Hedging with stock index futures: downside risk versus the variance

M. van der Nat, F. Brouwer

Research output: Working paperProfessional

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 considerseveral measures of downside risk: the semivariance according to Markowitz [ 19591 andthe various lower partial moments according to Fishburn's [ 1977] alpha-t model (alphaO).Analytically we show that for normal returns and biased futures markets there is an extracost associated with hedging lower partial moments if the minimum variance hedge ratioinstead of the optimal hedge ratio is used. We prove that the extra cost is different fromzero if a is bigger than or equals 1. Furthermore, in case futures markets are positively biased minimum lower partial moment hedge ratios are smallerthan 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 minimumvariance hedge ratiosare almost the same in size, (ii) minimum lower partial moment hedge ratios are smallerthan 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 reducedin the same proportion whereas the extra cost of using the minimum variance hedge strategy is negligible. In contrast to (iii), out-of-sample results
Original languageEnglish
Place of PublicationAmsterdam
PublisherFaculty of Economics and Business Administration, Vrije Universiteit Amsterdam
Publication statusPublished - 1995

Publication series

NameResearch Memorandum
No.1995-23

Fingerprint

Stock index futures
Hedging
Hedge ratio
Downside risk
Minimum variance
Lower partial moments
Hedge
Futures markets
Costs
Semivariance
Optimal hedge ratio
Stock market index
Proportion

Cite this

van der Nat, M., & Brouwer, F. (1995). Hedging with stock index futures: downside risk versus the variance. (Research Memorandum; No. 1995-23). Amsterdam: Faculty of Economics and Business Administration, Vrije Universiteit Amsterdam.
van der Nat, M. ; Brouwer, F. / Hedging with stock index futures: downside risk versus the variance. Amsterdam : Faculty of Economics and Business Administration, Vrije Universiteit Amsterdam, 1995. (Research Memorandum; 1995-23).
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van der Nat, M & Brouwer, F 1995 'Hedging with stock index futures: downside risk versus the variance' Research Memorandum, no. 1995-23, Faculty of Economics and Business Administration, Vrije Universiteit Amsterdam, Amsterdam.

Hedging with stock index futures: downside risk versus the variance. / van der Nat, M.; Brouwer, F.

Amsterdam : Faculty of Economics and Business Administration, Vrije Universiteit Amsterdam, 1995. (Research Memorandum; No. 1995-23).

Research output: Working paperProfessional

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van der Nat M, Brouwer F. Hedging with stock index futures: downside risk versus the variance. Amsterdam: Faculty of Economics and Business Administration, Vrije Universiteit Amsterdam. 1995. (Research Memorandum; 1995-23).