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Wow, I couldn't even get myself to finish reading this article. This is based on a very dangerous, ignorant understanding of how markets work. Whatever "advice" there is, please ignore it.
Could you expand a bit further on what you think the OP's misunderstanding of the market is?
One huge example is an assumption that portfolio returns are normally distributed. That’s not a minor nitpick, this invalidates every formula that goes after.
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OP does address this near the end of the post.
Well, you did say you didn't finish it. So would it surprise you to learn that topic is addressed directly?
Thats a fair assumption. But I did skim to the part that attempted to address non-normality—it doesn’t. Under non-normality, not a single formula in this post holds (“standard deviation” does not exist).
Hi, I wrote the post. I discussed the problem of non-normality in the post. Moreover, if non-normality is the problem, then pretty much all of modern finance is invalidated. Instead of saying its all bullshit, a better approach is to realize the assumptions of the model and use some discretion in trading based on its output.
> Moreover, if non-normality is the problem, then pretty much all of modern finance is invalidated.

I’d say, finance from the 70s is invalidated. And it has been invalidated countless times with all the major mutual funds going bust.

I’d love to encourage you to read more on this topic. Taleb’s “The Black Swan” is a good start, his other books are also good.

Black Scholes, VaR, factor models, CAPM, modern portfolio theory, etc are all based on the normal distribution and are all still used in industry today. Every quant fund in the world is using models that assume a log normal distribution of returns. Moreover, Taleb certainly used models based on log normal distributions at his hedge funds.
I wrote the article and I'm not offering advice, I'm delving into the mathematical implications of leverage on portfolio returns and volatility. I think you're deliberately being dismissive and rude without really offering any advice or constructive criticism. Moreover, I don't believe you actually understood the post, which isn't surprising, as you weren't even willing to read it.
I am sorry for being rude and dismissive.

My goal was not to hurt you (you are obviously learning, and I respect you for that), but to warn others who might think these ideas are reasonable and lose money as a result.

“ This strategy also greatly reduces the risk of ruin, as the S&P 500 would need to lose at least 1/3 of its total value in a single day for the fund to be wiped out. Though certainly imaginable, this event is unlikely as the biggest single day loss in the history of the S&P 500 was Black Monday in 1987, in which around 20% of value evaporated from the S&P 500 in a single day.”

That didn’t age well (article is from last October)

How? The recent losses were nothing compared to Black Monday, especially after a massive 2019.
It dropped 12% on one day in March, not as big as the 20% on Black Monday but not "nothing". And the bull market of 2019 isn't really relevant when the article focuses on ETFs that leverage single-day moves.
It's almost impossible to happen, there are three circuit breakers, 7, 13, and 20%. After 20% the market closes for the rest of the day. I think it's only possible if the 20-33% drop happens at the very end of trading where the circuit breaker no longer can occur for the day.
Existing leveraged ETFs are a scam, designed only to fleece "muppets" (as a Goldman Sachs guy once called us).

Here's a real life example. You can buy a financial instrument that purports to hold gold bars on your behalf. Its symbol is GLD. In the past year GLD price has moved from roughly $123 to $153, more or less equal to the price change in 0.1 oz of gold.

But that movement isn't enough for some people. They want leverage. So two leveraged instruments were invented. Cleverly named NUGT and DUST. Purported to achieve 2x moves in Bullish and Bearish gold directions, respectively.

But let's look at NUGT price from 1 year ago to now. $20.75 -> $7.72.

DUST is even worse. $17.33 -> $2.56.

A lot of this under-performance is because of the friction involved in leveraged ETFs borrowing and using futures. (This has been explained in great detail by others, I won't attempt it).

Summary: GLD (the commodity) 24% gain, NUGT 63% loss, DUST 85% loss.

Yes yes, the purveyors of NUGT and DUST will tell you that they're not meant to be held for 1 year. They're for very short term. But they're just trying to mislead you. The fact that both directions lost so much money means that these products do nothing but scam muppets.

The SEC should never have allowed ETFs like that.

Hi, I wrote the post. I'm wondering exactly what your issue is with leveraged ETFs? What, mathematically, makes them unsound? I think my post covers the risks and benefits of them while also proposing a new kind of leveraged ETF that might help mitigate the volatility drag associated with leverage.

Edit: I'm not familiar with the leveraged gold ETFs you mention, but I am familiar with UGLD, which tracks the 3x daily return of gold. Comparing UGLD vs GLD:

https://www.google.com/search?client=firefox-b-1-d&tbm=fin&s...

UGLD is up compared to GLD. Moreover, UGLD is correctly tracking the 3x daily move of GLD.

Also, the use of futures and leverage aren't really related. Sure, that's how most leveraged ETFs work, but there's no reason why there couldn't be a leveraged ETF that simply borrowed the money.

Edit2: both DUST and NUGT are based on the Gold Miners Index, which isn't the same as GLD (which tracks actual gold).

My issue with leveraged ETFs is, quite simply, the 30,000 foot view of results: They suck.

Even though NUGT and DUST are from the same fund company and purport to do the opposite of each other, they both lost substantial amounts of muppet money over the last year!!!

