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@ -0,0 +1,326 @@
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Math Black Magic Vol. 1: Why It Is Mathematically Impossible for Hedgies To Unfuk Themselves
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============================================================================================
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| Author | Source |
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| :-------------: |:-------------:|
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| [u/nydus_erdos](https://www.reddit.com/user/nydus_erdos/) | [Reddit](https://www.reddit.com/r/Superstonk/comments/nw8281/math_black_magic_vol_1_why_it_is_mathematically/) |
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---
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[DD 👨🔬](https://www.reddit.com/r/Superstonk/search?q=flair_name%3A%22DD%20%F0%9F%91%A8%E2%80%8D%F0%9F%94%AC%22&restrict_sr=1)
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DISCLAIMER: My first DD. Not financial advice. All credit to the authors of cited works. I am not trying to karma farm or be dramatic by breaking this up into parts. I tried to post it all at once, but the picture limit had other plans.
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ACKNOWLEDGEMENTS:
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Shout out to [u/sososhibby](https://www.reddit.com/u/sososhibby/). One of their comments got me started down this rabbit hole and they were nice enough to give my work a quick check before I posted. They've also posted about this topic as well: [Part 1](https://www.reddit.com/r/Superstonk/comments/nmaaaa/john_d_finnerty_excerpt_from_hoc_3_explained_pt1/), [Part 2](https://www.reddit.com/r/Superstonk/comments/nmdbzz/excerpt_from_hoc3_relevant_af_20_finnerty_fer/)
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Also, [u/JNWolman](https://www.reddit.com/u/JNWolman/) was all over this topic months ago. IMO, the post didn't get the exposure it was due. Give it a [read](https://www.reddit.com/r/GME/comments/mgmbkf/would_the_real_exit_strategy_please_stand_up/).
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--------------------------------------------------------------------------------------------------------------------------------------------------------
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A. What I Hope to Show
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In this volume I hope to present work (by brains much more wrinkled than mine) that show beyond a reasonable doubt, something we all already know: that hedgies are indeed mathematically fuk, in that they have naked shorted AT LEAST the same amount of shares outstanding.
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[u/atobitt](https://www.reddit.com/u/atobitt/)'s [H.O.C. III](https://www.reddit.com/r/Superstonk/comments/nlwqyv/house_of_cards_part_3/) mentions an [academic paper](https://www.sec.gov/comments/s7-08-08/s70808-318.pdf) titled "*Short Selling, Death Spiral Convertibles, and the Profitability of Stock Manipulation*" written March 2005 by John D. Finnerty, a finance professor.
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In the paper, Finnerty lays out a model to examine naked short selling. In particular, he demonstrates that in order to drive a firms price very close to zero, a manipulator MUST naked short AT LEAST the same number of shares as there are shares outstanding, doubling the float.
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-----------------------------------------------------------------------------------------------------------------------------------------------------
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B. Market Model Rundown
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In my opinion, Finnerty's paper is a thing of logical and [mathematical beauty](https://en.wikipedia.org/wiki/Mathematical_beauty). As god tier mathematician Paul Erdős would say, "[This one's from The Book](https://en.wikipedia.org/wiki/Mathematical_beauty#Beauty_and_philosophy)". Finnerty took a very complex system and expressed it elegantly and simply. As a math ape, it literally brought a tear to my eye when I finally understood it; which took me awhile (just because I like math doesn't make my brain any less smooth). There's no confirmation bias as sweet as mathematical confirmation bias.
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However, I am quite aware of my autistic tendencies and know most people and apes have a...*strained* relationship with math, so I read all 73 pages of the paper so you don't have to! I try to lay out his model as concisely as possible as to who are the participants, how the market behaves and why hedgies r thusly fuk.
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MARKET PARTICIPANTS:
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*Informed Investor*
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- Informed investors do short sell, but do not engage in abusive or naked short selling. They locate, borrow and return shares on time.
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- The informed investor has information advantage. They know if the true intrinsic value of the stock is high (*H)* or low *(L)*.
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- This group only shorts stocks that legitimately have low real intrinsic value *(L)*.
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- Assume there is only one informed investor in this model.
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*Manipulator*
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- The manipulator has the information advantage as well. Through research or by observing the informed investor, they know the true intrinsic value of the stock and seek to manipulate the stock below that value.
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- A manipulator can appear as an informed investor to other participants by copying the selling behavior of the informed investor.
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- Manipulator can be a Market Maker (MM).
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> Market makers have lower shorting costs since they can sell on a downtick and do not have to commit that they will be able to borrow shares before they sell short. Market makers are granted these exceptions to facilitate their market-making activities. A strategy a manipulator can employ to reduce its cost of shorting is to register as a market maker for the target stock. If naked shorting, there is zero cost. (Pg. 17, footnote 33)
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- There is only one manipulator in this model.
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*Active Traders*
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- Think of this group as regulation abiding MM's.
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- They can short sell, but do not engage in abusive or naked short selling.
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- Active traders does not have as much information as the manipulator and informed investor. They do not know the true value of the stock.
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- They can interpret market signals and see what the informed investor does, which gives them information advantage over retail investors.
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- They don't know if the informed investor they are watching is actually a manipulator in disguise.
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- They mostly base their moves on what the informed investor (or the disguised manipulator) does and only act after they do.
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- There is more than one active trader.
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*Uninformed Investors*
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- These are old type retail investors, not apes.
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- Uninformed investors have the ultimate information disadvantage, they have no idea how much the stock is really worth.
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- They always stand ready to buy more shares at lower prices than those currently prevailing, since they don't know the true intrinsic value of the stock.
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- This willingness to buy provides consistent cash flow (liquidity) to short sellers.
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- Uninformed investors demand for shares decreases as the amount they possess increases.
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- Once this group knows the true price of the stock they will sell, providing shares to the shorts to cover.
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- There are many uninformed investors.
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*Insiders and Long Term HODL'ers*
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- Passive group that does not take an active role in the market. They neither sell nor buy shares.
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- They exist in the model so there are shares for the shorts to borrow and to set the initial market price.
