Size isn’t everything — at least when it comes to exchange-traded funds.

While a large amount of assets under management sometimes can be a sign of a useful, positively performing fund, it’s not a guarantee. In fact, there are some heavily bought-into ETFs that have no redeeming qualities whatsoever — their attributes are so poor that their largesse is inexplicable; indeed, mind-boggling.

Here’s a look at three dud equity funds of at least $1 billion, as well as my pick for the ultimate loser:

ProShares UltraShort S&P 500

The S&P 500 closed trading on Sept. 22 up 16.1% year-to-date. Fast forward eight weeks to Nov. 16, and the index’s YTD gains were down to 8.13%, losing almost half its gains by percentage in just two months.

Despite the ugly fall markets, though, to bet against the index at this point seems like a big risk, especially if budget talks are successful and the fiscal cliff temporarily disappears. Take Monday’s trading for example — the S&P 500 took off on the previous Friday’s good news about the budget talks. By the end of the day, the index was up 1.75% and motoring higher into the close.

If you want to short the index, go ahead and use the SPDR S&P 500 ETF (NYSE:SPY). Purchasing the ProShares UltraShort S&P 500 ETF (NYSE:SDS) — so the so-called “professionals” can do it for you — is simply wasting money, not to mention exposing your portfolio to unnecessary risk.

You’re paying 0.89% to ProShares so it can deliver investment results (before fees and expenses) that’s double the inverse of the daily performance of the S&P 500. In other words, you’re a big-time bear who’s placing a leveraged bet that the index will decline on a given day. If the index gains 2% in a single day’s trading, you will lose 4%. If you hold the fund for more than one day, your losses will be magnified should the index continue to rise.

Borrowing to invest never makes sense, in my opinion, but it’s an especially dumb idea if you’re paying someone else for the privilege. The ProShares UltraShort S&P 500 ETF has more than $2 billion in assets under management specifically because traders like it when making leveraged bets for and against the markets.

If you’re not a professional trader, I can’t think of a single reason why you would mess with this fund.

Market Vectors Gold Miners ETF

In Warren Buffett’s 2011 letter to investors, he basically suggested that if you meld all the world’s gold together, you’d have a $9.6 trillion cube of gold that would do nothing but sit lifelessly in your backyard.

For years, proponents of gold have advocated owning the precious metal because it’s a hedge against inflation and the devaluation of the U.S. dollar. On a 10-year rally, it’s possible that gold will keep rising. For those who believe that to be the case, investing in the physical commodity makes a lot more sense than investing in the companies who mine the gold — that’s because the price someone is willing to pay for an ounce of gold is a lot more tangible than the profitability of one miner compared with another. The success or failure of a miner depends on its cost structure, etc. Why take a chance on mining stocks not doing well while gold pushes higher?

Year-to-date, the iShares Gold Trust (NYSE:IAU) — which seeks to replicate the day-to-day movement in the price of gold bullion — is up 9.32% while the GDX is down 9.6%. Extend that out five years, and the difference in performance is staggering; the IAU’s total return during the past half-decade is 16.5% versus 0.36% for the Market Vectors Gold Miners ETF (NYSE:GDX), which holds a host of primarily gold miners.

For that incredibly poor performance, investors have the privilege of paying an annual fee of 0.52%, 27 basis points higher than the IAU.

Frankly, it’s hard to believe the Van Eck fund has $9.3 billion in assets, which is just $2.7 billion less than the IAU. It’s a head-scratcher of the worst kind.

iShares MSCI Brazil Index Fund

The iShares MSCI Brazil Index Fund (NYSE:EWZ) seeks to replicate the performance of the MSCI Brazil Index, which captures about 85% of the market capitalization of the Brazilian stock markets. The fund has accumulated $8.6 billion in assets in a little more than 12 years, and it’s currently the 18th-largest ETF by assets and the largest single-country fund available to U.S. investors.

However, year-to-date, EWZ is down 9.2%, and 6.1% annually during the past five years.

The Vanguard MSCI Emerging Markets ETF (NYSE:VWO) invests in 21 different countries, with Brazil as its third largest weighting at 12.5%, behind only Korea and China. Year-to-date, the more diversified fund is up 7.8% compared to a big loss for the EWZ. And as a whole, single-country funds generally exhibit greater volatility than ETFs with diversification by country.

When you consider that the Vanguard fund’s expense ratio is 39 basis points less than the EWZ, you have to wonder why so many people are betting so aggressively on Brazil.

It simply hasn’t paid off most of the time.

(And as far as I’m concerned, the only single-country fund you should own is one investing right here in the United States.)

Bottom Line

Although I’m tempted to pick the ProShares ETF as the biggest loser because of its use of leverage while also shorting, in the end I have to go with the gold mining fund.

Investors have poured almost $10 million into GDX, making it the 17th-largest equity fund by assets in the U.S. — despite evidence that it never has performed worth a lick.

That’s just wrong.

As of this writing, Will Ashworth did not hold a position in any of the aforementioned securities.