Essays on gold performances across inflation and market risk regimes: parameter varying nonlinear threshold modeling approaches
Date
2017
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Publisher
University of Delaware
Abstract
The gold’s performance has attracted a lot of attention in the literature. The main branches of the gold’s performance studies include the gold’s inflation hedging property, the gold and market risk relation, and the gold’s relation with its various determinants. Existing studies have investigated these topics with a range of methodologies and reached fruitful findings. However, in the existing literature, applications of nonlinear modeling approaches to analyze the gold’s performance are still limited. The present study aims to implement nonlinear modeling approaches to capture the likely parameter-varying process in the gold’s behavior. Specifically, we construct the nonlinear frameworks by employing the rolling regression (RR), the Bai-Perron algorithm (BP), the threshold regression (TR), and the multivariate threshold VAR (TVAR) approaches. Three aspects of the gold’s performance are investigated: the gold’s inflation hedging property across inflation regimes (Chapter 1), the gold’s risk hedging ability across market risk regimes (Chapter 2), and the gold’s responses to its determinants across market risk regimes (Chapter 3). ☐ Can gold always hedge against inflation? Chapter 1 aims to provide an answer to this question from a regime-dependent perspective. We employ the rolling regression (RR) and the threshold regression (TR) approaches to observe and estimate the varying relationship between the real return of gold (RRG) and inflation (PI). Based on the sample period of 1968:5 - 2014:12, we find that when the lagged 3- month inflation rate is less than 0.47% (a 5.64% annualized term), the current month inflation does not significantly affect the current real return of gold(RRG). By contrast, when lagged 3-month rate of inflation is equal to or greater than 0.47% per month (a 5.64% annualized term), the current month inflation rate does have significant positive effects on the real return of gold(RRG). Therefore, gold is “a complete hedge” against inflation in low inflation regime, and it is “a more than complete hedge” in high inflation regime. The gold’s hedging ability is stronger in a high inflation regime than in a low inflation regime. Our study contributes to the existing research primarily in three ways. First, to our knowledge, this is the first study that employs the rolling regression (RR) and the threshold regression (TR) approaches to investigate the gold’s inflation hedging property. Second, the inflation threshold identified in this paper is endogenously determined. This is a quantitative improvement on the existing common practices in both academia studies and industry strategies. Third, the threshold regression (TR) model we build in this paper is an extension of the more conventionally discussed threshold autoregressive (TAR) model. We allow the independent variable and the threshold variable to be exogenous. To our knowledge, the implementations of the extended version of the TAR model, i.e. the TR model, is still scant in the research area of investigating macroeconomic conditions and financial assets. ☐ Gold has long been considered as a reliable commodity and a safe haven during times of market turmoil. The purpose of Chapter 2 is to investigate how gold is directly affected by the market risk condition, represented by the Baa-Treasury spread change indicator. We formulate the questions as whether the gold’s behavior is influenced by the Baa-Treasury spread change, whether it is a varying-parameter process, and whether the presence of nonlinearity is by time points or by a threshold variable. To accomplish this investigation, we apply three modeling approaches: the rolling regression (RR), the Bai-Perron algorithm (BP), and the threshold regression (TR). The constancy test associated with the rolling regression, the Tsay (1989) and Hansen (1997) nonlinearity tests are conducted as part of our model building. For the threshold regression (TR), three threshold candidates, the Baa rate to the10-year Treasury rate ratio (BAAY), the Baa-Treasury spread change (DDBAAY), and the volatility of the Baa rate (VOLBAA) are used. We find that the real return of gold (RRG) is significantly affected by the Baa-Treasury spread change (DDBAAY). The rolling regression (RR) and its associated constancy test demonstrate that the effect is time varying. The Bai-Perron (BP) algorithm detects that the relation has structure breaks at time points 1980:1 and 1980:7. And the threshold regression (TR) manifests that the relation is a threshold process, with the lagged 3-month spread change of a value of 0.17% as the threshold (DDBAAYt-3=0.17%). In the low risk regime, the real return of gold (RRG) does not have significant responses to the spread change (DDBAAY t-2). In the high risk regime, the real return of gold (RRG) significantly increases with the spread change (DDBAAYt-2). Thus, we find gold is “a complete hedge” against the Baa-Treasury spread change in the low risk regime, and “a more than complete hedge” against the Baa-Treasury spread change risk in the high risk regime. In other words, gold can hedge against the spread change risk, with stronger hedging ability in the high risk regime. Two alternative threshold candidates, the Baa to 10-year Treasury yield ratio (BAAY) and the Baa rate volatility (VOLBAA), are ruled out as effective threshold variables. This suggests that the threshold effect from the Baa-Treasury spread change (DDBAAY) on the real return of gold (RRG) does not depend on the Baa to 10-year Treasury yield ratio (BAAY) or the Baa rate volatility (VOLBAA). ☐ In Chapter 3, we explore the real return of gold (RRG) responses to the shocks on its determinants in different market risk regimes. After the Wald nonlinearity tests on the linear VAR model, we estimate a five-variable threshold vector autoregression (TVAR) model. The sample period is between 1987:7 and 2014:12. The generalized impulse responses (GIRF) with alternative shock sizes and signs are further generated by bootstrapping simulations. We provide layers of new evidences regarding the risk regime-dependency of the real return of gold (RRG)’s responses. First, the Wald nonlinearity tests significantly support the existence of nonlinearity in the VAR mechanism. Second, the RRG responses generally demonstrate larger fluctuations and take longer time to diminish in the high-risk regime than in the low-risk regime. Third, the RRG contemporaneously moves in the same direction with the real return of oil (RRO), the real growth of jewelry PPI (RJP), and the inflation (PI) in both the lowand high-risk regimes. The RRG co-moves with the TED spread (TED) after a contemporaneous drop in the high-risk regime and the RRG demonstrates almost identical responses to its own shocks one month after the shocks in both regimes. ☐ In sum, our findings from all three chapters essentially point out that the gold as an inflation hedge, a hedge against the Baa-Treasury spread risk and the real return on gold (RRG) in response to market risk are all subject to threshold effects. In Chapter 1, for the threshold regression(TR) of real return of gold (RRG) on inflation(PI), the threshold is searched out to be lagged 3-month inflation with a value of 0.47% (PIt-3=0.47% per month, a 5.64% annualized term). When the inflation rate is in the low regime, gold is “a complete hedge” against inflation. By contrast, when the inflation rate is in the high regime, gold is “a more than complete hedge” against inflation. In Chapter 2, in the threshold regression (TR) of the real return of gold (RRG) on the Baa-Treasury spread change (DDBAAY), the lagged 3-month BaaTreasury spread change with a value of 0.17% (DDBAAYt-3 =0.17%) is the threshold. In the low risk regime, gold is “a complete hedge” against the spread change risk. In the high risk regime, gold is “a more than complete hedge” against the spread change risk. In Chapter 3, for our five-variable TVAR model, lagged 1-month TED spread with a value of 0.8% (TEDt-1 = 0.8%) is searched out to be the threshold. The real return of gold (RRG) responses differently to market risk shocks across regimes. In the low market risk regime, the real return of gold (RRG) responses appear to be trivial and flat along the horizon. In the high market risk regime, the real return of gold (RRG) demonstrates a contemporaneous decline (rise) followed by re-bounces (declines) for the positive (negative) shocks on the TED spread.
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Keywords
Bai-Perron Algorithm, Gold, Inflation and Market Risk Hedge, Rolling Regression, Threshold Modeling, TVAR GIRF