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- Assume they own all outstanding shares.
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TIME BREAKDOWN:
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The paper has a timeline/progression of how the market behaves. There are four points expressed as time *t*.
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*Time 0*
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- This is right before anything happens and the model is at the initial conditions.
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- All shares are held by insiders and long term investors who do not plan on selling.
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*Time 1*
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- This is when the short sale can be initiated by the the informed investor or the manipulator or, depending on the situation, by both of them.
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- Also during this time the active traders are observing the informed investor (or a manipulator posing as one) and current market signals. They do not act during this time.
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*Time 2*
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- This is when the active trader takes action, they do what they saw the informed investor (or the manipulator posing as one) do.
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- The short sellers from time 1 can short additional shares if they decide to.
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- Market equilibrium forms at this time.
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- The informed investor or the manipulator can sustain a short position until time 3 but it is less expensive to sustain it to time 2 (unless the manipulator naked shorts and/or is a MM).
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*Time 3*
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- This is when the stocks true intrinsic value is revealed to all market participants to be *H* or *L*.
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- This represents the long run, and it may be very costly for the informed investor or the manipulator to maintain a short position (unless the manipulator naked shorts and/or is a MM).
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- If the legitimate shorts have not closed their short position already, this is were they cover.
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- Most of the paper's focus is on what happens at this time.
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MARKET EQUILIBRIUM
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At time 2, the market enters equilibrium. There are two basic forms of equilibrium: pooling and separating.
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*Pooling*
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This type of equilibrium is when the manipulator wants to remain undetected so the other market participants mistake him as an informed investor.
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The advantage to this is that the manipulator stands less of a chance of getting caught or squeezed. On top of this, active traders may pile on to short the stock as well when they see blood in the water. This causes the price to drop even lower, helping the manipulator.
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The disadvantage is that the manipulator loses profit to the extra competition and sole control over the price action.
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*Separating*
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This is when the manipulator doesn't care if they are detected. In some cases, they want to be detected to scare off competition. The advantage is that this strategy maximizes their profit and they have full price control. The disadvantage is they have a greater chance of getting caught or squeezed.
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-----------------------------------------------------------------------------------------------------------------------------------------------------
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E. Demand Curves & The Unravelling Problem
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*General Demand Curve:*
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This whole model is governed by the uninformed investors demand, since they are the buyers. Their demand is highly dependent on the supply of shares. The uninformed traders willingness to hold *Q* shares at time *t* is summarized by the demand curve (Pg. 15):
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[](https://preview.redd.it/zhhgr111fc471.png?width=1375&format=png&auto=webp&s=cc034e8ae681bdc7365ce2ab1851e18fca94cbed)
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General Demand Curve
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- The function *D(Q)* represents the uninformed investors demand which is equal to the price at time *t* represented by *P(t)*.
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- *H* and *L* are the potential true values of the stock revealed to active traders and uninformed investors at time 3.
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- *A* is a constant representing the current market price.
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- *B* is a constant representing the price at which uninformed investors buy, which is lower than the prevailing price.
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- Note that at time zero, all shares are in the hands of long term investors so *P(0) = A*.
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*The Unravelling Problem:*
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If the manipulator is not naked short selling, then they would have to cover at time 2, or at time 3 when the true price is revealed to everyone. This presents what the paper refers to as the unravelling problem.
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This is the issue shorts face when covering their positions. Since retail knows the real price at time 3 their demand curve shifts. Buying to cover at the real price causes the price to increase. Both factors cut into profits.
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*Problem When True Price = H*
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If true price is revealed to be *H* at time 3 then the demand curve shifts to:
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[](https://preview.redd.it/3rhkhwi6fc471.png?width=1406&format=png&auto=webp&s=9d6e0631707e552c444a5d8206535f54bad1b4ca)
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High Value Demand Curve
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This is the worst case scenario for hedgies. Not only did they not suppress the price to *L* they now have to buy to cover. The number of shares retail holds *Q* goes to zero since hedgies have to buy them back, which will push the price to *H* cutting into their tendies.
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*Problem When True Price = L*
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If true price is revealed to be *L*, at time 3 then the demand curve shifts to:
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[](https://preview.redd.it/45sv7u0afc471.png?width=1408&format=png&auto=webp&s=7bcc138e8344e98deab491f8f2b7d77275693377)
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Low Value Demand Curve
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Not as bad as the previous case, but even covering at *L* will push price a little bit higher and cut into the hedgies' tendies.
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-----------------------------------------------------------------------------------------------------------------------------------------------------
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F. Naked Short Selling
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Naked short selling removes the unravelling problem at no cost to the manipulator and it's quite literally free money:
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> Naked short selling and manipulating the price downward provide cash returns to the manipulator, who can withdraw cash from his clearing firm account as the shorted shares are marked to market at progressively lower prices. Through naked shorting, the manipulator realizes these returns without investing any cash (provided the market price never rises above the sale price). (Pg. 34, par. 1)
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> The clearing firm retains the cash proceeds from the short sale to secure the selling broker's delivery obligation. The clearing firm releases cash equal to the reduction in value of the shorted shares as the price of the shares declines (or demands additional cash margin if the share price rises). (Pg. 34, footnote 51)
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Here are some familiar signs of naked short selling:
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> The daily trading volume could be quite high if the manipulator is rapidly turning over its short position, but the daily trading and settlement activity may appear to be normal market making because the dealer's net position on the day does not change. (Pg. 44, footnote 64)
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> Pumping the trading volume also reduces the short interest ratio (short interest divided by the average daily trading volume) to help conceal the manipulation. (Pg. 44, footnote 64)
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Remember naked shorting creates phantom shares which increases the float.
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*True Shares Outstanding:*
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Based on the original demand curve we can calculate the total shares outstanding at time 0. Since this is during the initial conditions, this is the true value of shares outstanding.
