Fin Stuff

Understanding NOPE

2021-02-25T00:00:00+00:00

This post aims to provide a working understanding of what NOPE is and the theory behind it. I will cover:

Who is on the other side of your option trades
How they avoid being stuck holding the opposite position to yours
What this does to the market
What NOPE is measuring and how it does it

Prerequisites

This post is aimed at someone with a beginner-to-intermediate understanding of options trading. Specifically, I assume you already know:

What options are
What the order book is
A basic understanding of the options greeks
That the Black-Scholes formula exists and that it’s used to price options using the greeks. (But don’t need to know it or be able to derive it!)

If you don’t know these things, the good news is that there are many resources online that can teach you, right on the other side of your favourite search engine :)

I also assume you know who Lily is and have heard about this NOPE thing. Otherwise how did you even get here?

With that out of the way: let’s get started.

What happens when I make a trade?

It is natural to assume that when you make a trade, you are making a bet with someone else who wants to take the opposite position. For instance, if you’re buying a call, you’re buying it from someone who thinks you’re wrong, and thinks the security will go down.

This is, in general, completely incorrect.

The vast majority of the time you are actually interacting with a market maker. Per Investopedia:

A market maker (MM) is a firm or individual who actively quotes two-sided markets in a security, providing bids and offers (known as asks) along with the market size of each.

MMs place both bids and asks on the order book. Their goal is to make money from the difference between those two prices (known as the spread) - buy from people who want to sell now, sell to people who want to buy now, keep the change. That “keep the change” is the business model of a market maker - they have no interest in holding either long or short positions, so they need to get rid of any positions (or otherwise neutralize them) ASAP. Holding a position introduces a ton of risk that they don’t want.

In the case of trading stocks, there is typically enough volume that the amount of time they’re actually holding a security - between buying it from you and flogging it to someone else - is small, so the whole thing works nicely. Impatient people get to make their trades, the spread is narrowed, they pocket some change - everybody wins. This function is so important that exchanges approve designated market makers who are contractually obliged to place both bid and ask orders, in return for a commission fee.

However.

The “buy it and flog it to someone else quickly” approach does not work for options. The demand is just not there. Think of an options chain: a zillion dates, and a zillion strikes for each date, multiplied by two (for puts and calls). The daily volume for the most popular single option is less than the minutely volume for its underlying!

While a market maker will be very glad to sell the other side of your trades to anyone else who comes along, they have to be able to do something else in the meantime, because being forced to take positions (that you didn’t even choose!) is, um, terrible for your portfolio and not anywhere in your business model! That something else is called hedging, and it’s the core behaviour that NOPE watches.

I will note for the sake of any pedants reading that MMs are not the only people who hedge option trades; plenty of other institutions do it too, and for all sorts of reasons. Who is doing the hedging doesn’t matter; the how does. I will continue to say “market makers” in this piece, because saying “market makers and hedge funds and other institutions” every time is clumsy, I find it helpful to imagine a particular someone, and that someone may just as well be a market maker.

How do MMs avoid being stuck with the other side of my option trades?

Let’s say you are a market maker, and you just sold me 100 at-the-money SPY calls. You did this because you were contractually obliged to - you had no choice in the matter. At the moment I buy the calls from you, this is fine, because the options were priced fairly. By fairly we mean “we both value the calls to be worth the money I paid”, i.e. the cost of the premium I paid perfectly matches the risk that you’re taking. You could - assuming you found a buyer - pay someone the money I just gave you to take on your obligation, and they would choose the same price.

But of course the value of one SPY share (aka its spot price) is going to change, which means the value of the option is going to change. You’ll remember the value of an option changes by delta for every $1 the underlying moves deeper in-the-money.

In our example we said that the calls were at-the-money, so let’s say their delta is 0.52. This means that if the price of SPY goes up by $1, the price of the option will increase by $0.52. Multiply that by the 100 calls I bought, and in order to get rid of them you would now have to pay someone an extra $52, plus the money I originally paid you. Thus your portfolio is effectively worth $52 less.

