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!

### Conclusions

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!

**Disclaimers:** We have no affiliate relationship with the ETF providers mentioned here. We own the SPY ETF in our personal portfolio. Please check out our general disclaimer page, too.

Great post ERN! Hefty fees drag, tracking error, liquidity gaps, poor bid-ask spreads and what not. These inverse ETF shorts are essentially derivatives that I would stay far away from. You have quantitatively proven what I intuitively felt long back. Thanks for doing this analysis.

Thanks, TFR! Trying to debunk one myth at a time. One down, thousands more to go! 🙂

Cheers,

ERN

Woo! Up-down-up-down-B-A-B-A-select-start!

I had to get out the graph paper and slide rule for this one, ERN! Reedonkulous.

So, you know this area’s way more your province of expertise than mine, and I hadn’t even heard of this shorting inverse ETF thing. (One big-time upside to being lazy and boring with investing is to miss out on stuff like this.) But I’ve gotta say that, even in my elementary approach to financial markets (pretty sure I’m using something like third-grade math), I’ve found it’s purdy durn’d hard to find persistent pricing mistakes that can pay on a retail investor’s scale. And my intuition is that anything dealing with “mispricing” in ETFs (‘specially these days) is super-tough to do.

Thank you for the rigorous proof here. Amazing work.

Now, I dig your approach to the whole put option strategy. A smart way to augment returns, fo sho. But, as you fairly point out, that ain’t no free ride either.

If only we could be assured that, over the long-run, equities always would increase in value and pay divvies, this whole investing thing would be so easy! 🙂

Great stuff, as per usual, and many thanks for totally ruining one of my nice pieces of graph paper.

Also: Is your specialty time-series econometrics? I came across something the other day I’ve been thinking about but it’s got some weirdness in it that’s over my cabesa. I need to think about it some more but I might have a question or two if you’d be up for it. (It has nothing to do with investing or financial markets.) No worries either way.

Many, many thanks! You took that request (“lots of compliments, please”) to heart! Thanks as always for the thoughtful comments.

I did my thesis in grad school on something mostly theoretical, but there is only so much mileage you can get in theoretical macroeconomics, so over time I have shifted more and more into econometrics. So, at my current job I do a lot of that. If you like, send your questions over and I will see what I can do: ernretirenow [at] gmail [dor] com

Cheers!

ERN

A well written and thorough analysis on inverse ETFs. As the author of the guest post on WCI that he eludes to I think it should be mentioned that the beta-slippage and true value in shorting inverse ETFs comes when you are shorting those that are leveraged. The example above is SH and, although we have not anticipated shorting this fund for our clients, this confirms that would be a poor use of capital. We are more interested in shorting leveraged funds (QID, SDS, TWM etc.) and exploiting the inefficiencies in these derivative products. This part of our strategy has been very effective over the last 2.5 years. It would be interesting to see if the same conclusions are drawn in regards to these inverse leveraged ETFs.

Thank you, Chase, for taking the time to respond. We also had an interesting and constructive email exchange already. Quite a bit to digest, but I will write a detailed response to the issues you raised, both here and in your emails.

So much upfront: I believe that the degree of leverage, whether -1x or -2x or -3x does not change the rationale against shorting the inverse ETFs.

Cheers!

ERN

Here some additional thoughts on the issues you raised:

A: If you implement this strategy with less than daily rebalancing, i.e., you use the beta-drift over time:

I call it drift, not slippage, because the beta exposure can increase or decrease over time. Whether you use 1x or 2x or 3x inverse ETFs, it doesn’t change much in the calculations in the tables above. For example, if you split your portfolio into two halves, one shorts the 3x bullish ETF, one shorts the 3x bearish ETF, then the payoffs in the simple +R/-R example above are -9R^2, +9R^2, +9R^2, -9R^2. So, everything is scaled up by a factor of 4.5. Why not 9-times (=3^2)? That’s because in the original example I had a weight of 1x on the short 1x ETF and merely calculated the alpha via-a-vis the equity ETF. In the pair trade you use only half the portfolio for each ETF. Needless to say, in the 2x leverage pair trade the multipliers would be 4 instead of 9.

Result so far: in theory the pair trade with leveraged ETF suffers the same flaw of zero alpha. You make a lot of alpha if there is fast mean reversion, you lose a lot of money if there’s momentum (positive or negative). Unless you have more information than everybody else about where the market goes the next day you should make zero profit on average, negative profit after taking into account all the trading and shorting cost.