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So, since uninformed investors are always willing to buy at a lower price and, hypothetically, if the long term investors decided to sell all outstanding shares *Q* to uninformed traders then price would fall to *L*:
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[](https://preview.redd.it/2lucrstdfc471.png?width=1302&format=png&auto=webp&s=77adeb75401431094301b216caabcb71f4db680c)
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True Shares Outstanding
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*Naked Short Selling in Pooling Equilibrium: Driving Price Close to Zero*
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When True Price = *H*
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Using the previous equations we can find the amount of shares necessary to drive the final price at time 3 close to zero:
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[](https://preview.redd.it/qei47fuifc471.png?width=1284&format=png&auto=webp&s=65ea8f2f04eff9babd339b7c22a3a8f9c655fb7a)
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Shares Needed to Drive Price Close To Zero
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When True Price = *L*
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[](https://preview.redd.it/pedh454ofc471.png?width=1279&format=png&auto=webp&s=fe342a1d0872e3baa28292cd39d15d3cef259de6)
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Shares Needed to Drive Price Close to Zero
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It is also worth noting,
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> The manipulators profit depends on his ability to manipulate the firm's stock price and keep it depressed. The stronger the financial condition of the firm at time 3 (the higher *L* is), the greater the number of shares the manipulator has to sell short at time 3 to drive the price close to zero. (Pg. 45, par. 2)
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*More Shorted Shares than Outstanding:*
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We have the true shares outstanding, we know the amount of shares needed to short an *H* valued company to zero, and the amount of shares needed to short a *L* valued company to zero:
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[](https://preview.redd.it/twctyrcsfc471.png?width=1274&format=png&auto=webp&s=cd8be3285e939cac464dee89025027c780c3eb0b)
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Share Counts
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When Value Is *H*
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> Building a short position of *H/B* to drive *P(3)* to zero would involve naked shorting more shares than the firm has outstanding because *H/B > (A-L)/B*. (Pg. 45, par. 1)
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>
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> The manipulator can not drive the share price close to zero unless he can naked short an extraordinary number of shares. (Pg. 45, par. 1)
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So to drive the *H* company to zero hedgies have to naked short *Q_H* shares. But remember our general equations governing the demand curve:
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[](https://preview.redd.it/2pv8j1uxfc471.png?width=1362&format=png&auto=webp&s=b1f6323b28f83ff44706c06252eb8ef1decc802d)
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Hedgies r fuk: High Value Edition
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Proving that if hedgies want to short a company with a high intrinsic value to zero they must naked short more shares than are outstanding.
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When Value is *L*
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> Even if the manipulator's short position is *L/B*, it might still exceed the entire number of shares the firm has outstanding.
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>
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> The manipulators profit depends on his ability to manipulate the firm's stock price and keep it depressed. The stronger the financial condition of the firm at time 3 (the higher *L* is), the greater the number of shares the manipulator has to sell short at time 3 to drive the price close to zero. (Pg. 45, par. 2)
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If the final price (*L*) at time three (*P(3)*) is equal to the price at time 2 (i.e. if *L=P(3)=P(2)*) then the manipulator will naked short the same number of shares that the firm has outstanding. This next equation should look familiar:
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[](https://preview.redd.it/vfihc052gc471.png?width=1338&format=png&auto=webp&s=73f9ccd94ca522bfc4f57d548aa1fc0e3b51c2e5)
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Hedgies r fuk: Low Value Edition
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So then if *L>P(2)* then the manipulator will naked short more shares than firm has outstanding. By naked shorting the same number of shares that are outstanding, the manipulator has doubled the float. (Pg. 55, footnote 77)
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Which makes sense: If the price is higher turns out to be higher than they expected then they have to drive price down even more. Naked shorting is effective because it dilutes the float.
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What About Incremental Shorting?
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Almost forgot this case, so I'll have to put it here at the end. I'm not gonna go too much into the math cause it just adds another layer of unneeded complexity.
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Basically you just need to know this, Finnerty proves that unless the manipulator is naked shorting and/or is a MM, it is not profitable to incrementally short sell (i.e. shorting a little, then covering a little, repeat).
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> In a market equilibrium in which the informed investor sells the profit-maximizing number of shares, I show later in the paper that incremental short sales by the manipulator will not be profitable. (Pg. 16, footnote 29)
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This shows how huge of a win the rule changes were. Had apes not gotten them, Shitadel would have continued to abuse their MM privileges and not had to worry about margin call. Now, they can't naked short as freely and its actually costing them to maintain short positions, and its only going to get worse.
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------------------------------------------------------------------------------------------------------------------------------------------------
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||||
In the next volume, I'll explore :
|
||||
|
||||
1. The Majestic Ape Demand Curve
|
||||
|
||||
2. How apes fucked up the hedgies' algorithm
|
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|
||||
3. Why short attacks are getting weaker
|
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|
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4. Exponential & Log Chats
|
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|
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5. Why it is Impossible to Short Ape Curve Close to Zero
|
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|
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---------------------------------------------------------------------------------------------------------------------------------------------------
|
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|
||||
TL:DR -> Finance professor (not me) mathematically proves that it's impossible to short a stock to zero without naked shorting at least as many shares as there are outstanding, doubling the float in the process.
|
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|
||||
Hedgies r fuk.
|
||||
|
||||
BUY, HODL, VOTE
|
||||
|
||||
TA:DR -> Naked 🩳 + (🐒x🦍) + 🚀√🌕 =
|
||||
|
||||
(Hedgies r fuk) 2 + 🍗🍗🍗
|
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|
||||
--------------------------------------------------------------------------------------------------------------------------------------------------------
|
||||
|
||||
This post brought to you on behalf of Margery Nesbitt.
|
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@ -0,0 +1,208 @@
|
||||
Math Black Magic Vol 2: The Limit Does not Exist!
