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Hedging long-term exposures of a well-diversified portfolio with short-term stock index futures contracts. (English) Zbl 1407.91229

Summary: It is difficult for passive portfolio strategy to manage the long-term exposure of a well-diversified portfolio because stock index futures contracts have a finite life limited by their maturity. In this paper, we investigate the problem of the rollover hedge strategy for the long-term exposure of a well-diversified portfolio. First, we consider the rollover hedge strategy for the well-diversified portfolio when the portfolio is not adjusted during the period. In order to obtain the optimal solution of the proposed model, the auxiliary models are constructed using the equivalent transformation technique. Moreover, dynamic programming is employed to derive the optimal positions of stock index futures contracts for the long-term exposure of the well-diversified portfolio. In addition, we extend the result to the case of the rollover hedge strategy with transaction costs and derive the optimal number of stock index futures contracts.

MSC:

91G10 Portfolio theory
91G20 Derivative securities (option pricing, hedging, etc.)
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[1] Figlewski, S., Hedging performance and basis risk in stock index futures, Journal of Finance, 39, 3, 657-669 (1984) · doi:10.1111/j.1540-6261.1984.tb03654.x
[2] Figlewski, S., Hedging with stock index futures: theory and application in a new market, The Journal of Futures Markets, 5, 2, 183-199 (1985) · doi:10.1002/fut.3990050204
[3] indahl, L. M., Minimum variance hedge ratios for stock index futures: duration and expiration effects, The Journal of Futures Markets, 12, 1, 33-53 (1992) · doi:10.1002/fut.3990120105
[4] Holmes, P., Stock index futures hedging: Hedge ratio estimation, duration effects, expiration effects and hedge ratio stability, Journal of Business Finance and Accounting, 23, 1, 63-77 (1996) · doi:10.1111/1468-5957.00205
[5] Lee, H. C.; Chien, C. Y., Hedging performance and stock market liquidity: evidence from the taiwan futures market, Asia-Pacific Journal of Financial Studies, 39, 3, 396-415 (2010) · doi:10.1111/j.2041-6156.2010.01015.x
[6] Ghosh, A., Hedging with stock index futures: estimation and forecasting with error correction model, The Journal of Futures Markets, 13, 7, 743-752 (1993) · doi:10.1002/fut.3990130703
[7] Eftekhari, B., Lower partial moment hedge ratios, Applied Financial Economics, 8, 6, 645-652 (1998)
[8] Lien, D.; Tse, Y. K., Hedging downside risk with futures contracts, Applied Financial Economics, 10, 2, 163-170 (2000)
[9] Chen, S. S.; Lee, C. F.; Shrestha, K., On a mean-generalized semivariance approach to determining the hedge ratio, Journal of Futures Markets, 21, 6, 581-598 (2001)
[10] Park, T. H.; Switzer, L. N., Time-varying distributions and the optimal hedge ratios for stock index futures, Applied Financial Economics, 5, 3, 131-137 (1995) · doi:10.1080/758523000a
[11] Lypny, G.; Powalla, M., The hedging effectiveness of DAX futures, The European Journal of Finance, 4, 4, 345-355 (1998) · doi:10.1080/135184798337227
[12] Choudhry, T., Short-run deviations and optimal hedge ratio: evidence from stock futures, Journal of Multinational Financial Management, 13, 2, 171-192 (2003) · doi:10.1016/S1042-444X(02)00042-7
[13] Choudhry, T., The hedging effectiveness of constant and time-varying hedge ratios using three Pacific Basin stock futures, International Review of Economics and Finance, 13, 4, 371-385 (2004) · doi:10.1016/j.iref.2003.04.002
[14] Pattarin, F.; Ferretti, R., The Mib30 index and futures relationship: econometric analysis and implications for hedging, Applied Financial Economics, 14, 18, 1281-1289 (2004) · doi:10.1080/09603100412331313578
[15] Lai, Y.; Chen, C. W. S.; Gerlach, R., Optimal dynamic hedging via copula-threshold-GARCH models, Mathematics and Computers in Simulation, 79, 8, 2609-2624 (2009) · Zbl 1162.91519 · doi:10.1016/j.matcom.2008.12.010
[16] Lee, H. T., Optimal futures hedging under jump switching dynamics, Journal of Empirical Finance, 16, 3, 446-456 (2009) · doi:10.1016/j.jempfin.2008.12.001
