Hedging with stock index futures: downside risk versus the variance

M. van der Nat and F. Brouwer
Additional contact information
M. van der Nat: Vrije Universiteit Amsterdam, Faculteit der Economische Wetenschappen en Econometrie (Free University Amsterdam, Faculty of Economics Sciences, Business Administration and Economitrics

No 23, Serie Research Memoranda from VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics

Abstract: In this paper we investigate hedging a stock portfolio with stock index futures. Instead of defining the hedge ratio as the minimum variance hedge ratio, we consider several measures of downside risk: the semivariance according to Markowitz [ 19591 and the various lower partial moments according to Fishburn’s [ 1977] alpha-t model (alpha>O). Analytically we show that for normal returns and biased futures markets there is an extra cost associated with hedging lower partial moments if the minimum variance hedge ratio instead of the optimal hedge ratio is used. We prove that the extra cost is different from zero if a is bigger than or equals 1. Furthermore, in case futures markets are positively biased minimum lower partial moment hedge ratios are smaller than the minimum variance hedge ratio (strictly smaller in case a is bigger than or equals 1). We used the Dutch FTI contract to hedge three Dutch stock market indexes. The in-sample analysis shows that (i) minimum semivariance and minimum variance hedge ratios are almost the same in size, (ii) minimum lower partial moment hedge ratios are smaller than minimum variance hedge ratios (only slightly smaller for a is bigger than or equals 1) and (iii) except for the lower partial moment with a=0.5, hedging downside risk using the minimum variance hedge ratio instead of the optimal hedge ratio is appropriate. For both strategies risk can be reduced in the same proportion whereas the extra cost of using the minimum variance hedge strategy is negligible. In contrast to (iii), out-of-sample results show that the extra cost of hedging lower partial moments

Keywords: downside risk; hedging; futures (search for similar items in EconPapers)
Date: 1995
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://degree.ubvu.vu.nl/repec/vua/wpaper/pdf/19950023.pdf (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:vua:wpaper:1995-23

Access Statistics for this paper

More papers in Serie Research Memoranda from VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics Contact information at EDIRC.
Bibliographic data for series maintained by R. Dam ().