|
||||
=================================================
|
||||
|
||||
| Author | Source |
|
||||
| :-------------: |:-------------:|
|
||||
| [u/nydus_erdos](https://www.reddit.com/user/nydus_erdos/) | [Reddit](https://www.reddit.com/r/Superstonk/comments/nwy0oz/math_black_magic_vol_2_the_limit_does_not_exist/) |
|
||||
|
||||
---
|
||||
|
||||
[DD 👨🔬](https://www.reddit.com/r/Superstonk/search?q=flair_name%3A%22DD%20%F0%9F%91%A8%E2%80%8D%F0%9F%94%AC%22&restrict_sr=1)
|
||||
|
||||
DISCLAIMER: Second part of my first DD. Not financial advice. All credit to the authors of cited works. I am not trying to karma farm or be dramatic by breaking this up into parts. I tried to post it all at once, but the picture limit had other plans.
|
||||
|
||||
-----------------------------------------------------------------------------------------------------------------------------------------------------
|
||||
|
||||
ACKNOWLEDGEMENTS:
|
||||
|
||||
Shout out to [u/sososhibby](https://www.reddit.com/u/sososhibby/). One of their [comment](https://www.reddit.com/r/Superstonk/comments/nm3mtr/relevant_af/) got me started down this rabbit hole and they were nice enough to give my work a quick check before I posted. They've also posted about this topic as well: [Part 1](https://www.reddit.com/r/Superstonk/comments/nmaaaa/john_d_finnerty_excerpt_from_hoc_3_explained_pt1/), [Part 2](https://www.reddit.com/r/Superstonk/comments/nmdbzz/excerpt_from_hoc3_relevant_af_20_finnerty_fer/)
|
||||
|
||||
[u/JNWolman](https://www.reddit.com/u/JNWolman/) was all over this topic months ago. IMO, the post didn't get the exposure it was due. Give it a [read](https://www.reddit.com/r/GME/comments/mgmbkf/would_the_real_exit_strategy_please_stand_up/).
|
||||
|
||||
I'll also be using [charts](https://www.reddit.com/r/Superstonk/comments/nwwy5x/0610_update_broke_the_logfloor_by_1_5_in_linear/) from [u/JTH1](https://www.reddit.com/u/JTH1/), aka "exponential floor guy".
|
||||
|
||||
-----------------------------------------------------------------------------------------------------------------------------------------------------
|
||||
|
||||
A. Topics Explored
|
||||
|
||||
In [Vol. 1](https://www.reddit.com/r/Superstonk/comments/nw8281/math_black_magic_vol_1_why_it_is_mathematically/), I laid out [Finnerty's paper](https://www.sec.gov/comments/s7-08-08/s70808-318.pdf) which mathematically proves that to drive a firms price very close to zero, a manipulator MUST naked short AT LEAST the same number of shares as there are shares outstanding, effectively doubling the float.
|
||||
|
||||
This write up is more of my examination of the implications of Finnerty's paper and how it applies to GME. This is not meant to be proof, more of this smooth brain's musings. Feedback and constructive criticism are welcome. In this volume I'll examine:
|
||||
|
||||
- What I think the hedgies' algorithm and how apes fucked up said algo.
|
||||
|
||||
- I should note, that I believe the algos covered here have been modified since, but the damage has been done.
|
||||
|
||||
- Why short attacks are getting weaker.
|
||||
|
||||
- The negative volume that pops up every so often.
|
||||
|
||||
- Why it is Impossible to Short Ape Curve Close to Zero.
|
||||
|
||||
PROTIP: This volume is a bit more math heavy than the last, but don't let that intimidate you!
|
||||
|
||||
Don't focus too much on the letters, as long as you know who is doing what at each time and what greater than (>) , less than (<) and equal (=) means you'll be good. I'll try to clarify anything that gets too intense.
|
||||
|
||||
-----------------------------------------------------------------------------------------------------------------------------------------------------
|
||||
|
||||
B. Naked Short Selling: Separating Equilibrium
|
||||
|
||||
In separating equilibrium, the manipulator scares away the other participants with unconcealed, aggressive naked shorting. This maximizes profits by eliminating competition. Since the manipulator has price control it doesn't matter whether the time 3 price should be *H* or *L*.
|
||||
|
||||
The lack of competition also makes this strategy a bit more formulaic than the previous examples. The manipulator maximizes his short sale proceeds by naked shorting at time 1 (Pg. 48 par. 1, Pg. 54-55, par. 1):
|
||||
|
||||
[](https://preview.redd.it/n42c0ax4ag471.png?width=1058&format=png&auto=webp&s=042be52553c72a8b726c3cfe08aa169145c5b35e)
|
||||
|
||||
Price at Time 1
|
||||
|
||||
[](https://preview.redd.it/53iy2wm8ag471.png?width=1074&format=png&auto=webp&s=0c529a4731e2fe5e73009d21f13f45017923a87d)
|
||||
|
||||
Price at Time 2
|
||||
|
||||
[](https://preview.redd.it/hku7v10hag471.png?width=1116&format=png&auto=webp&s=cb29b1b65823c35eebd53733bdc417e1d330930c)
|
||||
|
||||
Price at Time 3
|
||||
|
||||
Note the rate of change:
|
||||
|
||||
> This has occurred with a huge volume of naked shorting and a precipitous decrease in share price that first cut the price in half and then reduced it close to zero. (Pg. 46, par. 2)
|
||||
|
||||
I found that statement slightly unclear as the price is reduced by a third then halved. At most it could be an editing mistake, but more than likely it is my smooth brain. Wrinkle brain help is appreciated.
|
||||
|
||||
-----------------------------------------------------------------------------------------------------------------------------------------------------
|
||||
|
||||
C. Inverted Demand Curve
|
||||
|
||||
First, lets put the original general demand curve into slope intercept (i.e. make it easier to graph as a line):
|
||||
|
||||
[](https://preview.redd.it/99u0fkwpbg471.png?width=1079&format=png&auto=webp&s=16e5c56e020759b1add8ca735ed16bf23d230d1b)
|
||||
|
||||
Slope Intercept Demand Function
|
||||
|
||||
This is a line with a downwards slope of *-B*. Recall that in Finnerty's model, *B* is the price that retail buys, which is always lower than the prevailing price. That means that as retail acquires more and more shares, the price/demand will decrease.