As a market maker, you want the total value of the securities you’re holding to be “net zero” at all times, because guessing which way the market is going isn’t your business model. So you need to offset this risk in such a way that if the price of SPY goes up $1, your portfolio somehow gains the $52 in value that it’ll lose from the calls you sold me.

Well, that’s easy: buy 52 SPY shares!

That way, if the price moves up $1, your 52 shares gain a dollar each, exactly offsetting the loss in value of the options you sold me. If the price moves down $1, the opposite happens, and you’re still good. If the price doesn’t move: even better! Perfect!

This is it. This is the key insight; if you can wrap your head around this, everything else will follow. It’s so important I’m going to write it again in bold.

Important Thing #1: MMs respond to option sales by taking positions in the underlying.

They do this as part of their effort to “net zero” their portfolio and insulate themselves from the risk of price movements. Doing things to protect yourself from risk is called hedging.

Um, the price isn’t going to move just once, though…

Right. You hedged the initial options, the underlying (spot) price moved, your hedge worked, but now you’re back to where you started - exposed to the risk of the price moving again. And because the option is further in-the-money now, delta is a little bigger, say 0.54. So if the spot price of SPY moves up $1, the total price adjustment for the calls you sent me would be $54.

Thankfully you already have the 52 shares, so if the price of SPY goes up $1, they’ll earn $52. So you’d only be $2 short of the $54 you’d lose, and can solve that by buying two more shares.

This corresponds to the 0.02 difference in delta between your last position and your current one. By buying those two extra shares, your delta is now back to “even” - we call this being delta neutral. Not surprisingly, the process of hedging your delta risk is called delta hedging.

And so you keep adjusting as delta fluctuates. If the spot price goes back down a dollar, you sell off those two shares. You do this repeatedly, as the spot price moves, in order to maintain your delta neutral position.

Important Thing #2: MMs holding option positions make predictable trades in the underlying as spot price changes.

This is interesting: by trading options, you force MMs to take certain positions in the underlying and force them to keep adjusting those positions in predictable ways until option expiry. How often do they re-hedge? We don’t know. But it’s a good question, and we’ll come back to it in a bit. For now, let’s take a step back, because we’ve learned a lot already.

What does this mean for the market?

Let’s write this all out explicitly:

Buying a call from a MM forces them to buy “delta” number of shares, and buy more as price goes up.
Selling a call to a MM forces them to sell (short) delta shares, and sell more as price goes up.
Buying a put from a MM forces them to sell (short) delta shares, and sell more as price goes down.
Selling a put to a MM forces them to buy delta shares, and buy more as price goes down.

The easy way to think about this is that in order to neutralize the other side of your option position, the MM replicates your option position, just using shares. If you profit if the price increases, they buy; if you profit if the price decreases, they sell.

There’s something important hiding in this list. Look at the impact of the MM hedges in each situation. In some cases, the MM hedge moves against the price action, providing a stabilizing effect. In other cases, the MM hedge moves with the price action. Notice anything?

Important Thing #3: Selling options to MMs stabilizes price action. Buying options from MMs amplifies price action.

Hmm. So that means the aggregate balance between option buying and option selling is important. If they’re in balance, the market moves normally. If option selling dominates, price movements are dampened, unable to move as much as they might otherwise. And if option buying dominates…

Uh oh.

Yeah. If more people are buying options than selling them, then MM hedging amplifies price moves.

So, is this happening? Can we tell?

The open interest for an option is the number of option contracts outstanding at each price. But that doesn’t tell you whether the non-MM side of the transaction bought or sold. For that you have to watch the trades as they happen - or just buy the historical data.

Of course, someone did that, so we know the answer:

Important Thing #4: Option buying outweighs option selling.

Which makes total sense from the perspective of any individual: buying options has limited downside risk, selling them has unlimited risk. Easy choice.

In Lily-speak, we are now in an options degenerate market (part 1, part 2). That is to say, a significant factor in price action is not how people value the asset but the forced moves that MMs make to hedge option trades.

What NOPE is measuring and how it does it

Let’s recap: we know option buying outweighs option selling, which means that price movements are amplified by MM hedging.

