Regression Coefficient Estimation (Baur & McDermott, 2010)

Estimates the time‐varying hedge ratio and its tail behavior following the model of Baur & McDermott (2010):

$$ \begin{aligned} r_{\mathrm{Gold},t} &= a + b_t r_{\mathrm{Stock},t} + e_t \quad &(1a)\\ b_t &= c_0 + c_1 D(r_{\mathrm{Stock},q_{10}}) + c_2 D(r_{\mathrm{Stock},q_{5}}) + c_3 D(r_{\mathrm{Stock},q_{1}}) \quad &(1b)\\ h_t &= \pi + \alpha e_{t-1}^2 + \beta h_{t-1} \quad &(1c) \end{aligned} $$

where \(r_{\mathrm{Gold},t}\) is the return of the hedging asset (e.g., gold), \(r_{\mathrm{Stock},t}\) is the return of the market (hedged) asset, and \(D(r_{\mathrm{Stock},q_i})\) is a dummy equal to 1 when the market return lies below its \(i\%\) quantile.

Usage

hedge_safehaven_bm10(hedged, hedge, dist = "norm")

Arguments

hedged

Numeric vector or zoo series of returns for the hedged asset (e.g., stock market). This is the driver in the mean equation.

hedge

Numeric vector or zoo series of returns for the hedging asset (e.g., gold).

dist

Conditional distribution for the GARCH model (default "norm").

Value

A data frame with columns:

Hedge

Quantile level ("c0", "0.10", "0.05", "0.01").

Coefficient_Sum

Estimated hedge coefficient (or sum up to that level).

p_value

Associated two‐sided p‐value.

Details

The mean equation incorporates interactions of the hedged asset returns with quantile dummies representing 10\ These interaction terms allow the hedge ratio \(b_t\) to vary during market downturns. The conditional variance follows an \(sGARCH(1,1)\) process.

The function returns the estimated base hedge coefficient (\(c_0\)) and cumulative sums for the 10\

References

Baur, D. G., & McDermott, T. K. (2010). Is Gold a Safe Haven? International Evidence. Journal of Banking & Finance, 34(8), 1886–1898.

Examples

if (FALSE) { # \dontrun{
data(hedgedata)
hedge_safehaven_bm10(hedgedata$SP, hedgedata$GLD)
} # }