Understanding the Math of Leveraged ETFs

Exchange Traded Funds provide investors with an assortment of ways to invest in very diverse instruments as if they were simple stock purchases.  The variety and scope of this market has become extremely vast and continues to grow.  One of the common flavors of ETF are leveraged ETFs.  These funds seek to duplicate the results of a multiple of the daily change of a given underlying asset.  While this may sound appealing, it is pivotal to understand that leveraged ETFs are generally for trading and not for holding for long periods of time.  The reason is simple mathematics.

When you purchase a leveraged ETF it is typically designated with a multiplier.  For example if you wanted to get double the effect of gold's daily movements you could go "double long" gold, which means that if gold goes up 5% in a day the ETF will go up 10%.  You can also go "double short" gold, meaning that if gold goes down 5% you will go up 10% and if gold goes up 5% you will go down 10%.  This can offer a good way to maximize a short term move, but let's look at the math over time.

Suppose that gold is trading at 100 and a double long ETF, let's call it DGLD is at 100 as well.  You buy in at 100.  The next day gold goes up 10%, meaning DGLD, our fictitious ETF, goes up 20%.  Now gold is at 110 and DGLD is at 120, great so far.  Now the next day gold goes back down to 100.  This is a move of basically 9.1%, which means DGLD will go down roughly 18.2%, leaving gold at 100 and DGLD 98.2.

Did you see what happened there?  The underlying asset, gold, is at its original price, but you've lost 1.8% on DGLD.  Because DGLD is trying to double the daily effect, you will typically have slippage over time if the underlying price fluctuates, instead of just moving in one direction.  You could easily underperform the asset itself if you hold it for a long time.  You can easily go test this historically with funds that are leveraged on other funds, for example SRS and IYR. 

Thus it's key before investing in leveraged ETFs to be aware that they are not good candidates for a "buy and hold" strategy.  They are more geared towards rewarding a belief that the price will move sharply in the short term.  While leverage can be dangerous in the best of times, it can be merciless if you don't fully understand its consequences.  Be wary before using these funds.