An Algebraic Model for Hedging Equity Index Portfolios with Stock Index Futures. Evidence from the IBEX 35

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This article develops a Hedging Algebraic Model (HAM) for equity index portfolios with stock index futures as an alternative to econometric models (OLS, ECM, and GARCH) and assesses the efficacy of the model when applied to the IBEX 35 for the period 2007-2015. The model is initially formulated based on the efficient market hypothesis and an infinitesimal time horizon. When we relax these assumptions in the empirical analysis and apply the model to the real market with a daily time horizon, we obtain 98.75% efficacy of the hedge, superior to that of the econometric models. The time series of econometric models used to date for the calculation of the optimal hedging ratio do not include the effect of discrete dividend payouts and are based on a series of next-to-expire future prices that are subject to jumps in price, as it is composed of a chained series of futures with different maturities. Although the efficacy of econometric models can be considered satisfactory in general terms, their limitations can generate significant errors at some points in the series. The HAM model presented here as an alternative approach to econometrics models yields superior results, both in hedging efficacy and in the ease of application in professional portfolio management.