|
||||
|
||||
[](https://preview.redd.it/26cayz89cg471.png?width=1052&format=png&auto=webp&s=070d5441380426260557d52bcd1db5fcdd3479e6)
|
||||
|
||||
Demand Curve Comparison
|
||||
|
||||
With apes, however, it works the opposite way. Yes, apes buy at any prices, but what I think fucked up the algorithm is apes buy at higher and higher prices because ape and FOMO. In this case, demand and price increase as supply increases. Meaning that if apes got all the shares, the price would rise to *H* This changes the slope of the demand curve positive:
|
||||
|
||||
[](https://preview.redd.it/mefhrczrcg471.png?width=1280&format=png&auto=webp&s=7ba9489b6191491937bd9e755e43b562fc731947)
|
||||
|
||||
Ape Demand Function
|
||||
|
||||
What I gathered from this is most of the hedgies' problem results from a simple change in sign. I take this a bit further and apply it to the exponential and log curves later on. I figure that the inverse of these functions is what fucked up what the algorithm originally intended.
|
||||
|
||||
*Exponential & Logarithmic Graphs*
|
||||
|
||||
The following list has the floors calculated by [u/JTH1](https://redditpreview.com/u/JTH1) (aka "exponential floor guy") and the inverted version of the curve I hypothesize the hedgies originally had planned:
|
||||
|
||||
[](https://preview.redd.it/a86fowc6eg471.png?width=1291&format=png&auto=webp&s=ddee910bdcee8a375241290b7608a740ad57736d)
|
||||
|
||||
Ape & Hedgie Curves
|
||||
|
||||
Based on this inverse hypothesis, I think this is the ideal curve hedgies wanted:
|
||||
|
||||
[](https://preview.redd.it/ys4mcl3mgh471.png?width=983&format=png&auto=webp&s=95a47f214cc84052888c2cf2182d910e3df536ed)
|
||||
|
||||
Hedgie Curves
|
||||
|
||||
If you want to see the current curve, check out exponential floor guy's posts (the most recent at the time of this writing is linked at the very top of the post).
|
||||
|
||||
D. Pareto Principle & Rate of Change
|
||||
|
||||
(This section is based heavily on a comment by sososhibby. This section makes a lot more sense if you read it. Its linked at the top.)
|
||||
|
||||
*Hedgie Case*
|
||||
|
||||
I thought it was interesting that the author stressed throughout the paper, that price is reduced CLOSE to zero and not zero.
|
||||
|
||||
Remember, in separated equilibrium naked shorting drops the price by a third, then halves it before it quickly drops close to zero.
|
||||
|
||||
That sounded like asymptotic behavior (asymptote = the thing the curve has to approach for the limit to exist, remember *Mean Girls?*), so I was curious to see the progression to zero so I kept it going and halved *P(2)* again and repeated the process with my result. I assume this is happening quickly between time 2 and time 3:
|
||||
|
||||
[](https://preview.redd.it/2o17ngi8lh471.png?width=973&format=png&auto=webp&s=1f44aafd13eb3f81ccb7f1f4db0214a41d84edd0)
|
||||
|
||||
[](https://preview.redd.it/ero04mjalh471.png?width=910&format=png&auto=webp&s=9aa8b4836a4a7b880224998176146a060b2a65e3)
|
||||
|
||||
Price Progression to Close to Zero
|
||||
|
||||
I'd take it further but you get the picture. So I took the points made a scatter plot. Didn't look like much. I got curious and wanted to see if I could fit the negative exponential curve. I had to use some scaling factors, but always try to base them as a proportion of 1.
|
||||
|
||||
[](https://preview.redd.it/ekvd81pmlh471.png?width=876&format=png&auto=webp&s=8c1448d0d623d47ca188bbf95a5e38596b682d2a)
|
||||
|
||||
[](https://preview.redd.it/4ell2arrlh471.png?width=834&format=png&auto=webp&s=7e10e0d89e6c936605b574fe7bfe56cc738fbbd7)
|
||||
|
||||
Hedgie Curve
|
||||
|
||||
Didn't look like much either, but the fact that it had asymptotic behavior at 0.2 or 20 percent. I figured it might be worth mentioning. Maybe somebody else can take it further.
|
||||
|
||||
*Ape Case*
|
||||
|
||||
Remember, in the normal case of naked shorting in separating equilibrium the price is dropped by a third, then halved, then taken close to zero.
|
||||
|
||||
In the ape case, the price increases. This is where the exponential/power function may come into play. I tried to find the rate of change by re-computing values using equations from earlier:
|
||||
|
||||
[](https://preview.redd.it/wpa0e8femh471.png?width=1056&format=png&auto=webp&s=ffb70662e8d057f9ecefcdca7b73ba7c913a845c)
|
||||
|
||||
[](https://preview.redd.it/c7cnltihmh471.png?width=975&format=png&auto=webp&s=fcfce22cebd58f6b95457afe6dafca3b775a1a38)
|
||||
|
||||
Ape Case
|
||||
|
||||
As with the last set of values, I wanted to examine the behavior of the ape curve to find a rate of change. It looks like the price increases by a third, then by 1.25 or 25 percent.
|
||||
|
||||
[](https://preview.redd.it/pekkb7kvmh471.png?width=910&format=png&auto=webp&s=679c9df194127816f03002feb58a8159c88a012a)
|
||||
|
||||
To the Moon!
|
||||
|
||||
I did the same process of scatter and fitting curve this time with the exponential:
|
||||
|
||||
[](https://preview.redd.it/m9sioly1nh471.png?width=903&format=png&auto=webp&s=18f5889fcf4610d3c84b4de88f05dc9d1cc370de)
|
||||
|
||||
Ape Curve
|
||||
|
||||
Also, not sure if there's anything here, but the number 0.8 or 80 percent stood out to me. Need more wrinkled feedback.
|
||||
|
||||
-----------------------------------------------------------------------------------------------------------------------------------------------------
|
||||
|
||||
E. Impossible to Short to Zero
|
||||
|
||||
I can use the same process as earlier to find the amount of shares needed to short the ape curve close to zero:
|
||||
|
||||
[](https://preview.redd.it/58fozggdnh471.png?width=989&format=png&auto=webp&s=69af8afc934a8c1bd51b42578ddf226dbc6acf52)
|
||||
|
||||
Shares Needed to Zero
|
||||
|
||||
These expressions violate our curve rules from earlier. All elements cannot be negative.
