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.
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:
- 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.
- 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.
- 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.
- 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.
- UPRO is down by e.g. 95% at the bottom of a S&P 500 bull market.
- 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.
- The S&P falls 50% in a bear market. It needs to go up 100% (2x) to get back to break even.
- 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.
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
- Erosion will override compounding in a S&P 500 bear market because the underlying market goes down more often than it goes up.
- 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.
- 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.
- 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.