Download Leveraged Exchange-Traded Funds: Price Dynamics and Options by Tim Leung, Marco Santoli PDF

By Tim Leung, Marco Santoli

This ebook offers an research, lower than either discrete-time and continuous-time frameworks, at the fee dynamics of leveraged exchange-traded money (LETFs), with emphasis at the roles of leverage ratio, learned volatility, funding horizon, and monitoring blunders. This learn offers new insights at the hazards linked to LETFs. It additionally results in the dialogue of latest danger administration innovations, corresponding to admissible leverage ratios and admissible chance horizon, in addition to the mathematical and empirical analyses of a number of buying and selling concepts, together with static portfolios, pairs buying and selling, and stop-loss ideas related to ETFs and LETFs. the ultimate a part of the publication addresses the pricing of suggestions written on LETFs. when you consider that various LETFs are designed to trace an analogous reference index, those money and their linked ideas percentage very comparable assets of randomness. The authors offer a no-arbitrage pricing procedure that continually price ideas on LETFs with assorted leverage ratios with stochastic volatility and jumps within the reference index. Their effects are beneficial for industry making of those strategies, and for deciding upon expense discrepancies around the LETF concepts markets. because the marketplace of leveraged exchange-traded items develop into a huge hooked up a part of the monetary marketplace, it can be crucial to raised comprehend its suggestions impression and broader marketplace influence. this can be vital not just for person and institutional traders, but additionally for regulators.

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Leveraged Exchange-Traded Funds: Price Dynamics and Options Valuation

This booklet offers an research, lower than either discrete-time and continuous-time frameworks, at the cost dynamics of leveraged exchange-traded money (LETFs), with emphasis at the roles of leverage ratio, discovered volatility, funding horizon, and monitoring mistakes. This learn presents new insights at the hazards linked to LETFs.

Extra resources for Leveraged Exchange-Traded Funds: Price Dynamics and Options Valuation

Example text

At time T , the return from this strategy is given by RT = 1 − ω L+ L− T T − (1 − ω) . 17), RT can be expressed as an explicit function of the return and realized variance of the reference index. 18). Note that the return RT over a short holding period such that LLT0 ≈ 1, one can pick an appropriate weight ω ∗ to approximately remove the dependence of RT on ST . 21) then the return from this strategy is given by RT ≈ −β− β+ β− VT − (f+ − f− )T + (f− − r)T. 22) LT L0 ≈ 1. 22). 21) reflects a linear dependence on the realized variance.

Consequently, the equation V aRα (β, τ ) = C always admits a unique strictly positive solution (note that V aRα (β, 0) = 0). 4 illustrates how ARHα varies for different values of β and μ. As we can see, the admissible risk horizon increases as |β| decreases. For any fixed positive leverage ratio, the admissible risk horizon tends to increase with drift μ. In addition, it is also preferable to choose a leverage ratio, say ˆ with the same sign as that of μ, since the corresponding admissible risk β, ˆ horizon is greater than that of −β.

At every point in time, the portfolio invests β times the value of the fund in the futures contract in order to achieve the required leverage. 16) j=1 where Lj is the value of a leveraged investment in gold and Pj is the value of our portfolio, each at trading day j. For this dynamic portfolio, there is no sample from which we will need to draw our weights or train our model in any way. 16). 9. 10. 687% 1 Leung and Ward (2015) show that the front-month futures is empirically most effective in replicating the spot gold price.

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