Volatility drag, or sometimes called variance drain, occurs in leveraged products when the returns differ substantially from the implied leverage factor over certain periods of time. In the massive Risk On investment environment we’ve been in for the past 15+ years, leveraged ETFs have been a popular way for aggressive traders to multiply their returns, if they’re willing to accept the greater risk to the downside as well.
UPRO is an exchange traded fund that is designed to offer 3x the daily return of the S&P 500 stock index. If the index increased by 1.5% in a given day, this ETF should produce a daily return of 4.5%. Similarly, if the index were to selloff by 2%, the ETF should return -6% on that day.
What confuses many casual investors, and even highly sophisticated traders, is the fact that leveraged funds can actually produce substantially different long-term results due to the effect of daily compounding. Say the S&P 500 is up 15% over a one-year period, that won’t necessarily equate to a 45% return in the leveraged fund. Even though it might be close, it is quite possible to see massive deviations in the expected return.
Oddly enough, due to this concept of volatility drag, it is even possible for an index to be up over a certain period of time while the leveraged version is down. Let’s take a look at an example:
The above chart looks at a series of assumed returns on an index. To illustrate the math, we assume the index will be up 2.1% tomorrow, down 2% the next day, up 2.1% the following day, and so on for a full year, or approximately 252 trading days. Under these circumstances, the 3x leveraged version of this index would return 6.3% tomorrow, then -6%, then +6.3% and so on for the same timeframe.
But look at the growth and decay of an initial $10,000 investment in both cases. Had you invested in the underlying asset without the leverage, your portfolio would have grown to $10,758 while the leveraged portfolio would have actually shrunk to $9,064 even though the underlying was up over the same timeframe.
Of course, this is not always the case though. In bull markets or periods of sustained upward trends, it is often possible that a leveraged fund can produce returns far in excess of the daily leverage factor. For instance, since UPRO’s inception in June 2009, the ETF has increased by an incredible 78-fold, while the S&P itself has increased by just about 6.5x. Over this period, the leveraged version has obviously returned far in excess of 3x the returns of the S&P 500 alone, again due to the effect of daily compounding in massive bull periods.
However, in choppy markets, and over certain periods, it is quite possible for a given index or benchmark to be up while the leveraged version of the same index is down, sometimes substantially. Let’s use Biotechs as an example. This industry by itself hasn’t performed nearly as well as the S&P 500 over the last decade, but is still up about 23% cumulatively since the end of 2015. However, over the same time period, LABU, the 3x leveraged biotech fund, is actually down a whopping 97%, all due to the concept of drag we outlined earlier.
So, although stocks, on average, tend to go up over time, investing in leveraged funds such as these can often put investors at a tremendous disadvantage if not wisely considered. In order for a long-term investment in a leveraged fund to work over time, there must be a great enough upward drift in the underlying benchmark to offset the volatility drag.
Upward Drift (per day) = μ− (1/2)σ^2
Where:
- μ: The average daily return (mean return).
- σ^2: The daily variance of returns.
- The term (–1/2)σ^2: adjusts for the difference between geometric and arithmetic averages, which matters for compounded returns.
Volatility Drag (per day) = L^2×((σ^2)/2)
Where:
- L: Leverage factor (e.g., L=3 for a 3x ETF).
- σ^2: Daily variance of returns for the underlying.
The reason UPRO has increased so vastly over time is because the upward drift in the S&P 500 has more than offset the volatility drag caused by the leverage. But even though that has been the case, investors should apply the caveat “past performance is not indicative of future returns”.
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