|
||||
|
||||
[](https://preview.redd.it/1ctkekv0oh471.png?width=938&format=png&auto=webp&s=9c66d9b4480d5a16c79b715e709d08516d654862)
|
||||
|
||||
Da Rules
|
||||
|
||||
This seems to imply that if apes continue to BUY & HODL the price cannot go to zero. It is mathematically impossible.
|
||||
|
||||
*Negative Volume*
|
||||
|
||||
This is a connection I just made today, so I'll have to shoehorn it in here.
|
||||
|
||||
For the last several months, negative volume will show up in the data feeds for various apes. [This](https://www.reddit.com/r/Superstonk/comments/nwta9j/what_is_this_fuckery_can_anyone_explain_a/) is the most recent incident.
|
||||
|
||||
Now Dave Lauer did say that those were most likely end of the day rebalancing and whatnot, so I'm not suggesting anything tin foil-y.
|
||||
|
||||
My hypothesis is simply that the negative candle is the manifestation of the algo doing something based on these curves. I don't know the algo is doing and I don't know if it is nefarious or not. I def need wrinkle brain feedback here.
|
||||
|
||||
-----------------------------------------------------------------------------------------------------------------------------------------------------
|
||||
|
||||
F. The Final Volume
|
||||
|
||||
The final volume will be the shortest, but the juiciest. Based on what we've discussed, there may be a way to calculate how many shorted shares there are and find out the true short interest.
|
||||
|
||||
-----------------------------------------------------------------------------------------------------------------------------------------------------
|
||||
|
||||
TL:DR -> At this point, the number of shares needed to short $GME to zero does not mathematically exist.
|
||||
|
||||
TA:DR -> $GME only go up! Math say so!
|
||||
|
||||
--------------------------------------------------------------------------------------------------------------------------------------------------------
|
||||
|
||||
This post brought to you on behalf of Margery Nesbitt. Help her find Kenny, he isn't taking her calls for some reason...
|
||||
@ -0,0 +1,124 @@
|
||||
Math Black Magic Vol. 3: Trillion Short Share Seance
|
||||
====================================================
|
||||
|
||||
| Author | Source |
|
||||
| :-------------: |:-------------:|
|
||||
| [u/nydus_erdos](https://www.reddit.com/user/nydus_erdos/) | [Reddit](https://www.reddit.com/r/Superstonk/comments/nya5ps/math_black_magic_vol_3_trillion_short_share_seance/) |
|
||||
|
||||
---
|
||||
|
||||
[DD 👨🔬](https://www.reddit.com/r/Superstonk/search?q=flair_name%3A%22DD%20%F0%9F%91%A8%E2%80%8D%F0%9F%94%AC%22&restrict_sr=1)
|
||||
|
||||
DISCLAIMER: Third part of my first DD. Not financial advice. All credit to the authors of referenced works.
|
||||
|
||||
--------------------------------------------------------------------------------------------------------------------------------------------------------
|
||||
|
||||
ACKNOWLEDGEMENTS:
|
||||
|
||||
I'll also be using equations from [u/JTH1](https://www.reddit.com/u/JTH1/)'s (aka "exponential floor guy") works.
|
||||
|
||||
--------------------------------------------------------------------------------------------------------------------------------------------------------
|
||||
|
||||
A. Quick Review
|
||||
|
||||
In [Volume 1](https://www.reddit.com/r/Superstonk/comments/nw8281/math_black_magic_vol_1_why_it_is_mathematically/), I break down an academic finance paper by John Finnerty. In it, he mathematically proves that it's impossible to short a stock to zero without naked shorting AT LEAST as many shares as there are outstanding, doubling the float in the process.
|
||||
|
||||
In [Volume 2](https://www.reddit.com/r/Superstonk/comments/nwy0oz/math_black_magic_vol_2_the_limit_does_not_exist/), I lay out how I think apes fucked up hedgies' algos initially, make conjecture on rates of change in our exponential graphs and show (through Finnerty's theories) that, at this point, the number of shares needed to short $GME to zero does not mathematically exist.
|
||||
|
||||
--------------------------------------------------------------------------------------------------------------------------------------------------------
|
||||
|
||||
B. Goal of This Volume
|
||||
|
||||
So far we an equations that relate *P(t) to Q*
|
||||
|
||||
[](https://preview.redd.it/sbv13sumfu471.png?width=648&format=png&auto=webp&s=63e2d69f476bb6add74ff9a5081c3e681283356f)
|
||||
|
||||
Demand Curves
|
||||
|
||||
And equations that relate *P(t)* to *t*
|
||||
|
||||
[](https://preview.redd.it/j2vdkh7cgu471.png?width=521&format=png&auto=webp&s=f27f8d220bb288937c388e6d32e89f861d82401b)
|
||||
|
||||
Thanks to Exponential Floor Guy
|
||||
|
||||
My goal is to find an equation that can relate Q and t. That equation can possibly be used to find the real short interest.
|
||||
|
||||
--------------------------------------------------------------------------------------------------------------------------------------------------------
|
||||
|
||||
C. Hedgies' Curves
|
||||
|
||||
*Case 1*
|
||||
|
||||
The hedgies' curves are the second equation in each list. First, I tried setting them equal to each other:
|
||||
|
||||
[](https://preview.redd.it/8xr7dbtuiu471.png?width=1289&format=png&auto=webp&s=7ae5032792440214363242a29e88f9d59d687833)
|
||||
|
||||
No new information here
|
||||
|
||||
But, this doesn't really help me cause of I don't know *B*, so ~~I tried a little calculus~~ ~~did a little simple calculus~~ I had a math séance. Cover your eyes and skip to the next section if math horrifies you. I will begin the ritual with the traditional chant *ahem*
|
||||
|
||||
[](https://preview.redd.it/76u4fk2aku471.png?width=1048&format=png&auto=webp&s=207ca8ca3213db1948f54ce3883639064350a637)
|
||||
|
||||
Yu Mo Gui Gwai Fai Di Zao, Yu Mo Gui Gwai Fai Di Zao, Yu Mo Gui Gwai Fai Di Zao...
