The Amazing Math of Leveraged ETFs

An Exchange Traded Fund (ETF) is a fixed portfolio of assets meant to mirror a specific market index. The portfolio is only changed to reflect changes in the composition of the index. An ETF trades on secondary markets like a typical share of common stock. Since ETFs are market traded, investors can enter and exit positions very rapidly, intraday if they so desire. In contrast, most mutual funds settle only at the day’s closing net asset value.

A leveraged ETF multiplies the risk in the underlying index. A 2X leveraged ETF would move twice as much as the related index in a single day. An inverse 2x ETF would move twice as much in the opposite direction, so that if the market index fell by 1 percent in a single day the inverse index would rise by 2 percent that same day. A full description of leveraged ETFs and the associated risks is contained in an article by Paul Justice, "Warning: Leveraged and Inverse ETFs Kill Portfolios," at Morningstar.

Leveraged ETFs will mirror the linked index over short periods. However, over longer holding periods they dramatically depart from the value of the underlying index. This is explained in the article by Paul Justice and in the accompanying video from Morningstar. The primary reason is that leveraged movements will produce greater absolute dollar changes at higher index values than at lower index values, so that the dollar movement from a leveraged 10 percent upward movement in an index is less than the dollar movement from a leveraged subsequent 10 percent downward movement. Consequently, the pattern of movements will affect the ultimate value of the leveraged ETF.