Option-implied distribution in a portfolio selection model : an empirical study

Abstract

Estimation of parameters such as mean and volatility from historical prices are used as inputs to a portfolio model. Recently, researchers found that the estimation parameters based on option prices have made a significant improvement in the performance of a portfolio. To date, the usefulness of an option-implied distribution in a portfolio selection model is still an open question. The main contribution of this thesis is based on the extension information embedded in option prices for an asset allocation model. This thesis aims to shed some light on this conundrum based on the Dow Jones Industrial Average (DJIA) index data. This thesis consists of three parts: risk-neutral density (RND) estimation, transforming RND into risk-world density (RWD), extraction of option-implied moments and their applications in a portfolio selection model. The first objective is to extract risk-neutral density (RND) of the underlying asset from option prices by differentiating the option prices twice. However, interpolation and extrapolation techniques are needed in order to provide continuum option prices as required in RND assumption. This thesis examines the performance of interpolation approaches, which are second-order polynomial, fourth-order polynomial and cubic smoothing spline. The performance is evaluated using three ways: statistical test, forecasting accuracy and leave-out-one-cross validation. The second objective is to convert RND into RWD. Since RND estimation does not incorporate risk premium, an adjustment is required to ensure that it represents the true distribution. The RND is calibrated using parametric and nonparametric calibrations in order to obtain RWD. The option-implied moments which are calculated based on the RND and RWD are used as inputs to a portfolio model. The third objective is to compare the performances of a naïve portfolio with that of option-implied distribution portfolio. Empirical evidence shows that the portfolio based on option-implied distribution outperforms the naive portfolio in which it gives lower volatility and higher Sharpe ratio. In addition, portfolios based on RWD-P and RWD-NP perform better than that of the portfolios based on RND. This thesis can be considered as a reference to researchers in terms of using forward-looking information in asset allocation model instead of using backward-looking information. In Malaysian perspectives, RND and RWD can be applied using FTSE Bursa Malaysia KLCI option (OKLI) since the characteristics of these options are the same with that of DJIA options.