|
||||
|
||||
EDIT: I made a mistake in notation, the derivative of the linear equation should be taken with respect to Q (d/dQ). This will not change the answer as P(t) = D(Q)
|
||||
|
||||
Now that we've completed the ritual and the dark gods have gifted us an equation lets plot that bad boy and find the amount of shares:
|
||||
|
||||
[](https://preview.redd.it/co6mjaatlu471.png?width=952&format=png&auto=webp&s=1ef2e94f1ab30e25e3c5e1366ee1033573f589d2)
|
||||
|
||||
[](https://preview.redd.it/kiy1tob5nu471.png?width=974&format=png&auto=webp&s=fe08f2b2eebc2644acc7fd9d3868624224bdb58b)
|
||||
|
||||
1.4 TRILLION SHARES
|
||||
|
||||
*Case 2*
|
||||
|
||||
For such a huge number, I figured I should try the calculation again with a value of 40 dollars and see what I got:
|
||||
|
||||
[](https://preview.redd.it/b5bnuvhcou471.png?width=852&format=png&auto=webp&s=12a2acbd89881b3770b72f34efb9f842816bb6e7)
|
||||
|
||||
[](https://preview.redd.it/1sqnpp1gou471.png?width=934&format=png&auto=webp&s=f4d7b7039e64470915de0b656377fc3055f4a75d)
|
||||
|
||||
[](https://preview.redd.it/9wyb54dmou471.png?width=973&format=png&auto=webp&s=8c8b8016ce118d76979b89215db3a0ebb8fafe66)
|
||||
|
||||
116 BILLION SHARES
|
||||
|
||||
--------------------------------------------------------------------------------------------------------------------------------------------------------
|
||||
|
||||
D. Ape's Curves
|
||||
|
||||
I will now perform part two of the math séance, by repeating the process above for the ape curve:
|
||||
|
||||
[](https://preview.redd.it/ukba2075pu471.png?width=1007&format=png&auto=webp&s=d0f81c578fb481cab287a3fb4846cf9326f6062c)
|
||||
|
||||
[](https://preview.redd.it/fitnd4a8pu471.png?width=1036&format=png&auto=webp&s=47b616777fedf483dc2004b9108e6457b32e1cfc)
|
||||
|
||||
I Implore the Spirit of Isaac Newton, Aid Me In My Dark Deed...
|
||||
|
||||
Now this is what things get VERY interesting, check out that asymptote:
|
||||
|
||||
[](https://preview.redd.it/xdb6gd56qu471.png?width=871&format=png&auto=webp&s=6f34aa774b64c4ddbf0bc0b3161142ef0fe9ed36)
|
||||
|
||||
[](https://preview.redd.it/59673f2aqu471.png?width=1025&format=png&auto=webp&s=af9d1952760e62ad7324eb3ac0551141188dc258)
|
||||
|
||||
837 MILLION SHARES
|
||||
|
||||
I'm not sure what the asymptote implies or represents, but I feel that its significant.
|
||||
|
||||
--------------------------------------------------------------------------------------------------------------------------------------------------------
|
||||
|
||||
E. Conclusion
|
||||
|
||||
Thanks for coming to my APE Talk. Constructive criticism is always welcome!
|
||||
|
||||
TL:DR -> Hedgies have naked shorted, at most, about 1.4 trillion shares and, at least, about 837 million shares.
|
||||
|
||||
TA:DR -> Hedgies have pissed off math gods. Hedgies r fuk.
|
||||
|
||||
--------------------------------------------------------------------------------------------------------------------------------------------------------
|
||||
|
||||
F. Questions I Could Use Help With
|
||||
|
||||
- What does that asymptote represent? Is this when it no longer becomes possible for hedgies to dilute the float meaningfully? Is this the stalemate that occurs when the shares are being bought at higher rate?
|
||||
|
||||
- Have I calculated how many shares have been naked shorted or how many shares retail holds? The way Finnerty frames it, I believe the shares I calculate are the amount of shares naked shorted. However, the demand curve equation says it describes how many shares retail investors hold. I think it can describe both, but I'm sure what context the results of my calculations are in.
|
||||
@ -0,0 +1,68 @@
|
||||
Math Black Magic, Final Vol: Epilogue
|
||||
=====================================
|
||||
|
||||
| Author | Source |
|
||||
| :-------------: |:-------------:|
|
||||
| [u/nydus_erdos](https://www.reddit.com/user/nydus_erdos/) | [Reddit](https://www.reddit.com/r/Superstonk/comments/odrnbv/math_black_magic_final_vol_epilogue/) |
|
||||
|
||||
---
|
||||
|
||||
[DD 👨🔬](https://www.reddit.com/r/Superstonk/search?q=flair_name%3A%22DD%20%F0%9F%91%A8%E2%80%8D%F0%9F%94%AC%22&restrict_sr=1)
|
||||
|
||||
Not financial advice. All credit to the authors of cited works
|
||||
|
||||
THE PREVIOUS VOLUMES ARE ESSENTIAL TO UNDERSTANDING THIS POST: [Vol. 1](https://www.reddit.com/r/Superstonk/comments/nw8281/math_black_magic_vol_1_why_it_is_mathematically/), [Vol. 2](https://www.reddit.com/r/Superstonk/comments/nwy0oz/math_black_magic_vol_2_the_limit_does_not_exist/), [Vol. 3](https://www.reddit.com/r/Superstonk/comments/nya5ps/math_black_magic_vol_3_trillion_short_share_seance/)
|
||||
|
||||
----------------------------------------------------------------------------------------------------------------------------------------------------
|
||||
|
||||
1\. Quick Recap
|
||||
|
||||
In 2005, finance professor John Finnerty published a paper entitled: [Short Selling, Death Spiral Convertibles and the Profitability of Stock Manipulation](https://www.sec.gov/comments/s7-08-08/s70808-318.pdf). Using math and game theory he presents a model depicting a manipulated market. I covered the paper extensively in Vol. 1 and applied some of the concepts in Vol. 2 and 3 to try to estimate the total number of shares shorted. I stand by my methods, but they needed refinement. I reworked some things and I feel much more confident about my results here.
