A Markowitz Portfolio Approach to Options Trading

In this paper, we study the problem of option portfolio design under the Markowitz mean-variance framework. We extend the common practice of a pure-stock portfolio and include options in the design. The options returns are modeled statistically with first- and second-order moments, enriching the conventional delta-gamma approximation. The naive mean-variance formulation allows for a zero-risk design that, in a practical scenario with parameter estimation errors, is totally misleading and leads to bad results. This zero-risk fallacy can be circumvented with a more realistic robust formulation. Transaction cost is also considered in the formulation for a proper practical design. We propose an efficient BSUM-M-based algorithm to solve the optimization problem. The proposed algorithm can perform as well as the off-the-shelf solvers but with a much lower computational time—up to one order of magnitude lower. Numerical results based on real data are conducted and the performance is presented in terms of Sharpe ratio, cumulative profit and loss, drawdown, overall return over turnover, value at risk, expected shortfall, and certainty equivalent.