In practice, I don’t see much alpha either. You say that you shorted the SDS over the last 2.5 years (no rebalancing). With the values I got from Yahoo Finance, the SPY gained 21.7% between 3/31/2014 and 9/30/2014. The short SDS gained 42.2% over that period, and that is before trading costs and shorting costs which can be substantial (mid to high single digit % p.a. I heard). No alpha here. By the way, what are your shorting costs on an annual basis?

Philosophically, I have trouble to grasp how the beta-drift between rebalancing dates can cause sustainable alpha over time because the active weights are purely a function of past returns. No forward-looking information is used.

But let’s assume that someone is convinced that this simple beta-drift creates alpha. Then why not implement it through futures? They are cheap to trade, tax efficient, and because the cumulative beta drift isn’t very large over shorter periods, the absolute weights on your futures positions are small. You use only a small portion of your cash for margin and can use the remainder of your margin cushion to get some bond yield. Much easier than playing with these illiquid and expensive to short exotic ETFs.

B: If you rebalance this daily:

Whole different story! None of the beta-slippage arguments work any more. Or your initial +43/-30% nor my beta-drift calculations.

This brings us to the paper you mentioned in the email, written by some folks in the Math department at NYU. Thanks for sharing! I looked at the paper and found some pretty bad flaws, both conceptually and shoddy data work.

I will probably write up a more detailed response and post it on SeekingAlpha.com because it’s too technical for the blog here. But I’m not sure when I have time for that. Maybe over the Thanksgiving break.

Cheers,

ERN

Thanks for the interesting post.

My thoughts:

– Some of the disadvantages disappear if shorting is replaced by deep in the money puts.

– The taxes can be reduced within a hedge fund.

Thanks!

I agree that in many instances shorting should be replaced with just a put option. Much cheaper! But in this case I’d be afraid that’s throwing out the baby with the bath water. First, I showed that the beta-slippage cannot generate alpha if the market follows a random walk. The only alpha left comes from shorting the large expense ratio of the ETF. But I would think that this negative carry would already be priced into the put option value. Right?

Also, I’m not sure how a hedge fund would avoid the tax issue. Hedge funds are normally set up as an LLC or LP and they are both pass-through entities that have no ability to hide or defer taxable events. You get a K-1 statement with a lot of short-term capital gains if you implement this through a hedge fund. Or am I missing something?

Cheers!

Ran across his post and thought I’d add my two cents. A bet on mean reversion/beta slippage only pays out alpha in times of volatility so essentially you’re betting on volatility. So why not short SVXY or UVXY leveraged vix ETP’s? Well as the most recent uptick in volatility showed. If you shorted SVXY shares you made a ~97% return, pretty good. BUT if you just shorted SVXY betting on volatility with put options you made a return of 6,600%!! Indeed, some hedge funds out there booked returns of +8,000% by shorting the leveraged SVXY product but they didn’t do so through the shares

I like that idea. There might be the problem that the “rental fee” for the shorts is too expensive. But you might be able to this with put options if they have those for the ETPs.

Your logic is at least (and probably more) as flawed as the original premise! In computing the average returns, you conveniently assume that four scenarios (UP, UP) (UP, DOWN),(Down, UP) and (DOWN,DOWN) are equally likely. They never are. Especially for ETFs for market indexes (NASDAQ, DOW), (UP,UP) is far more likely than other three scenarios (since markets moves over time). Further, examples do not prove anything; they only illustrate what YOU want to illustrate under YOUR assumptions (e.g. your assumption of equal but opposite change over two days). Give a proper justification; do not just play with numbers.

Not withstanding the original claim, you have not not proven otherwise.

At least as flawed? The rationale for shorting these ETFs relies on up/down and down/up being the only options. I believe that 25/25/25/25 is probably a better description for reality than 50/50/0/0 for the probabilities of UD/DU/DD/UU.

But you raise a valid point: Since the market goes up with a probability of slightly more than 50%, the 25/25/25/25 assumption is not 100% accurate. But a) it’s better than the 50/50/0/0 assumption and b) the whole math I presented here works the same way even when you assume the market goes up with, say, 52% probability.

Lesson learned here: Before leaving a vacuous comment like that, you should try to understand the math and the assumptions behind my post!