures are traded in NYMEX over a 24 h trading day (pit and electronic). We focus on gold futures prices, rather than spot prices, due to the low transaction costs associated with futures trading, which makes the analysis more relevant for practical applications in the context of hedging and/or safe-haven analyses.

In-sample findings

Table 2 summarizes the estimation results for realized volatility for the full sample period. Estimation results are computed using the R programming environment (R Core Team (2017)). Newey-West robust standard errors are computed using the R packages “sandwich” (Zeileis, 2004). We estimate, in the first step, the core HAR-RV model. In the second step, we add risk aversion as a predictor. In the third step, we include the other predictors and compare the forecasting performance of the competing

Concluding remarks

This paper examines the predictive power of risk aversion over gold-return volatility by utilizing a recently developed measure of time-varying risk aversion, which distinguishes the time variation in economic uncertainty from the time variation in risk aversion. We employ the popular heterogeneous autoregressive realized volatility (HAR-RV) model developed by Corsi (2009) to model and forecast the realized volatility of gold returns as this widely-studied model accounts for several stylized

Acknowledgments

We thank two anonymous reviewers for helpful and constructive comments. The usual disclaimer applies.

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