Risk minimisation using options and risky assets

Abstract

We consider mean-risk portfolio optimisation models, with risk measured 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 FTSE 100 and index options on FTSE100. Numerical results show that, for low risk-low return and to medium risk-medium return portfolios, the addition of an index put further reduces the risk to a considerable extent, particularly in the case of mean-CVaR efficient portfolios, where the left tail of the portfolio return distribution is dramatically improved. For high risk-high return portfolios, the inclusion of an index call improves the right tail of the return distribution, creating thus the opportunity for considerably higher returns.

Portfolio Optimization Model with and without Options under Additional Constraints

“…In this section, we use options in the portfolio that ensure the investment against unfavorable outcomes. ey reduce the risk and come, however, at some costs that decrease the return of the portfolio [35]. ese costs (options prices) are formulated based on the risk-neutral interest rate as follows:…”

“…ey found that controlling the risk of the market with options had a significant effect on performance of portfolio relative to currency risk. Authors in [35] showed that option reduces the risk and leads to better portfolio performance. Other studies also have investigated portfolio optimization models with options, for example, see [36][37][38][39][40][41][42].…”