Understanding the risk of leveraged ETFs

The purpose of this paper is to clarify the risks of leveraged ETFs. We do this by showing how to construct a k-times leveraged ETF as a dynamic portfolio in the ETF and a money market account. This construction characterizes the return distribution of the leveraged ETF over any investment horizon. As a corollary, we show that a k-times leveraged ETF will not earn k times the return of the ETF. It differs due to a term involving the ETF's volatility and the interest paid on the borrowing over the investment horizon.