Calculating the optimal hedge ratio: constant, time varying and the Kalman Filter approach

Abstract

A crucial input in the hedging of risk is the optimal hedge ratio – defined by the relationship between the price of the spot instrument and that of the hedging instrument. Since it has been shown that the expected relationship between economic or financial variables may be better captured by a time varying parameter model rather than a fixed coefficient model, the optimal hedge ratio, therefore, can be one that is time varying rather than constant. This study suggests and demonstrates the use of the Kalman Filter approach for estimating time varying hedge ratio – a procedure that is statistically more efficient and with better forecasting properties.

Acknowledgements

We would like to thank an anonymous referee and the co-editor of this journal for the useful comments that resulted in a significant improvement of this paper. The usual disclaimer applies.

Notes

¹ Floros and Vougas (2004) have demonstrated that this is the case whether prices or returns are used (see p. 129 for formal proof).

² It should be mentioned that a potential measure of the cost of hedging could be obtained by evaluating the difference between the integral of the fixed hedge ratio (h) and the time varying hedge ratio (h_t ).