Hold on though. A while back we asked how often MMs hedge price movements, and we said we didn’t know. But we can watch the option trades as they happen. So for each one, we can calculate the required hedge in the underlying, and then expect to see that trade come through. If we watch all option trades on all strikes on all expirations, we can build up a picture of “how much the price has been shifted because of MM hedging”.

This is what NOPE is doing. In brief, the NOPE calculation is:

Add up the deltas of all calls across all strikes across all expirations, weighted by volume; call it all-call-deltas
Add up the deltas of all puts across all strikes across expirations, weighted by volume; call it all-put-deltas
NOPE = (all-call-deltas - all-put-deltas) / total-shares-traded

A rising NOPE implies more calls have been sold and thus that the price has been artificially bid up past its usual by MM hedging. (Option buying increases the numerator, MM share buying increases the denominator by the same absolute amount.) The price may have been pushed out of balance - away from its “correct” level, if you like - and could move back down as people sell the underlying shares for a profit. Those share sales increase the denominator without affecting the numerator, and NOPE reverts.

You’ll notice this isn’t perfect. In particular, it’s not paying any attention to the ratio of buys to sells for each option; the calculation assumes that all options traded are buys and none are sells. Given that we know that there are more buys than sells this means that NOPE will give us some signal but it won’t have the fidelity it could if you kept up with every single trade.

It’s also a unitless indicator. This means it’s not measuring an amount of anything: it’s just a floaty number. The number varies wildly for each security (though it is always centred around zero) and it takes some experience to learn each security’s normal range. There was a brief attempt to build an indicator that normalized the values to a moving average standard deviation, called NOPE_MAD, but it got shelved in favour of other projects.

Important Thing #5: Lily already knows NOPE isn’t perfect. You don’t need to tell her.

Lily has had people approach her making this point (and other criticisms of NOPE) countless, innumerable times. She has explicitly said “the nope calculation is shit”. She recognizes it is a very handwavey approximation. If you want to write a better implementation, go for it! Just… don’t bug her about it, okay? Just… be cool.

That’s it. You did it!

Congratulations - you made it! We’ve covered a lot: the existence of market makers, how they hedge the risk of options trades, what this means for the market, and how NOPE watches options to guess at upcoming MM hedges. You now have a decent understanding of how NOPE works!

In the next post, we’ll take a deeper look into how the behaviour of market makers can make things worse when markets go screwy. Stay tuned!

References

Sources I used to wrap my head around this:

Want to trade NOPE?

NOPEChart - buy the premium version, it’s worth the money
Hole Corporation video on how to use NOPE

Thanks

Proofreaders:

@tilmonedwards
@hunterspecs (author of The NOPE Brain Worm, linked above)

Analyzing GME fails-to-deliver to look for illegal naked short selling

2021-02-01T00:00:00+00:00

Like a lot of people I read this interesting comment on Reddit. I stayed up until 2am watching all the videos and it got me pretty worked up.

If you haven’t seen the videos, a brief summary follows. (I am not at all a finance person and am just repeating my understanding, so I might be completely or subtly wrong here.) When you short a stock, you do the following:

Borrow a stock from someone (for the cost of ongoing interest);
Sell it to someone else (at full cost);
Wait for the share price to go down, then buy it back and return it to the person in #1;
Congrats, the difference is your profit.

The system contains a little bit of wiggle room in step 2, where you sell the borrowed share. The money the buyer gives you settles immediately, but you have a few days to deliver the share. This is reasonable, because the share might be in a bank vault or the back of a closet or something. To keep things running smoothly, in this situation you write a notional “IOU 1 real stock”, and that goes to the buyer’s broker. This IOU is treated “as good as” one stock, because the expectation is you’ll make good on the IOU. Once you’ve yanked the share out of the closet, you swap it for the IOU and all is well. You have two days after the trade date to do this.

If you are a Bad Hedge Fund willing to do some crimes, you can take advantage of this by simply writing the IOUs without ever having found and borrowed the stock from someone. You can write as many IOUs as you like, and since everyone assumes they’re equivalent to a real share, you’re essentially inflating the supply of shares beyond those that actually exist. This is extremely illegal and is called naked short selling (because you have no real stock to “cover” yourself with). It is also sometimes called counterfeiting.

