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Hedge Ratios for short and leveraged ETFs

Keywords: lio Optimization , Hedging , Cross Hedge , Insurance and Immunization of portfolios , short leveraged Exchange Traded Funds (ETFs) , Mean–Variance , Target-Shortfall-Probability , Monte Carlo Simulation

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Exchange Traded Funds (ETFs) exist for stock-, bond- and commodity markets. In most cases the underlying of an ETF is an index. Fund management today uses the active and passive way to construct a portfolio. ETFs can be used for passive portfolio management. Then ETFs with positive leverage factors are preferred. In the frame of active portfolio also the ETFs with negative leverage factors can be applied for the hedge or cross hedge of a portfolio. These hedging possibilities will be analyzed 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 e.g. 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 seem not to be until to get 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 which have a low correlation with the index return should not be used high leverage factors for hedging, due to the higher volatility and target-shortfall-probability.


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