How to calculate conditional hedge ratios in R or Eviews or any other software?

24 May 2023 1 7K Report

I am already familiar with the process of calculating hedge ratios with linear regression (OLS). I am already running 4 different regressions for calculating hedge ratios between emerging markets and different hedging assets like gold. This is done on in-sample data.

That would look something like this: EM=a+b*GOLD+e

I then construct a portfolio and test the standard deviation of the portfolio and compare that with the non-hedged portfolio of only emerging market equities in the out-sample: R-b*GOLD

However, I want to compare these OLS hedge ratios to conditional hedge ratios from for instance a BEKK GARCH or a DCC GARCH.

I have already tried to work with R and I used the rugarch and rmgarch packages and created a model, modelspec and modelfit, but I do not know how to go from there.

Sajib Sarker

Calculating conditional hedge ratios using models like BEKK GARCH or DCC GARCH in R or EViews involves a slightly different approach compared to OLS regression. Here's a general outline of the steps you can follow:

Data Preparation: Ensure that you have your data ready in the appropriate format. Make sure you have the returns or log returns of the relevant variables, such as the emerging markets (EM) and the hedging asset (e.g., GOLD). Ensure that the data is properly aligned and covers the desired time period.

Model Specification: Specify the appropriate conditional volatility model, such as BEKK GARCH or DCC GARCH. In R, you can use the rugarch package for both models. For BEKK GARCH, you can use the ugarchspec function with the appropriate specifications, such as the variance model (variance.model) and covariance model (distribution.model). For DCC GARCH, you can use the dccspec function.

Model Estimation: Estimate the specified model using the ugarchfit function for BEKK GARCH or the dccfit function for DCC GARCH. Provide the returns of the EM and hedging asset as inputs to the estimation function. The output will be a fitted model object (e.g., fit_bekk or fit_dcc) that contains the estimated parameters and other relevant information.

Extract Conditional Covariance: Extract the conditional covariance matrix from the fitted model object. In the case of BEKK GARCH, you can use the rcov function on the fitted model object (fit_bekk@fit$rcov). For DCC GARCH, you can use the rcov function on the fit_dcc@fit$R object.

Calculate Conditional Hedge Ratios: Compute the conditional hedge ratios based on the extracted conditional covariance matrix. The conditional hedge ratio can be obtained by dividing the covariance between EM and the hedging asset by the variance of the hedging asset. In the case of BEKK GARCH, you can use the formula: conditional hedge ratio = (covariance EM-GOLD) / (variance GOLD). For DCC GARCH, you can use the formula: conditional hedge ratio = (conditional correlation EM-GOLD) * (conditional standard deviation EM) / (conditional standard deviation GOLD).

Compare Results: Compare the conditional hedge ratios obtained from the GARCH models with the OLS hedge ratios you calculated previously. Assess the differences and evaluate the effectiveness of each approach in terms of risk reduction or portfolio performance.

It's important to note that the specific syntax and function names may vary slightly depending on the version of the packages you are using. Make sure to refer to the package documentation and examples for more detailed guidance.

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