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The Impact of Basis Risk on Optimal Hedging and Hedge Efficiency

Joachim Paulusch

R+V Lebensversicherung AG

March 16, 2012

We analyze the dependency of the optimal hedge and its efficiency on the correlation between the asset to be hedged, and the hedge instrument. The optimal portion of the hedge instrument depends on this correlation, and on the ratio of the volatilities. Efficiency is defined as the percental decrease in volatility caused by the hedge. The connection between the efficiency E of the optimal hedge, and the correlation rho is given by E = 1 - sqrt(1 - rho^2)

This means that basis risk is really substantial whenever the absolute value of the correlation is smaller than 1. The result is independent of any assumptions on distributions.

The mathematics of our result are not new. Arguments like this are used in the theory of Monte Carlo simulation.

Number of Pages in PDF File: 4

Keywords: hedge, optimal hedge, correlation, efficiency, basis risk

JEL Classification: C00, D81, G11

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Date posted: March 19, 2012 ; Last revised: April 4, 2014

Suggested Citation

Paulusch, Joachim, The Impact of Basis Risk on Optimal Hedging and Hedge Efficiency (March 16, 2012). Available at SSRN: http://ssrn.com/abstract=2024978 or http://dx.doi.org/10.2139/ssrn.2024978

Contact Information

Joachim Paulusch (Contact Author)
R+V Lebensversicherung AG ( email )
Raiffeisen Platz 1
Wiesbaden, 65189
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