[17] Hou, Y.; Li, S., Hedging performance of Chinese stock index futures: an empirical analysis using wavelet analysis and flexible bivariate GARCH approaches, Pacific-Basin Finance Journal, 24, 109-131 (2013) · doi:10.1016/j.pacfin.2013.04.001
[18] Sim, A. B.; Zurbruegg, R., Dynamic hedging effectiveness in South Korean index futures and the impact of the Asian financial crisis, Asia-Pacific Financial Markets, 8, 3, 237-258 (2001) · Zbl 1054.91546
[19] Wang, J.; Hsu, H., Hedge ratio stability and hedging effectiveness of time-varying hedge ratios in volatile index futures markets: evidence from the Asian financial crisis, Asia-Pacific Journal of Financial Studies, 39, 5, 659-686 (2010) · doi:10.1111/j.2041-6156.2010.01026.x
[20] Yang, W.; Allen, D. E., Multivariate GARCH hedge ratios and hedging effectiveness in Australian futures markets, Accounting and Finance, 45, 2, 301-321 (2005) · doi:10.1111/j.1467-629x.2004.00119.x
[21] Floros, C.; Vougas, D. V., Hedge ratios in Greek stock index futures market, Applied Financial Economics, 14, 15, 1125-1136 (2004) · doi:10.1080/09603100412331297702
[22] Pok, W. C.; Poshakwale, S. S.; Ford, J. L., Stock index futures hedging in the emerging Malaysian market, Global Finance Journal, 20, 3, 273-288 (2009) · doi:10.1016/j.gfj.2009.06.002
[23] Aragó, V.; Salvador, E., Sudden changes in variance and time varying hedge ratios, European Journal of Operational Research, 215, 2, 393-403 (2011) · doi:10.1016/j.ejor.2011.05.055
[24] Alizadeh, A.; Nomikos, N., A markov regime switching approach for hedging stock indices, Journal of Futures Markets, 24, 7, 649-674 (2004) · doi:10.1002/fut.10130
[25] Laws, J.; Thompson, J., Hedging effectiveness of stock index futures, European Journal of Operational Research, 163, 1, 177-191 (2005) · Zbl 1066.91044 · doi:10.1016/j.ejor.2004.01.007
[26] Kofman, P.; McGlenchy, P., Structurally sound dynamic index futures hedging, Journal of Futures Markets, 25, 12, 1173-1202 (2005) · doi:10.1002/fut.20185
[27] Wei, Y.; Wang, Y.; Huang, D., A copula-multifractal volatility hedging model for CSI 300 index futures, Physica A: Statistical Mechanics and its Applications, 390, 23-24, 4260-4272 (2011) · doi:10.1016/j.physa.2011.06.042
[28] Wen, X.; Wei, Y.; Huang, D., Speculative market efficiency and hedging effectiveness of emerging chinese index futures market, Journal of Transnational Management, 16, 4, 252-269 (2011) · doi:10.1080/15475778.2011.623989
[29] Kostika, E.; Markellos, R. N., Optimal hedge ratio estimation and effectiveness using ARCD, Journal of Forecasting, 32, 1, 41-50 (2013) · Zbl 1397.62418 · doi:10.1002/for.1249
[30] Neuberger, A., Hedging long-term exposures with multiple short-term futures contracts, Review of Financial Studies, 12, 3, 429-459 (1999)
[31] Hilliard, J. E., Analytics underlying the metallgesellschaft hedge: short term futures in a multi-period environment, Review of Quantitative Finance and Accounting, 12, 3, 195-219 (1999)
[32] Lien, D.; Shaffer, D. R., Multiperiod strip hedging of forward commitments, Review of Quantitative Finance and Accounting, 18, 4, 345-358 (2002)
[33] Godbey, J. M.; Hilliard, J. E., Adjusting stacked-hedge ratios for stochastic convenience yield: a minimum variance approach, Quantitative Finance, 7, 3, 289-300 (2007) · Zbl 1142.91524 · doi:10.1080/14697680600989535
[34] Leobacher, G., On a class of optimization problems emerging when hedging with short term futures contracts, Mathematical Methods of Operations Research, 67, 1, 65-90 (2008) · Zbl 1145.91024 · doi:10.1007/s00186-007-0179-4
[35] Carchano, Ó.; Pardo, Á., Rolling over stock index futures contracts, Journal of Futures Markets, 29, 7, 684-694 (2009) · doi:10.1002/fut.20373
[36] Fu, J.; Zhang, W. G.; Yao, Z.; Zhang, X., Hedging the portfolio of raw materials and the commodity under the mark-to-market risk, Economic Modelling, 29, 4, 1070-1075 (2012) · doi:10.1016/j.econmod.2012.03.025
[37] Li, D.; Ng, W. L., Optimal dynamic portfolio selection: multiperiod mean-variance formulation, Mathematical Finance, 10, 3, 387-406 (2000) · Zbl 0997.91027 · doi:10.1111/1467-9965.00100
[38] Reid, R. W.; Citron, S. J., On noninferior performance index vectors, Journal of Optimization Theory and Applications, 7, 11-28 (1971) · Zbl 0204.46803 · doi:10.1007/BF00933589
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