The Simple, And Dangerous Math, Behind Leverage ETFs

So you think by buying a double-long ETF on the S&P you'll get twice the return? Well, guess again….and while you're at it, read the fine print. Exchange-traded funds that use leverage are dangerous if you don't know what you're doing.

Some examples of leveraged funds are the ProShares Ultra S&P500, which returns double the S&P500 index return daily, and the ProShares Ultrashort S&P500, which returns double of the opposite of the S&P500 index return. There are a number of other providers and some leveraged funds are also 3X or triple the return of the underlying index.

Double-long (or 2x leveraged) ETFs are designed to return twice the return of the underlying index and double-short are designed to return twice the return in the opposite direction. For example, if an index is down 1% in a day, the double-short should return 2% up.

But they don't work so smoothly over the longer term, where returns can easily better than or less than 2X.

Why, and how, does this happen? The issue is that these funds are designed to double the index's return (or double the inverse of the return) on a DAILY basis. The math doesn't work over the longer term. That's because leveraged funds amplify the power of compounding. The impact of compounding on a 2x leveraged fund is generally greater than twice the impact of compounding on an equivalent unleveraged investment such as plain vanilla index fund or savings account. As a result, the longer-term return of a leveraged fund can be significantly greater than or less than two times the return of its underly­ing index for the time period. It all depends on what the market is doing: whether it's going up, down or is just plain volatile.

Here are three scenarios, and the simple math behind how gains and losses can occur much faster and to a greater degree. (Granted, the index returns are a tad extreme, but I'm trying to emphasize a point.)

Upward-trending market

Here, compounding can result in longer-term leveraged returns that are greater than two times the return of the unleveraged investment.

An investor starts off with $100 and the market grows 10% in one day. If she's in a leverage fund, that would be 20%. If that happened two days in a row, then she would wind up with compounded return of $144 (or $100 X (1+20%) X (1+20%)).

Downward-trending market

Here, compounding can also result in longer-term leveraged returns that are less negative than two times the return of the unleveraged investment.

So if the market falls 10% each day, then the $100 investment in the 2X leveraged fund would only lose 36% and wind up at $64 (or $100 x (1-20%) x (1-20%).

Volatile market

Here it get's really messy. Without giving it much thought, one might expect that a market movement upward would be cancelled out by a movement downward. Not so, remember the power of compounding. Compounding can result in leveraged longer-term returns that are significantly greater than or less than 2X the return of an unleveraged investment.

Say the market increases by 10% one day and the next, it decreases by 10%. The $100 investment would wind up losing 4% ($96) after two days in a 2X leveraged fund. Here's the simple arithmetic: ($100 X (1+20%) X (1-20%)). Compare this to an unleveraged index fund that would have lost just 1% under the same market circumstances. Compounding can also result in returns that are in the opposite direction of the underlying index during periods of unusual volatility.

The Net-Net

Leverage adds risk. That's why it's important to understand how it works and what factors affect the value of your investments. The effect of compounding can help returns in upward- and downward-trending markets and hurt in volatile markets, assuming all other variables remain the same. Leveraged funds are not suitable to most investors and have to be actively monitored on a daily basis. If you don't have the time or don't want to do the math, better to stay away from them.