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Leveraged Exchange-Traded Funds
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This Brief provides an§analysis, under both discrete-time and§continuous-time frameworks, on the price dynamics of§leveraged exchange-traded funds (LETFs), with emphasis on the roles§of leverage ratio, realized volatility, investment horizon,§and tracking errors. This study provides new insights on§the risks associated with LETFs, and leads to the discussion of trading§strategies, including pairs trading and stop-loss strategies, with§mathematical justification and formulas, along with a host§of examples using empirical data. The final part of the Brief addresses§the pricing of options written on LETFs. Since different LETFs§are designed to track the same reference index, these funds and their§associated options share very similar sources of randomness. The§authors provide a no-arbitrage pricing approach that consistently value§options on LETFs with different leverage ratios with stochastic volatility§and jumps in the reference index. Their results are useful for market making of§these options, and for identifying price discrepancies across the§LETF options markets.
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