### Abstract

Original language | English |
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Place of Publication | Amsterdam |

Publisher | Faculty of Economics and Business Administration, Vrije Universiteit Amsterdam |

Publication status | Published - 1995 |

### Publication series

Name | Research Memorandum |
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No. | 1995-23 |

### Fingerprint

### Cite this

*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.

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

Research output: Working paper › Professional

TY - UNPB

T1 - Hedging with stock index futures: downside risk versus the variance

AU - van der Nat, M.

AU - Brouwer, F.

PY - 1995

Y1 - 1995

N2 - 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

AB - 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

M3 - Working paper

T3 - Research Memorandum

BT - Hedging with stock index futures: downside risk versus the variance

PB - Faculty of Economics and Business Administration, Vrije Universiteit Amsterdam

CY - Amsterdam

ER -