The power of derivatives in portfolio optimization under affine GARCH models

This paper demonstrates the benefits, from an expected utility perspective, of including a derivative into the universe of tradeable assets under the affine GARCH model proposed by Heston and Nandi (Rev Financ Stud 13(3):585–625, 2000. https://doi.org/10.1093/rfs/13.3.585). For this purpose, we first introduce a Power Option into the market, derive its value and moment generating function thanks to the affine GARCH structure. We then expand on the results presented by Escobar-Anel et al. (Oper Res Perspect 9:100216, 2022) by solving for the optimal investment allocations into the stock, a cash account and the option. We show that investors who are able to include a derivative indeed outperform those who only invest into the stock and the bank account. In this spirit, investors who fail to include, even a low level of exposure to the derivative, could see up to 7% annual wealth-equivalent losses. This confirms findings in continuous-time models dating to Liu and Pan (J Financ Econ 69(3):401–430, 2003). An empirical analysis on the S &P500 confirms the superiority in terms of Sharpe ratio, and maximum drawdown of portfolios with options, in-sample and out-of-sample.