Math Black Magic Vol. 3: Trillion Short Share Seance
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| 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/) | 

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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)

DISCLAIMER: Third part of my first DD. Not financial advice. All credit to the authors of referenced works.

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ACKNOWLEDGEMENTS:

I'll also be using equations from [u/JTH1](https://www.reddit.com/u/JTH1/)'s (aka "exponential floor guy") works.

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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.

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B. Goal of This Volume

So far we an equations that relate *P(t) to Q*

[![r/Superstonk - Math Black Magic Vol. 3: Trillion Short Share Seance](https://preview.redd.it/sbv13sumfu471.png?width=648&format=png&auto=webp&s=63e2d69f476bb6add74ff9a5081c3e681283356f)](https://preview.redd.it/sbv13sumfu471.png?width=648&format=png&auto=webp&s=63e2d69f476bb6add74ff9a5081c3e681283356f)

Demand Curves

And equations that relate *P(t)* to *t*

[![r/Superstonk - Math Black Magic Vol. 3: Trillion Short Share Seance](https://preview.redd.it/j2vdkh7cgu471.png?width=521&format=png&auto=webp&s=f27f8d220bb288937c388e6d32e89f861d82401b)](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.

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C. Hedgies' Curves

*Case 1*

The hedgies' curves are the second equation in each list. First, I tried setting them equal to each other:

[![r/Superstonk - Math Black Magic Vol. 3: Trillion Short Share Seance](https://preview.redd.it/8xr7dbtuiu471.png?width=1289&format=png&auto=webp&s=7ae5032792440214363242a29e88f9d59d687833)](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*

[![r/Superstonk - Math Black Magic Vol. 3: Trillion Short Share Seance](https://preview.redd.it/76u4fk2aku471.png?width=1048&format=png&auto=webp&s=207ca8ca3213db1948f54ce3883639064350a637)](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:

[![r/Superstonk - Math Black Magic Vol. 3: Trillion Short Share Seance](https://preview.redd.it/co6mjaatlu471.png?width=952&format=png&auto=webp&s=1ef2e94f1ab30e25e3c5e1366ee1033573f589d2)](https://preview.redd.it/co6mjaatlu471.png?width=952&format=png&auto=webp&s=1ef2e94f1ab30e25e3c5e1366ee1033573f589d2)

[![r/Superstonk - Math Black Magic Vol. 3: Trillion Short Share Seance](https://preview.redd.it/kiy1tob5nu471.png?width=974&format=png&auto=webp&s=fe08f2b2eebc2644acc7fd9d3868624224bdb58b)](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:

[![r/Superstonk - Math Black Magic Vol. 3: Trillion Short Share Seance](https://preview.redd.it/b5bnuvhcou471.png?width=852&format=png&auto=webp&s=12a2acbd89881b3770b72f34efb9f842816bb6e7)](https://preview.redd.it/b5bnuvhcou471.png?width=852&format=png&auto=webp&s=12a2acbd89881b3770b72f34efb9f842816bb6e7)

[![r/Superstonk - Math Black Magic Vol. 3: Trillion Short Share Seance](https://preview.redd.it/1sqnpp1gou471.png?width=934&format=png&auto=webp&s=f4d7b7039e64470915de0b656377fc3055f4a75d)](https://preview.redd.it/1sqnpp1gou471.png?width=934&format=png&auto=webp&s=f4d7b7039e64470915de0b656377fc3055f4a75d)

[![r/Superstonk - Math Black Magic Vol. 3: Trillion Short Share Seance](https://preview.redd.it/9wyb54dmou471.png?width=973&format=png&auto=webp&s=8c8b8016ce118d76979b89215db3a0ebb8fafe66)](https://preview.redd.it/9wyb54dmou471.png?width=973&format=png&auto=webp&s=8c8b8016ce118d76979b89215db3a0ebb8fafe66)

116 BILLION SHARES

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D. Ape's Curves

I will now perform part two of the math séance, by repeating the process above for the ape curve:

[![r/Superstonk - Math Black Magic Vol. 3: Trillion Short Share Seance](https://preview.redd.it/ukba2075pu471.png?width=1007&format=png&auto=webp&s=d0f81c578fb481cab287a3fb4846cf9326f6062c)](https://preview.redd.it/ukba2075pu471.png?width=1007&format=png&auto=webp&s=d0f81c578fb481cab287a3fb4846cf9326f6062c)

[![r/Superstonk - Math Black Magic Vol. 3: Trillion Short Share Seance](https://preview.redd.it/fitnd4a8pu471.png?width=1036&format=png&auto=webp&s=47b616777fedf483dc2004b9108e6457b32e1cfc)](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:

[![r/Superstonk - Math Black Magic Vol. 3: Trillion Short Share Seance](https://preview.redd.it/xdb6gd56qu471.png?width=871&format=png&auto=webp&s=6f34aa774b64c4ddbf0bc0b3161142ef0fe9ed36)](https://preview.redd.it/xdb6gd56qu471.png?width=871&format=png&auto=webp&s=6f34aa774b64c4ddbf0bc0b3161142ef0fe9ed36)

[![r/Superstonk - Math Black Magic Vol. 3: Trillion Short Share Seance](https://preview.redd.it/59673f2aqu471.png?width=1025&format=png&auto=webp&s=af9d1952760e62ad7324eb3ac0551141188dc258)](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.

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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.

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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.