If you take longer than two days after the trade date to settle the IOU, this is known as a “failure to deliver”. Twice a month, the SEC publishes the number of outstanding fails-to-deliver shares for any security with more than 10,000 outstanding fails-to-deliver shares.

The theory behind the videos linked above is that a campaign of aggressive naked shorting led to the collapse of Lehman Brothers in 2008. The video shows a significant and sustained uptick in fails-to-deliver shares of Lehman right around the time the price tanked, which is what you would expect to see if a shady hedge fund took a short position and decided to counterfeit shares to artificially depress the price. If you like 90 minute PowerPoint lectures with dense financial data the videos are a good watch and have more information; I have summarized what’s relevant for this post.

Since there have been some rumors swirling that GME short sellers were doing so illegally as part of a campaign to manipulate the price, I decided to pull the FTD data from SEC and take a look at GME. Below is a graph which shows the aggregate number of FTD shares over time, and also the price of GME. As of today, the SEC has released data up to January 14th and no further.

Analysis is further complicated by the fact that the SEC reports only the total number of FTD shares; if a day’s FTD shares count is 1000, you can’t tell the difference between “all 1000 shares were outstanding yesterday too” and “all of yesterday’s FTD shares were settled and these are fresh new ones”.

That said, here’s the graph:

A graph of the SEC's FTD reports for GME vs price.

I will not analyze this for you but I will leave some comments and observations.

It does not appear that there was a severe and sustained uptick on outstanding FTD shares. Even where there are periods of sustained volume, they do clear back to zero; that is to say, the shares seem to eventually be delivered.
The mere existence of FTD shares is not evidence of any illegal activity. As mentioned before, some degree of FTD is a normal part of yanking-shares-out-of-the-closet and is fine.

There is one more wrinkle here. My understanding is that the SEC only reports FTDs for trades that were settled in the National Securities Clearing Corporation (aka NSCC). This is most but not all trades, as it’s possible for brokers to settle trades between themselves directly; this trades are said to settle “ex-clearing”. I have no idea how many trades are settled ex-clearing and have no FTD data on them. One could make the argument that there are four quadrillion counterfeit shares that have entered the system through ex-clearing, or one could make the argument that there are zero, and there would be no way of telling either.

Trading SPAC warrants

2020-10-20T00:00:00+00:00

Introduction

A warrant is a kind of security that’s redeemable for a share at a certain exercise price, usually $11.50. So a holder of a warrant can opt to pay $11.50 and get a share, regardless of the price of the share. The intrinsic value of a warrant is thus share_price - 11.50, though its traded price can drift from that (in either direction) for various reasons.

Warrants are often issued by SPACs. SPACs are “special purpose acquisition companies” - companies that list on the stock exchange for the express purpose of acquiring another company. It’s a way for the acquired company to get listed without having to go through an IPO process - they just merge with a SPAC who finds them appealing.

A warrant is thus a cheap incentive to get people invested in SPACs. If the SPAC fails to merge with a target company within the time allotted (usually two years), the warrants are worthless. The warrants are also worthless if, post-merger, the acquired company is trading below $11.50. (A holder of a warrant usually has to wait until 30 days after the merger has been completed to exercise their warrant.)

Despite the risk of their value going to zero, warrants are appealing to trade because:

They’re cheap - single-digit dollars, often under $1 while a SPAC is still searching for a target.
Small relative changes in the share price make for large relative changes in the warrant price. This allows for the possibility of large multiples of gains (a recent SPAC’s warrants briefly traded at $13.50).

The aim of this project is to determine if and how warrants should be traded over the life of a SPAC.

What does the warrant price look like over the lifecycle of a SPAC?

