Understanding ETF erosion & why it's not a big problem for UPRO


My Medium-Long Term Model invests in UPRO, which is the S&P 500’s 3x leveraged ETF. ETF’s (especially leveraged ETF’s) sometimes have a problem called “erosion”, whereby the ETF does a poor job at matching the underlying market.
Here’s the underlying market VIX.

Here’s VXX, which is VIX’s non-leveraged long ETF.

Obviously VXX is an extreme case of erosion. But UPRO faces some erosion too.
Erosion for non-leveraged ETFs is usually caused by the shape of the underlying market’s futures curve.

Some markets like VIX and oil are usually in “contango”. This is when futures contracts that are farther out in time are more expensive than futures contracts that are closer to today.

Here’s an example of contango in VIX

Erosion can also happen in leveraged ETFs when the underlying futures market doesn’t have contango issues. This is caused by math.
UPRO has this erosion problem sometimes. Let’s look at the math behind it.

UPRO’s erosion

ETFs try to match the underlying market on a day-to-day basis. UPRO seeks to match the S&P 500’s daily % change by 3x. So if the S&P closes 1% lower than yesterday, UPRO tries to close 3% lower than yesterday.
UPRO does a good job at matching the S&P’s daily percentage change by 3x. UPRO’s erosion comes from a long term mathematical issue.
Here’s a chart for the S&P 500 since 1950.

Here’s a chart for theoretical UPRO (UPRO only began in 2009).

Notice 2 things:

  1. The S&P’s value in 2000 was almost the same as the S&P’s value in 2007. UPRO in 2007 was much lower than UPRO in 2000.
  2. The S&P today is much higher than it was in 2000. UPRO is still lower today than it was in 2000.

This is erosion that’s caused by the way UPRO is calculated.

  1. UPRO matches the underlying market’s DAY-TO-DAY change. It does not match the underlying market’s (S&P 500) month-to-month or year-to-year change.
  2. Hence, large declines cause erosion in UPRO. The larger the decline, the more severe the erosion. Bear markets (e.g. 40%+ declines in the S&P) account for the majority of UPRO’s erosion.

UPRO’s erosion in a bear market

UPRO will not go to $0 unless the S&P 500 falls more than 33.33% in a single day. Here’s what would happen if the S&P fell 33.33% over 4 days.

As you can see, UPRO matches the S&P’s % movement each day by 3%. But over multiple days (from Start to Day 4), UPRO does not fall 3x the S&P’s decline.
UPRO will fall by 90-95% in a S&P 500 bear market. This causes UPRO’s long term erosion.

  1. UPRO is down by e.g. 95% at the bottom of a S&P 500 bull market.
  2. UPRO compounds on the way up during the next bear market. But UPRO will make a new all-time high long after the S&P makes a new all-time high because UPRO’s “base $” at the bottom of the bear market is too low.

For example, if you lose 50% of your money, you need to make back 100% to get to breakeven. You’re “base $” is too low. Here’s UPRO’s example.

  1. The S&P falls 50% in a bear market. It needs to go up 100% (2x) to get back to break even.
  2. UPRO falls 95% in a bear market. It needs to go up 20x to get back to break even.

UPRO matches the S&P by 3x. A 2x gain in the S&P = a 6x gain in UPRO. UPRO still needs to go a long way to get back to breakeven AFTER the S&P has already gotten back to breakeven.

UPRO’s compounding

Inversely, UPRO matches the S&P’s gains by 3x each day during a bull market. Hence, UPRO goes up much more than the S&P during a bull market, even when accounting for the 3x factor. UPRO “compounds” on itself. Here’s an example.

Which factor overrides the other: compounding or erosion

  1. Erosion will override compounding in a S&P 500 bear market because the underlying market goes down more often than it goes up.
  2. Compounding will override erosion in a bull market because the S&P 500 goes up more often than it goes down.

Erosion is a small problem during corrections within bull markets.

  1. UPRO loses a little bit of value from erosion when the S&P goes down during corrections. The loss from erosion isn’t significant because the S&P doesn’t fall a lot.
  2. UPRO gains value from compounding when the correction ends & the S&P rallies to new highs.

In conclusion, the bigger the S&P’s decline, the more value UPRO loses from erosion. Erosion is a problem during “significant corrections” within bull markets, but it isn’t a big problem.
We can see this in historical “significant corrections”.
The S&P made a new high on November 4, 2010 after a “significant correction”.

UPRO lost 2.6% from erosion during this time.

11 comments add yours

    • Shorting an inverse ETF caps your gains at 100%. By being long UPRO your profits can vastly exceed 100%. Inverse ETFs have erosion problems, which makes them better for day trades and short term trades.

  1. Thanks Troy,
    That was one heck of a response! 😉
    It was very informative to see the historical perspective (theoretical), and the more recent history in a significant correction too.
    Regards,
    Mark

    • I don’t short in the Medium-Long Term portfolio. When you short, the max you can gain is 100%. Your profits are limited, losses are theoretically unlimited.

  2. Thanks for your guidance and education. I have a question. Why not buy longer term leap options on the SPY? Wouldn’t there be less erosion? Thx Walter

  3. Troy,
    In a new trading realm/world of hft’s and non human rapid fire trading markets as we have witnessed last week with a record breaking 10 trading day 12.5% correction, It is very worrisome that we can witness at any moment a 20% flash crash where upro would be down by 60%. This could happen in this day and age and as carl Icahn said on cnbc last week that the markets witnessed the 1st stage of earth quake rumblings. Evidenced by the historic 10 day 12.5% correction. I would be scared out of my mind knowing that a 1-day 20% event could erode a upro portfolio of 60% in value, and the amount of time it would take for the portfolio to recover. It would create a class action securities erosion lawsuit just like the guy I caddie for created as lead class action against triple leveraged financial bear etf FAZ. It’s a new day and age we live in without sec involvement of these products. Look at what happened to Xiv last week it went from 100 to 9 in 1-day. Just sayin

    • XIV’s destruction was clearly the act of someone who figured out how to make a lot of money by triggering the “cut loss at -80%” rule.
      As for the S&P 500’s decline: a 5% drop in 1 day isn’t unprecedented.

  4. HI Troy,
    I read your UPRO long position explanation. My question is if we all expecting recession in 2 years, can we short upro now and wait till it reach the price of 25 from 130 today’s price?
    Thanks

    • No. If you short now and the bull market lasts another 2 years, you will be forced to cover your short position at a loss. UPRO can go up by more than 2x in the final 2 years of a bull market.
      Regards,
      Troy

Leave a Comment