A while back, I came across an interesting blog post. A guest writer on the White Coat Investor blog put forward an intriguing, almost too good to be true, money-making scheme. Unfortunately, it is too good to be true. It works neither in practice nor in theory. The more I looked into this subject, the more flaws I found with the analysis and I thought people might find it useful when I share my notes here.
It would have been so nice to announce here – with great fanfare – that, yes, there is a way to consistently beat the stock market. But it wasn’t meant to be. Oh, well, sometimes it’s just as insightful to understand why things don’t work!
The proposed strategy involves shorting an “inverse equity ETF.” An inverse equity ETF consistently short-sells an equity index (through index futures contracts), so it is a bearish instrument, normally held for short periods only. That’s because shorting an asset that tends to grow over the long term will consistently erode your investment, albeit you do see some short-term spikes upward during the major equity market drawdowns, which is, obviously, the whole idea of this exercise.
Shorting an inverse ETF will look a lot like investing in a regular equity ETF (shorting a short = double negative = positive equity exposure) but due to some purported inefficiencies in the inverse ETF, the writer claims, you can squeeze out higher returns than with a simple equity ETF.
Specifically, the writer on the WCI blog made the following sequence of claims:
- Inverse equity ETFs are costly; they charge a hefty expense ratio (many times more than that of a standard equity ETF). In addition, the ETF operator is forced to constantly rebalance the portfolio and the trading commissions cause additional drag. Shorting the ETF one can actually earn this drag as income. Sweet!
- Inverse equity ETFs are inefficient in that they suffer from what some people call “beta-slippage” which will, it is claimed, cause a constant additional drag on performance. Shorting an inverse ETF will pick this up as alpha.
- In light of points 1+2, it would be attractive to short-sell the inverse ETF to grab a constant and reliable stream of excess return (“alpha”) over a simple equity ETF.
In today’s post, I would like to debunk all three claims
- The drag from a high expense ratio is real. So is the cost of rebalancing inside the ETF. But this drag is not big enough to overcome the hassle of shorting an ETF, which involves two major headaches: higher marginal taxes on shorting profits and costs to borrow the shares to be shorted.
- The beta-slippage argument is completely wrong. Complete bogus! Both in theory and in practice. More on that below.
- In light of 1+2, i.e., in the absence of any exploitable alpha opportunity, it is likely not a good idea to short an inverse ETF.
The hassle of shorting an ETF
Folks over at this blog counted ten unpleasant side-effects to consider before shorting any stock (or ETF). I agree with all of them but among the ten I like to point out these two especially bad headaches:
- You cannot really sell an ETF that you don’t currently own. Rather, you have to borrow the ETF from someone who currently owns it. Your brokerage will charge you a fee for loaning you the ETF and this fee can be as low as 0.3% p.a. but can go as high as several percentage points per annum. The Proshares short S&P500 (Ticker: SH) fund has an expense ratio of 0.89% and depending on how much you pay in the “rental fee” for shares you want to short, a good portion or even the entire ETF management fee alpha could be wiped out.
- Regardless of your holding period, the short-sale profits are treated as short-term capital gains for the purpose of U.S. income taxes. Even if you shorted an ETF for more than a year! The IRS interprets the short sale transaction as if you had sold the asset on the same day (!) you bought the asset back to close the transaction. That’s about as short-term as it gets! Oh, well, here’s the solution: simply do the short transaction in a tax-deferred retirement account, right? Wrong! Shorting equities and ETFs is not allowed in retirement accounts. Any potential alpha is quickly wiped out by the disadvantageous tax treatment of shorting!
Beta-Slippage isn’t alpha
But what about beta-slippage? People throw around “techie” phrases like “beta-slippage” but I have the feeling that most folks have no clue what the phrase actually means. Case in point, the WCI blog post. The writer falsely claims that beta-slippage causes reliable excess returns when you short an inverse ETF.
The calculation often goes as follows: Imagine the index goes up by 10% the first day and then drops by 10% the second day (geez, what kind of index has that kind of volatility – but bear with me). Your equity ETF would have lost a total of 1%: (1+0.10)(1-0.10)-1=-0.01. It turns out that an inverse ETF would have also lost 1%: (1-0.10)(1+0.10)-1=-0.01. But since you shorted the ETF, your gain would have been +1%, a full 2 percentage points higher than holding a regular boring equity ETF.
Is that alpha? Unfortunately not. Here’s why. Bear with me because it takes seventh-grade algebra (or is it sixth-grade?) to show that this “beta-slippage=alpha” calculation is bogus. To keep things as simple and general as possible assume that on two consecutive trading days the underlying index can either go up or down by a rate of R. There are four different possibilities for return paths (up-up, up-down, down-up, down-down) and we can calculate the P&L of the different strategies: (1) equity ETF, (2) short inverse ETF, and (3) the excess return (alpha) of the short inverse ETF over the equity ETF (simply the difference between columns (2) and (1):
Of course, we know that shorting the inverse ETF outperforms if there is mean reversion (up-down or down-up), but the short inverse ETF underperforms if there is either positive momentum (up-up) or negative momentum (down-down). If we assume that the stock market follows a random walk, all four possibilities should be equally likely. Beta slippage works in your favor half the time and against you half the time for a net gain of exactly zero. Beta-slippage isn’t alpha, my friends! Unless, of course, you knew for sure that after an up day the market will mean revert again and go down (or vice versa). Though, if you knew that for sure why not just trade futures to bet on mean reversion? You don’t need to short an ETF to accomplish that.
What about asymmetric payoffs?