The “golden path” lifecycle of a SPAC is:

Searching for target. Low volume and not much price movement because there’s no information. If the managers of the SPAC are well known there may be hype based on that alone.
Letter of Intent (LOI). They publish a formal letter to some private company saying “we’d like to acquire you. Are you interested?”. This is the first news the public gets of any discussion. There is usually a bump around here, since this means probable progress.
Definitive Agreement (DA). The target company says yes, we’d like to merge with you and become a publically traded company. Another bump.
Merger vote. The shareholders of the SPAC vote on whether to go ahead with the merger. They will not do this if they think the target company will trade under $10, as the SPAC will refund $10 of share value to any shareholder if the SPAC doesn’t acquire a company within the allotted two years. Recent SPACs have seen a large sell-off at this point, as long-time investors take their profits.
Merger executed. The companies officially merge: the SPAC ticker changes to the target company’s ticker, and all shares and warrants are converted to the new ticker. The SPAC is now a publically traded company just like any other.
Warrants exercisable. 30 days after the merger, warrants can be exercised. By this time both the warrant and share prices will have adjusted such that warrant_price = share_price - 11.50.

So, to recap, the price action is:

Flat and very low volume while the SPAC is searching.
A bump at LOI, followed by a tail-off as people lose interest.
Another bump at DA when the deal is done.
Get the hell out before the long-term investors take their profits.

Some examples of SPAC price graphs follow. The first three are small, the others are larger.

As you can see, the LOI and Definitive Agreement both show clear bumps but their respective sizes vary.

Outlier cases:

Multiple LOIs, if one of the potential companies isn’t interested.
The merger vote fails.
The SPAC fails to find a target company within the allotted two years.

The idea of this project is to pick up warrants during the searching phase, hold them until LOI and/or DA, and then sell.

Research

I pulled the list of all SPACs from the SEC for the years 2015-2020 and found all their warrants. I will skip the part where gathering and cleaning this data was a nightmare 🙂 The dataset contains all SPACs that IPO’d during that period and subsequently issued warrants, regardless of whether they successfully merged with a target. This should (hopefully) eliminate survivorship bias.

Results

There were 214 warrants that met the criteria. Our dataset is biased towards smaller SPACs where warrants traded well below $1 for long periods of time. (74% of the SPACs in our dataset never had warrants trading above $3, whereas we now see some big name SPACs trading $3 warrants at launch.)

I selected their highest traded price and picked the lowest price before that date to calculate a maximum return.

	min	median	mean	max
low price	$0.01	$0.45	$0.61	$5.20
high price	$0.08	$1.73	$2.58	$17.50
max return (hi/lo)	1x	3.58x	12.26x	383.51x

If you attempted to buy every SPAC at $1.50, the best price to sell at would be $6.83. This would net you a return of 1.24x. However, this would be extremely stupid, as a lot of these warrants trade well below $1.50 for long periods. Of the 120 SPACs (56% of our dataset) that failed to hit $2, their median max return was 2.86x, with a mean of 7.36x. It’d be extremely obvious that you were overpaying at $1.50.

Catching the high and low prices accurately is hard. If you bought at triple the low price and sold for a third of the high price, your median return would be 0.4x - a 60% loss! - but your mean return would still be 1.36x. You shouldn’t use this strategy, but if you did, you’d likely see a string of losses before one SPAC took off and saved your account. Not for the faint of heart!

Here’s a chart of some potential entry prices, and some limit order numbers that X% of SPACs that ever reached that price subsequently hit. Note that “best sell price” means “you sell all your warrants if they hit this price”, thus you never get the upside. At low entry prices it is heavily skewed by the few SPACs that took off (better to sell high and maximize returns from outliers than get more reliable returns across the board). If you want more reliable returns, use the percentiles for guidance.

entry price	95% SPACs reach	80%	50%	25%	best sell price	return at best sell price
0.10	0.28	0.39	0.74	1.11	5.10	4.64
0.25	0.29	0.50	0.95	2.10	14.20^†	3.50
0.50	0.31	0.64	1.29	2.84	2.80	1.45
1.00	0.38	0.76	1.38	2.56	1.90	0.73
1.50	0.40	0.85	1.53	2.90	1.90	0.55
2.00	0.41	0.89	1.65	2.99	2.00	0.42

^{† Beware: this price is likely an artifact of one SPAC that reached 0.25 and then took off.}

Unsurprisingly, bigger gains come from lower initial prices. By the time you’re willing to buy warrants above $0.50, there’s someone willing to sell you a warrant worth $0.10, which drags your return ratio downward. If you want to make sure that you at least break even (on average), your highest entry price should be somewhere between $.5 and $1.