You're trying to analyze these things mathematically, I'm just saying "look at the actual results over a years time".

I suspect (without checking in detail) that UGLD is doing better is because it's an ETN and not an ETF. Usually an ETN is a debt obligation of a financial counter-party, in this case Credit Suisse.

How Credit Suisse manages their debt agreement (the ETN) is up to them. These can be black boxes to the outside world. It's possible that CS is buying or selling physical gold or gold futures to hedge their exposure, but they don't have to be. It's simply a financial contract.

Right now CS is a good financial risk. But the same might have been said about Lehman Brothers before the great recession. They were counter-parties to some ETNs and people who owned those were screwed when Lehman went bust: https://www.etf.com/sections/features-and-news/lehman-bros-e...

I agree with you that a leveraged ETF they can simply borrow money to increase leverage. (Not much different from how leveraged hedge funds operate). But for some reason they don't operate that way. So it must be somehow advantageous for them to use futures. Maybe because it's difficult to "short" something like e.g. WTI crude in a standardized way on an exchange? You can be long or short a futures contract for gold or WTI, that's a liquid market. But shorting the physical commodity might be harder?

The leveraged ETFs have a few extra footguns, don't they? Did you see that Direxion suddenly changed the ratios on a bunch of 3x down to 2x on March 31? Scary stuff to me.

https://www.marketwatch.com/story/direxion-is-accelerating-t...

In 2009 a leveraged ETF trading at $100 ended up paying about $85 as a dividend (I think because it was excess profit by being long vol.) That would be an overnight tax hit if you are in the wrong type of account. I don't recall which one it was, maybe FAZ?

The SEC should just not call them ETFs.
NUGT, DUST, JNUG, JDST are not based on the gold, but on the gold miners. NUGT/DUST & JNUG/JDST are based on GDX and GDXJ respectively.

Usually gold miners (GDX/GDXJ) lag behind gold prices. Many in the market know that gold price is range bound. That's why you can't expect similar moves across GLD and GDX/GDXJ.

Leveraged ETFs are bad if the underlying is more volatile. Gold miners are more volatile than biotech(say, IBB), which is more volatile than SPY, QQQ.

Go for leveraged bull ETFs on the less volatile underlying, and in the bull market: TQQQ, UPRO, etc. If one wants to capture some short term gains, go for LABU (3x IBB).

Leveraged instruments are path dependent. If the underlying ETF is choppy, you are not going to make any money--be it leveraged bull/bearish ETF. An example of choppy/sideway moves in week: 0.5%, -0.45%, +1.2%, -1.3%, 0.25%. In such a market, just stay away from leveraged ETFs.

If one wants to capture some short term gains, go for LABU (3x IBB).

A perfect example of the fleecing of the muppets I'm talking about. IBB one year performance is $114 -> $106. In the same timeframe LABU $65 -> $20.

How does the SEC allow that? It's fucking disgusting.

The only way to "win" with ETFs like that is to short them, short them, and short them again.

Edit: sorry. Didn't emphasize the obvious, real, way to "win" with ETFs like that. You create them and sell them to muppets. Billy Ray figured this out pretty quickly in Trading Places:

Mortimer Duke: Tell him the good part.

Randolph Duke: The good part, William, is that, no matter whether our clients make money or lose money, Duke & Duke get the commissions.

Mortimer Duke: Well? What do you think, Valentine?

Billy Ray: Sounds to me like you guys a couple of bookies.

Randolph Duke: [chuckling, patting Billy Ray on the back] I told you he'd understand.

I mean, look at UPRO (3x levered bull S&P 500 ETF). From inception (2009) to date it's returned 1000% compared to the S&P 500's 170%. And from inception to Feb it's returned 3300%. I've personally held UPRO from 2014 until late January and have made a truckload of money off of it. I then made a truckload more money buying VIX futures before the VIX spiked to over 80. People say that you shouldn't hold these things long-term, but that's simply not true. All you're doing with leverage is increasing your beta. Obtaining 2x leverage on the S&P 500 is going to look pretty much the same as buying stocks in the S&P 500 with a beta of 2. Yet no one complains about high beta stocks being a scam.

You're telling me you would short UPRO? If you shorted UPRO pretty much anytime between 2009 and the beginning of 2020, you would have lost either all of your money, or in the best case, most of your money.

Excellent market strategy and timing!

I wouldn't short any chart that moves from the lower left -> upper right. The ones I mentioned previously do the opposite. Their chart goes from the upper left -> lower right.

Still, timing is so important. If you had gone long UPRO on Feb 18, you would have seen $80 -> $24 in about 6 weeks. Losing 70% of your money would be a little unsettling.

You're obviously one of the "big boys". Most people don't dare play in VIX futures, because of the intrinsic high leverage and because of the high volatility. Wouldn't it be less risky to trade VIX options instead? I don't follow either closely, I'm genuinely asking.

