Constructing an �α-maximizing option trading strategy in a multidimensional setting

Bosschaart, Peter (2013) Constructing an �α-maximizing option trading strategy in a multidimensional setting.

Abstract:In this thesis we derive a trading strategy which maximizes its excess returns, whilst controlling for the standard deviation of these excess returns, by dynamically investing in a portfolio of European call options on one or multiple benchmark assets and the benchmarks themselves. We show that this implies that the Sharpe ratio of these excess returns is maximized and that this is equivalent to the maximization of Jensen’s alpha, the intercept in the ordinary least squares regression of these excess returns on the excess returns on the complete US equity market. The strategy is constructed such that the exposure of the obtained excess returns to the excess returns on the complete US equity market is statistically insignificant. The portfolio selection procedure for this strategy turns out to be a variant of Markowitz portfolio selection, adapted to admit derivatives in the selection. The strategy’s performance is studied in a theoretical framework, where the benchmarks follow geometric Brownian motions and options are priced at the benchmark’s volatility with the Black- Scholes formula. We find that in this setting it is hard to generate superior performance as the statistical significance in the generated alphas is low. We also study the performance of our strategy with historical market data on four major stock indices on the US equity market over 1996-2013. In this setting we do find alphas that are significantly larger than zero and substantial Sharpe ratios, even in times of high volatility on the benchmarks, and that one obtains even better results when considering more benchmarks to invest on.
Item Type:Essay (Master)
Faculty:EEMCS: Electrical Engineering, Mathematics and Computer Science
Subject:31 mathematics
Programme:Applied Mathematics MSc (60348)
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