The WCI blog post and a few other folks talking about beta-slippage use a slightly different assumption than the +R/-R returns. Instead, they pick the market up and down movement so that the equity ETF returns to exactly zero after two days. For example +25% and -20%. Or +43% and -30% as in the WCI blog post. Now, I don’t know how anybody can assume that an equity index can go up and down that much on two consecutive days. But let’s still roll with this clearly unrealistic assumption, for the sake of academic curiosity. Specifically, let’s assume that the up move is a return of R1 and the down move is a return of -R2. Now we get the calculations in the table below:
It turns out that if R1 is different from R2 the short inverse ETF strategy still outperforms in the down-up and up-down scenario and underperforms in the down-down and up-up scenarios, but you can actually show that on average there is negative alpha. Ahh, the beauty of the binomial formulas. My middle school teacher would be proud of me now!
Another salient fact that comes out of this analysis: The mean-reversion alpha is not proportional to the equity volatility, but volatility-squared. If we work with daily return volatility of around 1% (instead of the unrealistic +43%/-30% returns), you are picking up beta-slippage “alphas” in the order of magnitude of 2 x 0.01^2=0.02%. Much less impressive than the sample calculations assuming +43%/30%!
Monte Carlo simulations
Ok, maybe the simple return pattern of +R/-R or +R1/-R2 is too trivial. How about a continuous return distribution? Glad you asked. Here, I simulated 100,000 draws of two-day returns with a 7% annualized mean return and 15% annualized risk (so daily mean return = 0.07/262, daily risk = 0.15/sqrt(0.15), assuming 262 trading days per year). Let’s plot the alpha of the short inverse ETF over the market return (i.e., the column labeled (3) in the tables above on the y-axis) as a function of the equity ETF return (=column labeled (1) in the tables above).
We get exactly the same picture as before: If the market return is close to zero over the two days, the beta-slippage causes what looks like excess returns for the short inverse ETF strategy. But for very large positive or very large negative returns you significantly underperform the equity ETF. We also found that beta-slippage, on average, is actually working against you. Very slightly: The short inverse ETF strategy underperforms the equity ETF by about 0.002% over the 2-day window (about 0.27% p.a.) over the 100,000 Monte Carlo draws. Beta-Slippage does not create alpha in theory!
Actual inverse ETF returns:
Let’s look at the short-SH ETF excess returns over the SPY ETF in practice. Unfortunately, there is a lot of noise and tracking error over two-day windows, so I look at the performance over 63 trading day windows (~3 months). As a function of the realized SPY total return (dividends reinvested), the short-SH strategy alpha has that exact same inverted parabola shape as above. You may generate some alpha if the market bounces around without clear direction, but if the SPY either performs very well or very poorly the short ETF underperforms. Quite significantly!
Also notice one crucial difference between the 2-day Monte Carlo simulation and reality: There are plenty of examples where the market finishes around 0% and the short ETF underperforms. That’s because of the 63-day windows.
The average 63-day window returns are listed in the table in the top-right. The short SH outperforms the SPY by around by 0.40% p.a. but notice that this is before trading costs, the borrowing fee and the nasty tax bill for the shorting profits. There is no alpha!
Just for completeness, I also include the 2-day window return stats table in the same chart. Over these short windows, you have a negative alpha of -0.80% p.a. even before the other fees and taxes. No alpha here either!
Actual inverse ETF returns: long-term returns
What if you were to short an inverse ETF over longer horizons and not just two or 63 days? Glad you asked! The Proshares ETF (ticker SH) has a 10-year history. Had you shorted $100 worth of SH you would have significantly underperformed the regular S&P500 equity index fund (e.g. the iShares SPY fund).
Why the underperformance in the long-term? Very simple: By shorting the inverse ETF, the maximum you can earn is +100% if the ETF goes to zero, while the regular equity ETF has infinite upside potential. And on the downside, it’s the other way around. With the short ETF you can have a loss greater than your principal (now we understand why shorting is not allowed in retirement accounts!), hence, the bigger drawdown in 2008/9!
And we say it here for the record again: The long-term underperformance of shorting the inverse ETF is because of beta-slippage. There is a limit of how much the inverse ETF can fall, so starting in around 2012, your short-SH will have less market exposure than the SPY (your beta literally slipped!) and you miss the full recovery of the equity market! Beta-slippage is an alpha-destroyer!
My confidence in the universal wisdom “if it’s on the internet it has to be true” has been fundamentally shaken. I am shocked. Shocked! Uhhmmm, just kidding: everybody should know by now that we don’t take anything at face value, especially if it’s on the web (prime example here). But I have to admit, before doing my own analysis, the short-inverse ETF strategy sounded like something that might have merit. But it doesn’t work, and here’s why:
- Beta slippage exists, but it can go in your favor (market mean-reverts) or against you (positive or negative momentum). In fact, if you short the inverse ETF, you will lag behind the market in the very long-term. Not despite but because (!) of beta-slippage.
- The proposed strategy of shorting an inverse ETF is a bet on mean-reversion in disguise. It’s a very good disguise because it took me some thinking to figure out what’s going on, but I’m sure most people talking about the “inefficiencies” of leveraged ETFs are completely oblivious to what they are actually doing.
- There is nothing wrong with mean-reversion. As a valuation kind-of-guy, I also believe in long-term mean reversion. I also believe that sometimes markets overreact in the short-term (especially on the downside, remember the Brexit?) and create buying opportunities. But this kind of mean-reversion strategy can be implemented much more easily: buy more equities on dips or get a futures trading account and trade S&P500 equity futures for microscopically (!) small trading costs and tax-advantaged treatment by the IRS. Personally, we also use a put option strategy that has a similar mean-reversion focus and payoff profile (and documented volatility premium). We don’t need a convoluted, contrived, tax-inefficient and opaque strategy messing around with the exotic ETFs to implement mean-reversion!
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