On the Properties of Leveraged ETFs

In this paper, we examine if, for a successful long-term investment of leveraged ETFs, it is necessary to adjust the level of leverage according to the fluctuations of the financial markets. For this purpose, we illustrate in particular the behavior of the Leverages ETF based on the optimal leverage introduced by Giese (2009). This latter one, which is based on the growth rate expectation, behaves as a function of the prevailing market environment. More precisely, it implies that the investor should use high leverage in low volatility markets and low leverage in high volatility markets. We study also how the degree of leverage depends on the main factor of market environment, namely the volatility of the market in force.

Does the Lending Rate Impact ETF's Prices?

In this paper we developed an econometric model to empirically test the hard-to-borrow model of Avellaneda and Lipkin (2009) where asset prices jump as result of ``buy-in" procedures. The model is estimated using an extent version of simulated maximum likelihood (SML) for a selected group of Leveraged ETF, mainly short LETFs, because these instruments have been sporadically hard-to-borrow and are liquids. In general we do not find enough statistical evidence supporting that hard-to-borrow effect impacts LETFs prices. On the other hand, we did find statistical evidence supporting the jump-diffusion model for some Leveraged ETFs.

Optimal leverage ratio estimate of various models for leveraged ETFs to exceed a target: Probability estimates of large deviations

In this paper, we study the deviation probability estimate for a leveraged exchanged-traded fund (LETF). By large deviation principle, we derive explicitly the logarithmic limit of the tail probability when the price of a LETF exceeds a given reference asset, which allows us to compute the underlying leverage ratio. Then we apply our results to various existing models, including the geometric Brownian motion (GBM) model, generalized autoregressive conditional heteroskedasticity (GARCH) model, inverse GARCH model, extended Cox–Ingersoll–Ross (CIR) model, 3/2 model, as well as the Heston and 3/2 stochastic volatility models, and to present their corresponding optimal leverage ratios, respectively.