If you can mystically refrain from buying a warrant until it reaches the bin where it won’t go any lower (e.g. you hold off buying a warrant at $0.25 because you somehow know it will later go below $0.10), your odds get better:

entry price	95% SPACs reach	80%	50%	25%	best sell price	return at best sell price
0.10	0.28	0.39	0.74	1.11	5.10	4.64
0.25	0.31	0.63	0.99	2.94	14.20	5.28
0.50	0.58	0.93	1.55	3.01	6.80	1.87
1.00	0.74	1.01	1.66	2.50	1.70	0.85
1.50	1.50	1.71	2.85	3.25	2.65	1.06
2.00	1.76	2.24	2.52	3.21	2.30	0.92

You can probably get closer to this kind of return by continuing to invest in a warrant as its share price drops; more below.

Here’s a graph of low prices (x-axis) against ROI (y-axis). Note the log-scale on the Y. The truly eye-watering returns come when the low prices are VERY low.

  1000 +--------------------------------------------------------------------+
       |                                                                    |
       |                                                                    |
       |                                                                    |
       |                                                                    |
       |                                                                    |
       |.                                                                   |
   100 |..                                                                  |
       |  .                                                                 |
       | ..                                                                 |
       |. .                                                                 |
       | ..                                                                 |
       |. . ..                                                              |
       |...  .                                                              |
    10 |......  .                                                           |
       |.......                                                             |
       | ... .. .    . .                                                    |
       |........ . ..   .                                                   |
       | ...... ..  ... .            .                                      |
       | ...........  ...    . .                                   .        |
       | .  ........... ..   .      .     .                                 |
     1 +--------------------------------------------------------------------+
       0           1          2           3          4           5          6

Some 52-week lo/hi values and ratios for famous recent SPACs:

HYLN: 0.15 - 29, 193x(!)
VLDR: 0.05 - 7.90, 158x
SPAQ: 0.27 - 7.6, 28x
IPOB: 2.6 - 6.95, 2.7x

Conclusion

Assuming these patterns hold, - i.e. assuming that past performance predicts future performance:

The main takeaway is fairly obvious in hindsight: the cheaper you can pick up a warrant, the more return you’ll make on it. Chasing high-value SPACs will only limit your profit.

The real money is in buying cheap warrants. If you can pick up a warrant at 0.5, you’ll make around 145% in the long run. If you can pick one up for 0.1, you can get 464% returns.

I’m greedy. Can we do better?

Yes.

First: you can dollar cost average into your positions. As the price of a warrant drops, the return ratio increases, but the probability it will cover its earlier cost decreases. You will do better spending $100 on a warrant at 0.5 and another $100 at 0.1 than simply spending the $200 at 0.5. This will increase the likelihood that you’ll make back enough money to cover your (expensive in hindsight) purchase at 0.5.

Second: Don’t just set a limit order to sell everything. Manage your trades!

If your limit order triggers, the price is likely to keep going up. So cash out some, and then have fun trying to call the top.
Alternatively, trigger an alert at your limit price, and then set up your sell order as a trailing stop. Now you can ride the price action much closer to the top.
Similarly: pay attention to the SPAC’s lifecycle and be prepared to cut your losses if the limit order doesn’t hit. The calculations here assume that if you don’t hit your limit price, you lose 100% of your initial investment. This isn’t going to be true in practice; the price of your warrants will peak when the SPAC signs Definitive Agreement, so if you’ve passed that phase and your limit order hasn’t been hit, get out with whatever profits you can.

Epilogue

This was written in late 2020, using data going back to 2018. Around this time, the SPAC craze really kicked off, and everyone launched a SPAC (including Shaq! Shaq SPAC!). The market massively oversaturated; very few SPACs found a target, and of those that did, few traded above the $11.50 required for warrants to be profitable. I would be very surprised if the results still hold!