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tl;dr - 1) Stock prices move continuously because different market participants end up having different ideas of the future value of a stock. 2) This difference in valuations is part of the reason we have volatility. 3) IV crush happens as a consequence of future possibilities being extinguished at a binary catalyst like earnings very rapidly, as opposed to the normal slow way. submitted by
I promise I'm getting to the good parts, but I'm also writing these as a guidebook which I can use later so people never have to talk to me again.
In this part I'm going to start veering a bit into the speculation territory (e.g. ideas I believe or have investigated, but aren't necessary well known) but I'm going to make sure those sections are properly marked as speculative (and you can feel free to ignore/dismiss them). Marked as [Lily's Speculation]
As some commenters have pointed out in prior posts, I do not
have formal training in mathematical finance/finance (my background is computer science, discrete math, and biology), so often times I may use terms that I've invented which have analogous/existing terms (e.g. the law of surprise is actually the first law of asset pricing applied to derivatives under risk neutral measure, but I didn't know that until I read the papers later). If I mention something wrong, please do feel free to either PM me (not chat) or post a comment, and we can discuss/I can correct it! As always, buyer beware.
This is the first section also where you do
need to be familiar with the topics I've previously discussed, which I'll add links to shortly (my previous posts:
--- A Random Walk Down Bankruptcy
A lot of us have probably seen the term random walk, maybe in the context of A Random Walk Down Wall Street
, which seems like a great book I'll add to my list of things to read once I figure out how to control my ADD. It seems obvious, then, what a random walk means - when something is moving, it basically means that the next move is random. So if my stock price is $1 and I can move in $0.01 increments, if the stock price is truly randomly
walking, there should be roughly a 50% chance it moves up in the next second (to $1.01) or down (to $0.99).
If you've traded for more than a hot minute, this concept should seem obvious, because especially on the intraday, it usually isn't clear why price moves the way it does (despite what chartists want to believe, and I'm sure a ton of people in the comments will tell me why fettucini lines and Batman doji tell them things). For a simple example, we can look at SPY's chart from Friday, Oct 16, 2020:
I'm sure again 7 different people can tell me 7 different things about why the chart shape looks the way it does, or how if I delve deeply enough into it I can find out which man I'm going to marry in 2024, but to a rationalist it isn't exactly apparent at why SPY's price declined from 349 to ~348.5 at around 12:30 PM, or why it picked up until about 3 PM and then went into precipitous decline (although I do have theories why it declined EOD, but that's for another post).
An extremely clever or bored reader from my previous posts could say, "Is this the price formation you mentioned in the law of surprise post?" and the answer is yes
. If we relate it back to the individual buyer or seller, we can explain the concept of a stock price's random walk as such:
Most market participants have an idea of an asset's true value (an idealized concept of what an asset is actually worth), which they can derive using models or possibly enough brain damage. However, an asset's value at any given time is not worth one value (usually*), but a spectrum of possible values, usually representing what the asset should be worth in the future. A naive way we can represent this without delving into to much math (because let's face it, most of us fucking hate math) is:
Current value of an asset = sum over all (future possible value multiplied by the likelihood of that value)
In actuality, most models aren't that simple, but it does generalize to a ton of more complicated models which you need more than 7th grade math to understand (Black-Scholes, DCF, blah blah blah).
While in many cases the first term - future possible value - is well defined (Tesla is worth exactly $420.69 billion in 2021, and maybe we all can agree on that by looking at car sales and Musk tweets), where it gets more interesting is the second term - the likelihood of that value occurring. [In actuality, the price of a stock for instance is way more complicated, because a stock can be sold at any point in the future
(versus in my example, just the value in 2021), and needs to account for all values of Tesla at any given point in the future.]
How do we estimate the second term - the likelihood of that value occurring? For this class, it actually doesn't matter, because the key concept is this idea: even with all market participants having the same information, we do anticipate that every participant will have a slightly different view of future likelihoods.
Why is that? There's many reasons. Some participants may undervalue risk (aka WSB FD/yolos) and therefore weight probabilities of gaining lots of money much more heavily than going bankrupt. Some participants may have alternative data which improves their understanding of what the future values should
be, therefore letting them see opportunity. Some participants might overvalue liquidity, and just want to GTFO and thereby accept a haircut on their asset's value to quickly unload it (especially in markets with low liquidity). Some participants may just be yoloing and not even know what Fastly does before putting their account all in weekly puts (god bless you).
In the end, it doesn't matter either the why
, but the what
: because of these diverging interpretations, over time, we can expect the price of an asset to drift from the current value even with no new information added. In most cases, the calculations that market participants use (which I will, as a Lily-ism, call the future expected payoff function
, or FEPF) ends up being quite similar in aggregate, and this is why asset prices likely tend to move slightly up and down for no reason (or rather, this is one
interpretation of why).
At this point, I expect the 20% of you who know what I'm talking about or have a finance background to say, "Oh but blah blah efficient market hypothesis contradicts random walk blah blah blah" and you're correct, but it also legitimately doesn't matter here. In the long run, stock prices are clearly
not a random walk, because a stock's value is obviously tied to the company's fundamentals (knock on wood I don't regret saying this in the 2020s). However, intraday, in the absence of new, public
information, it becomes a close enough approximation.
Also, some of you might wonder what happens when the future expected payoff function (FEPF) I mentioned before ends up wildly diverging for a stock between participants. This could happen because all of us try to short Nikola because it's quite obviously a joke (so our FEPF for Nikola could, let's say, be 0), while the 20 or so remaining bagholders at NikolaCorporation
decide that their FEPF of Nikola is $10,000,000 a share). One of the interesting things which intuitively makes sense, is for nearly all stocks, the amount of divergence among market participants in their FEPF increases substantially as you get farther into the future.
