Hedge is an asset negatively correlated with stock on average and if this negative correlation preexists in a crisis period, will it maintain the status of safe haven?
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However, there is no theoretical model that explains why gold is usually referred to as a safe haven asset, an important reason might be that it was among the first forms of money and was traditionally used as an inflation hedge. In addition, it is thought to be uncorrelated with other types of assets which is an important feature, especially, in the era of globalization characterised by increasing correlations among most asset types.
The econometric methodology is based on a regression model in which gold returns are regressed on equity and bond returns and two interaction terms that test whether gold indeed serves as a safe haven if share or bond markets fall or exhibit extreme negative returns. The error term is assumed to exhibit conditional autoregressive heteroscedasticity. You can specify an asymmetric GARCH model (e.g. TGARCH).
Traditionally gold has been considered as a safe haven asset. In long term gold works as an inflation hedge. This can be checked by taking 50 or more years of data. When volatility increases in markets $ price increases as investors reduce their risk by shifting to $. If $ falls or is weak they shift to gold. Those who do not have access traditionally shift to gold when economic uncertainty increases or markets crash or currency depreciates. The relationships can be built by identifying the major reasons, and studying the parameters over a long period of time.