Risk minimisation using options and risky assets

Abstract

We consider mean-risk portfolio optimisation models, with risk quanti ed by symmetric measures (variance) as well as downside or tail measures (Lower Partial Moments, Conditional Value at Risk). A framework for including index options in the universe of assets, in addition to stocks, is provided. The exercise of index options is settled in cash, making this implementable with a variety of strike prices and maturities. We use a dataset with stocks from the FTSE 100 and index options on the FTSE100. Numerical results show that, for low to medium risk portfolios, the addition of an index put further reduces the risk to a considerable extent, particularly in the case of mean-CVaR e cient portfolios, where the left tail is dramatically improved. For higher risk portfolios, the inclusion of an index call improves the right tail of the portfolio distribution, creating thus the opportunity for considerably higher returns.