Portfolio selection with position limits

This thesis finds long-short portfolios of call and put options on a single underlying asset and expiration, with different strike prices, so to maximize the Sharpe Ratio of portfolio returns. From analytical and numerical optimization methods we select those that can tackle the problem of high dimensionality. Combining analytical covariance estimation with quadratic constrained optimization, optimal options portfolios on the S&P 500, Nasdaq 100 and Dow Jones Industrial generate positive excess returns over the past two decades, controlling for their exposure to the underlying and accounting for the large bid-ask spreads in options’ prices. Optimal options portfolios typically entail nonzero positions in few strikes.

This thesis also derives sharp lower bounds for L p -functions on the n-dimensional unit hypercube in terms of their p-ths marginal moments. Such bounds are the unique solutions of a system of constrained nonlinear integral equations depending on the marginals. For square-integrable functions, the bounds have an explicit expression in terms of the second marginals moments. This work is motivated by the dual problem in option portfolio optimisation for multiple underlyings, where the minimal stochastic discount factor satisfies marginal constraints - the prices of European options on each underlying.