Mean Variance Analysis of Instantaneous Options Returns
Randomness in portfolios of options and their common underlying originates from two major sources of uncertainty: the price of the underlying and the implied volatility smile. Within the subset of portfolios whose unique source of uncertainty is the volatility smile, we derive an explicit formula for the weights, mean, and variance of the instantaneously mean-variance efficient portfolios. This is done by applying principal component analysis (PCA) to the smile. The mean-variance characteristics do not depend on the appreciation rate of the underlying, and are therefore attractive for applications