In previous articles (here) I have analyzed leveraged and inverse stock ETFs to examine how well they tracked their underlying index. Since these articles appeared over 15 months ago, I will update some of this analysis in the near future.

But first I wish to turn our attention to government bond ETFs. What with tapering and a new Fed Chairman, the bond market has been turbulent over the past year.

I will compare the performance of:

The former is a *leveraged ETF,* specifically 2x, meaning it is expected to perform twice as well (or poorly!) on a day to day basis than the underlying simple bond ETF. For example if the bond ETF gained 3% today you would expect UBT to gain 6%. More about this later.

Investors should pay attention to two issues when analyzing ETFs. One is *tracking error.* This simply describes how well the ETF tracks its target, or *bogey,* index. Below is a chart of the S&P 500 Index and its eponymous SPDR ETF (NYSEARCA:SPY). Can you tell them apart? I didn't think so.

source: www.bigcharts.com

With leveraged, or 2x and 3x ETFs, another factor comes into play. This is referred to as *volatility drag.* This peculiarly named problem occurs because leveraged ETFS rebalance their entire portfolio at the end of each trading day.

A simple example will show the nefarious effects of such drag.

Suppose you bought a stock for $20 a share. The first day it rises to $25; the second, it falls to $15, and the third day it goes back up to $20. A buy-and-hold investor has broken even. What happens to an ETF designed to "track" this one stock?

OOPS! Not so good, especially a double index. On the first day the stock gained 25%, doubled this is 50%. On the second day it fell 40%; doubled, this is an 80% loss; and on the third day it rose about 33%, for a 66% doubled gain. What is your overall result if you rebalance each of the three days? Turning the percentages into decimals, and multiplying we have

- (1.00 + .50) for day 1;
- (1.00 - .80) for day 2; and
- (1.00 + .66) for day 3. The final result is

(1.5)x(.2)x(1.66) or approximately .50.

Returning to percentages (isn't math fun!) you have 50% of your investment remaining. You have lost half your money.

Losing half your money is a drag, indeed... so this weakness of leveraged ETFs is worth keeping an eye on.

To see how bad this drag is, we can compare the two bond ETFs mentioned near the top of this article. Fortunately, 2013 offered a variety of investment environments for bondholders. Bonds rose for the first few weeks, then fell sharply over the summer with Fed taper talk, and then ended the year trading flat for several months.

Lets look at these three periods.

- from March 8th to April 30th bonds had a smart move upward. Compare the two ETFs in the chart below.

Bonds went up about 7.1%, and the double index gained a trifle more than 15%. Looks like a bit of over performance. Not any evidence of volatility drag here.

- from May 1st to August 22nd bonds sold off sharply. Compare the two ETFs in the chart below.

Bonds sagged 17%, and the double index again appears to have done a bit better (or, more exactly, *less worse)* than that. Actually however for such a large percent change we need to make the mathematical calculations more clear for leveraged ETFs.

Bonds fell 17%. This means you now have 17% less than you did before, or 83% of your original capital remaining. Changing this percentage to a decimal...

- you must then
*square it,*since this is a 2x leveraged fund. - (.83) x (.83) = (.69)

Returning to percentages (isn't math fun) you have 69% of your funds remaining, which is a 31% decline, and this is exactly how much UBT fell over this period.

I don't perform this calculation to split hairs, but to demonstrate that even over periods of several months, volatility drag continues to have minimal effect on the returns of ETFs that I have followed.

Hmmm... no drag in an up market... no drag in a down market. Would drag show up in a sideways market?

- from September 16th to December 19th bonds traded flat. So did the 2x ETF, as we can see here.

So with bonds funds as with broad index funds like SPY, volatility drag appear to be minimal, even over intermediate time frames such as a few months.

Why, given my example at the top of this article? Simple: the day to day changes in portfolios of bonds or index funds is very, very small, often less than 1% and rarely over 2%. For such small changes volatility drag is negligible. In fact, for small percentage moves you can just "double" the underlying, you don't have to "square" the result. That, and a bit of math phobia even among investors is why they are usually called 2x funds, not "square funds."

In my next article I will look at whether *inverse bond funds,* and *leveraged* inverse bond funds, have significant volatility drag. This is important since many folks on Wall Street use these inverse funds in lieu of short selling. The daily rebalancing (and the mathematics) are trickier, however.

**Disclosure**: I am long XLK, IHI and XLV. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.

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