Yeah, totally, you can really lose your lunch with VIX futures (both going long or short). It's a dangerous game, I wouldn't really recommend it to anyone. I manage a small/moderate amount of money for friends and family as well as myself (in a different account), and the kind of plays I do for them are very different than what I do for myself (if I lost all of my money I would be fine, it I lost all of their money I don't think I'd be able to live with myself). While I do use leverage in my family and friends fund, it's never above 1.5x, while with my own money I usually run between 2.5-3.25x.

I myself don't touch options because I feel like I don't have a good academic grasp of them. I work in portfolio analytics for equities and futures, so those are pretty much the only things I hold in both my family and friends fund (actually in that fund it's just ETFs) and my own personal fund. Would options have been the better risk/reward play? Probably/maybe, but it's never a good idea to invest in things you don't have a complete understanding of.

The ultimate point I'm making about leveraged ETFs I guess is that people have different risk tolerances. Just accepting whatever the market gives you rarely makes sense as the return to vol ratio is probably either higher or lower than your personal risk tolerance. My risk tolerance is very high, so I invest in ways that align with it, yours might be low, so likewise, invest accordingly. But don't just take whatever the market throws at you.

This. I was going to write a comment but you nailed every point. These are not "leveraged" ETFs in any sense of the word. These are vehicles designed by savvy bank trading desks to drain noobs of their money. One way to think of them is casino bets with very high carry costs. Hold them long enough and you will give back gains and most of your capital to the house.

I admire the article writer's effort but he seems to lack a working understanding of leveraged ETFs and how they are constructed.

> Hold them long enough and you will give back gains and most of your capital to the house.

How, why? Everyone says this (which is why I wrote my post), but no one has actually explained it to me. A leveraged SPY ETF does not have a high carry cost. Sure, if there's an ETF that's buying long-dated contango futures, then yeah, you're going to lose money in most environments (TVIX, etc). But leveraged equity ETFs do not have this property. Moreover, if you really think that most of your money is going to go to the house with any of these products, surely you should just be able to short all of them and make a risk-free profit, right?

I know I have learned a ton from HN comments. They are a goldmine of information and people willing to explain and mostly engage in educational respectful discourse.

I don't think anyone here will have a problem explaining the mechanics to you if you politely asked or were open to it. Your tone comes off as extremely aggressive and defensive to boot. Statements like - "what exactly is your problem" does not engender mutually beneficial back and forth.

It takes time to craft a correct and well-researched response. It is not incumbent on me to correct your misunderstandings. I might consider volunteering my time if you presented a minimal facade of civility and gratitude.

You have shown none of these.

Leveraged ETFs are not leveraged in the traditional since as one might expect. The article misses this point and the author should rectify and clarify immediately.

Leveraged ETFs promise the daily return. They are reset every single day. So your return over N days is completely path dependent.

Even a positive return of the benchmark may result in a negative return in a leveraged ETF if that path was volatile...

Leveraged ETFs are trading tools. Do not hold them in your portfolio for more than a few days.

Whoever buys leveraged ETFs should know that "leverage" is not used in the traditional sense. I don't see nothing wrong with the author's usage of leverage.
"These ETFs simply aim to match the relative daily returns of their respective index and occupy the bottom left spot on the aforementioned two dimensional spectrum. A closely related (albeit far less popular) type of product that occupies the bottom middle is the leveraged ETF. A leveraged ETF seeks to obtain a daily exposure on an underlying index scaled by a constant l; which, at this time, is somewhere between -3 and 3 for products currently on the market. If l is less than zero, the ETF provides short exposure to the index and are often called "bear" ETFs; conversely, if l is greater than zero, the ETF provides long exposure to the index, commonly referred to as "bull" ETFs. These securities are usually implemented by means of a rolling futures strategy."

"At face value, a retail investor might assume that if the S&P 500 returned 10% in a given year, a 3x leveraged ETF would return 30%. Fortunately or unfortunately depending on your perspective, this is not the case as the ETF seeks to maintain a 3x multiple on the daily return of the S&P 500 instead of the annualized return."

The post is about how the conventional wisdom behind these ETFs as "trading tools" is simply not true. All these ETFs do is to increase your beta exposure, in much the same way that buying high beta stocks increase your beta exposure. Practically speaking, there's little difference between a portfolio of stocks with an average beta of 2 and a 2x levered S&P 500 ETF. The risks are the same. Yet, no one goes around calling AMD (which has a beta of 2.83) a single day "trading tool." In fact, holding AMD is way riskier than holding a 3x S&P 500 ETF!

Just curious, what does it mean to say that they are reset everyday?
You have to return the leverage at the end of the work day. Meaning the shares have to be sold at the end of the day and then brought again the following morning.

Meaning you are getting 3x the increase from the start of the work day until the end of the work day but also 3x the potential loss.

The problem is that you are exposed to volatility and cannot just ride out a storm. This is a day trading feature and not something for the long term investor.

If you have a crystal ball and know that you'll have more up days than down days, then you are good. Otherwise it is akin to speculating rather than investing.

They are probably good for a late stage boom cycle (if you could time the bust).

(Based on the Leveraged ETF's I have found)

Three questions:

What is the cost of the leverage and how does that affect returns

What is the friction cost of all the trades needed?

Where is part 2?