This intuitively makes sense, even if you've already quit trying to understand what I'm saying. It's quite easy to say, if at 12:51 PM SPY is worth 350.21 that likely at 12:52 PM SPY will be worth 350.10 or 350.30 in all likelihood. Obviously there are cases this doesn't hold, but more likely than not, prices tend to follow each other, and don't gap up/down hard intraday. However, what if I asked you - given SPY is worth 350.21 at 12:51 PM today, what will it be worth in 2022?
Many people will then try to half ass some DD about interest rates and Trump fleeing to Ecuador to value SPY at 150, while others will assume bull markets will continue indefinitely and SPY will obviously be 7000 by then. The truth is -- no one actually knows, because if you did, you wouldn't be reading a reddit post on this at 2 AM in your jammies.
In fact, if you could somehow figure out the FEPF of all market participants at any given time, assuming no new information occurs, you should be able to roughly predict the true value of an asset infinitely far into the future (hint: this doesn't exactly hold, but again don't @ me).
Now if you do
have a finance background, I expect gears will have clicked for some of you, and you may see strong analogies between the FEPF divergence I mentioned, and a concept we're all at least partially familiar with - volatility. Volatility and Price Decoherence ("IV Crush")
Volatility, just like the Greeks, isn't exactly a real thing. Most of us have some familiarity with implied volatility on options, mostly when we get IV crushed the first time and realize we just lost $3000 on Tesla calls.
If we assume that the current price should represent the weighted likelihoods of all future prices (the random walk), volatility implies the following two things:
[Ignore this section if you aren't pedantic]
- Volatility reflects the uncertainty of the current price
- Volatility reflects the uncertainty of the future price for every point in the future where the asset has value (up to expiry for options)
There's obviously more complex mathematics, because I'm sure some of you will argue in the comments that IV doesn't go up monotonically as option expiry date goes longer and longer into the future, and you're correct (this is because asset pricing reflects drift rate and other factors, as well as certain assets like the VIX end up having cost of carry).
Volatility in options is interesting as well, because in actuality, it isn't something that can be exactly computed -- it arises as a plug between the idealized value of an option (the modeled price) and the real, market value of an option (the spot price). Additionally, because the makeup of market participants in an asset's market changes over time, and new information also comes in (thereby increasing likelihood of some possibilities and reducing it for others), volatility does not remain constant over time, either.
Conceptually, volatility also is pretty easy to understand. But what about our friend, IV crush? I'm sure some of you have bought options to play events, the most common one being earnings reports, which happen quarterly for every company due to regulations. For the more savvy, you might know of expected move
, which is a calculation that uses the volatility (and therefore price) increase of at-the-money options about a month out to calculate how much the options market forecasts the underlying stock price to move as a response to ER. Binary Catalyst Events and Price Decoherence
Remember what I said about price formation being a gradual, continuous process? In the face of special circumstances, in particularly binary catalyst events
- events where the outcome is one of two choices, good (1) or bad (0) - the gradual part gets thrown out the window. Earnings in particular is a common and notable case of a binary event, because the price will go down (assuming the company did not meet the market's expectations) or up (assuming the company exceeded the market's expectations) (it will rarely stay flat, so I'm not going to address that case).
Earnings especially is interesting, because unlike other catalytic events, they're pre-scheduled (so the whole market expects them at a certain date/time) and usually have publicly released pre-estimations (guidance, analyst predictions). This separates them from other binary catalysts (e.g. FSLY dipping 30% on guidance update) because the market has ample time to anticipate the event, and participants therefore have time to speculate and hedge on the event.
In most binary catalyst events, we see rapid fluctuations in price, usually called a gap up or gap down, which is caused by participants rapidly intaking new information and changing their FEPF accordingly. This is for the most part an anticipated adjustment to the FEPF based on the expectation that earnings is a Very Big Deal (TM), and is the reason why volatility and therefore option premiums increase so dramatically before earnings.
What makes earnings so interesting in particular is the dramatic effect it can have on all market participants FEPF, as opposed to let's say a Trump tweet, or more people dying of coronavirus. In lots of cases, especially the FEPF of the short term (3-6 months) rapidly changes in response to updated guidance about a company, causing large portions of the future possibility spectrum to rapidly and spectacularly go to zero. In an instant, your Tesla 10/30 800Cs go from "some value" to "not worth the electrons they're printed on". [Lily's Speculation]
This phenomena, I like to call price decoherence,
mostly as an analogy to quantum mechanical processes which produce similar results (the collapse of a wavefunction on observation). Price decoherence occurs at a widespread but minor scale continuously, which we normally call price formation
(and explains portions of the random walk derivation explained above), but hits a special limit in the face of binary catalyst events, as in an instant rapid portions of the future expected payoff function are extinguished, versus a more gradual process which occurs over time (as an option nears expiration).
Price decoherence, mathematically, ends up being a more generalizable case of the phenomenon we all love to hate - IV crush. Price decoherence during earnings collapses the future expected payoff function of a ticker, leading large portions of the option chain to be effectively worthless (IV crush).
It has interesting implications, especially in the case of hedged option sellers, our dear Market Makers. This is because given the expectation that they maintain delta-gamma neutral, and now many of the options they have written are now worthless and have 0 delta, what do they now have to do?
They have to unwind. [/Lily's Speculation]
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