Hedge ratios for short and leveraged ETFs

Exchange-traded funds (ETFs) exist for stock, bond and commodity markets. In most cases the underlying feature of an ETF is an index. Fund management today uses the active and the passive way to construct a portfolio. ETFs can be used for passive portfolio management, for which ETFs with positive leverage factors are preferred. In the frame of an active portfolio management the ETFs with negative leverage factors can also be applied for the hedge or cross hedge of a portfolio. These hedging possibilities will be analysed in this paper. Short ETFs exist with different leverage factors. In Europe, the leverage factors 1 (e.g. ShortDAX ETF) and 2 (e.g. DJ STOXX 600 Double Short) are offered while in the financial markets of the United States factors from 1 to 4 can be found. To investigate the effect of the different leverage factors and other parameters Monte Carlo simulation was used. The results show for example that higher leverage factors achieve higher profits as well as losses. In the case that a bearish market is supposed, minimizing the variance of the hedge seems not to obtain better hedging results, due to a very skewed return distribution of the hedge. The risk measure target-shortfall probability confirms the use of the standard hedge weightings, which depend only on the leverage factor. This characteristic remains when a portfolio has to be hedged instead of the underlying index of the short ETF. For portfolios that have a low correlation with the index return high leverage factors should not be used for hedging, due to the higher volatility and target-shortfall probability. -- portfolio optimization ; hedging ; cross hedge ; insurance and immunization of portfolios ; short leveraged exchange-traded funds (ETFs) ; mean-variance ; target-shortfall probability ; Monte Carlo simulation