|
||||
|
||||
----------------------------------------------------------------------------------------------------------------------------------------------------
|
||||
|
||||
2\. Method
|
||||
|
||||
My methods are pretty much the same as last time, so this post will be relatively short and not so many graphs or derivations. There are nuances, but I'm saving most of them for the next series since they require a lot of background knowledge. If there's something that seems like I didn't explain fully, it'll be covered extensively later.
|
||||
|
||||
Using the pattern laid out earlier, I analyzed the largest drops I could find before the Sneeze, during the Sneeze, and after. I used Finnerty's formulas to calculate quantity of shares shorted and combined them with price data. Using data processing software, I ran several scenarios, based on Finnerty's model and choose the lowest reasonable answer based on past behavior and revealed data. Using all this I found cumulative SI.
|
||||
|
||||
I did not have an explicit control, however now that we have some idea of the real short interest stated in the recent Robinhood document, I used that data to calibrate the model. I also used an example referenced in the paper regarding a company called Charter Communications:
|
||||
|
||||
> "The NASD reported that Charter had short interest of 88,520,000 shares inJanuary 2005, but Charter reported having a float of only 36,600,000 shares."Pg. 45, footnote 66
|
||||
|
||||
That's about 2.4 times the float. I tried to find more info about Charter, but it seems like its hard to get any info about stocks pre-2010. Anyway, it gave me some reference point of what a highly shorted stock (at that point) looked like.
|
||||
|
||||
This model only goes from 10/30/15 to 4/12/2021. Past there I couldn't find any meaningful large drops. Since this model is still general, complexity is the enemy at this point. Future projects involve refining the model with more complexity in mind. Until then, I wouldn't feel confident in any answer I got from a smaller drop.
|
||||
|
||||
----------------------------------------------------------------------------------------------------------------------------------------------------
|
||||
|
||||
3\. Refined Results
|
||||
|
||||
As of 4/12/2021:
|
||||
|
||||
- Shitadel and Co. had cumulatively shorted approximately 3 billion shares
|
||||
|
||||
- The short interest was about 4,302 percent. That's 43 times shares outstanding.
|
||||
|
||||
- At current average daily volume (~7.6 million) that's 400 days to cover, which amounts to 1.6 trading years.
|
||||
|
||||
----------------------------------------------------------------------------------------------------------------------------------------------------
|
||||
|
||||
4\. What's Next
|
||||
|
||||
My next series will be titled *The Chronicles of Short and Shorter*. In order to write it I had to gain a deeper understanding of the concepts we've used. This led me to the most intense knowledge binge of my adult life: microeconomics. Holy fuck. What a blessed rabbit hole. This is the subject that's pretty much the basis for everything Finnerty wrote. As I am a veryyy autistic ape, it never occurred to me to try to find what the field was called. It allowed to me to take some of Finnerty's concepts further and answer some more questions. So, over the next series we'll:
|
||||
|
||||
- Go over some economic concepts
|
||||
|
||||
- Dissect Shitadel and Co.'s strategy and patterns of attack in the pre-Sneeze period, during the Sneeze and post-Sneeze period.
|
||||
|
||||
- Estimate Shitadel and Co.'s cost function
|
||||
|
||||
- Give my idea on what exponential floor guy's findings might be caused by
|
||||
|
||||
----------------------------------------------------------------------------------------------------------------------------------------------------
|
||||
|
||||
TL;DR ==> See section 3.
|
||||
|
||||
TA;DR ==> Math gods are still pissed at hedgies. Hedgies r still fuk.
|
||||
22
README.md
22
README.md
@ -16,8 +16,21 @@ This repository of GME-related content and relevant information serves two prima
|
||||
|
||||
> Please note most if not all of this content is not my own. All authors and sources are linked at the top of each file, and I encourage you to read the content via the source. There are a lot of intelligent apes who spent copious amounts of time doing their research and deserve your upvote!
|
||||
|
||||
## How to Help
|
||||
Can't find content in wikAPEdia that you think should be archived? Don't hesitate to reach out to me on [Reddit](https://www.reddit.com/user/Meticulous-)!
|
||||
---
|
||||
|
||||
## Key Features
|
||||
|
||||
### Search by Title
|
||||
|
||||
|
||||
### Search by Date
|
||||
|
||||
|
||||
### Browse by Theme
|
||||
|
||||
|
||||
### Save a Copy for Yourself
|
||||
|
||||
|
||||
---
|
||||
|
||||
@ -39,7 +52,7 @@ _Check out the [Must-Read](https://github.com/verymeticulous/wikAPEdia/tree/main
|
||||
|
||||
---
|
||||
|
||||
## Some People to Look Out For by [u/zedinstead](https://www.reddit.com/u/zedinstead/)
|
||||
## 🦍 Some People to Look Out For by [u/zedinstead](https://www.reddit.com/u/zedinstead/) 🦍
|
||||
|
||||
|
||||
*Banner created by [GameStop](https://twitter.com/GameStop?ref_src=twsrc%5Egoogle%7Ctwcamp%5Eserp%7Ctwgr%5Eauthor)*
|
||||
@ -106,6 +119,9 @@ Quant guy 2 - [u/myplayprofile](https://www.reddit.com/u/myplayprofile/)
|
||||
|
||||
---
|
||||
|
||||
## 🆘 How to Help 🆘
|
||||
Can't find content in wikAPEdia that you think should be archived? Don't hesitate to reach out to me on [Reddit](https://www.reddit.com/user/Meticulous-)!
|
||||
|
||||
### Buy, Hodl, ~~Vote~~ 💎🙌
|
||||
|
||||
|
||||
|
||||
Reference in New Issue
Block a user