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Offline nomoreheroes7

Newbie Shorting Questions
« on: September 19, 2014, 06:03:19 PM »

Hi all,

When shorting, am I right in thinking that theoretically the best you can do is come close to doubling your BTSX? Say I have 5,000 BTSX and short all of it at a given price (say 30 BTSX/BitUSD, so a short of $166.66 BitUSD), and BTSX someday soars to $10 per BTSX (0.1 BTSX/USD), would I then be able to cover with only 16.66 BTSX, netting me 5,000 BTSX held as collateral + 4,983.34 BTSX released from the short = 9,983.34 BTSX?

Also, I think I'm getting confused by the collateral part -- if I have 5,000 BTSX, can I short this full amount, or can I only short half of it because the other half is needed to cover collateral?

Appreciate any input.

Offline Riverhead

Re: Newbie Shorting Questions
« Reply #1 on: September 19, 2014, 06:30:29 PM »
Here's how I think of it...I also want to know if I have it correct as I feel I'm just barely grasping it.

To answer the OP: You don't short BTSX you short bitUSD. You'd be able to short up to 2500 BTSX worth of bitUSD (assuming no transaction fees). At market prices that'd be about 80 bitUSD.

Now for my scenario question :) . Is this explanation correct?

Shorting bitUSD is like getting a car loan. You borrow 10 bitUSD from the bank and put 20 bitUSD worth of BTSX up as collateral which is currently about 625 BTSX at $0.032 bitUSD/BTSX.

You sell the car bitUSD for 10 bitUSD worth of BTSX (this is the actual short, the 10 bitUSD is minted and you now are in debt to the bank and have 312.5 BTSX from the sale of the bitUSD they just lent you).

At some point in the future when you want to pay the bank the back you need to come up with 10 bitUSD. You either already have it or you need to buy it on the open market. Assume BTSX goes to 10 bitUSD/BTSX. You can buy 10 bitUSD on the open market for 1 BTSX.

« Last Edit: September 19, 2014, 11:10:32 PM by Riverhead »

Offline tonyk

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Re: Newbie Shorting Questions
« Reply #2 on: September 19, 2014, 06:38:26 PM »
Here's how I think of it...I also want to know if I have it correct as I feel I'm just barely grasping it.

To answer the OP: You don't short BTSX you short bitUSD. You'd be able to short up to 2500 BTSX worth of bitUSD (assuming no transaction fees). At market prices that'd be about 80 bitUSD.

Now for my scenario question :) .

Shorting bitUSD is like getting a car loan. You borrow 10 bitUSD from the bank and put 20 bitUSD worth of BTSX up as collateral which is currently about 625 BTSX at $0.032 bitUSD/BTSX.

You sell the car bitUSD for 10 bitUSD worth of BTSX (this is the actual short, the 10 bitUSD is minted and you now are in debt to the bank and have 312.5 BTSX from the sale of the bitUSD they just lent you).

At some point in the future when you want to pay the bank the back you need to come up with 10 bitUSD. You either already have it or you need to buy it on the open market. Assume BTSX goes to 10 bitUSD/BTSX. You can buy 10 bitUSD on the open market for 1 BTSX.

End Result: You borrowed 10 bitUSD and sold it for 312.5 BTSX and tied up 625 BTSX in the process as colllateral. Now that you've covered you get your 625 BTSX collateral back plus the 312 BTSX from the original sale. So for the cost of 1 BTSX you made 312.5 BTSX, a profit of 311.5 BTSX or just over 30,000%.

I like this one better : https://bitsharestalk.org/index.php?topic=8390.msg115336#msg115336
i.e. leave the profit calculation out of it. Especially in, this case, as one can argue how/what is the correct way to do it.
.0002BTSX
Lack of arbitrage is the problem, isn't it. And this 'should' solves it.

Offline nomoreheroes7

Re: Newbie Shorting Questions
« Reply #3 on: September 19, 2014, 06:45:44 PM »
I think I'm starting to understand a bit better...so in that case, the best you can really do is increase your BTSX holding by close to 50%? The part that's really confusing me is the double amount needed as collateral. If I were to short with say 2495 worth of BTSX in the original example, when the short is sold does that mean the other 2495 I'm still holding will immediately get locked as collateral? And if that's the case, what if I put a short order worth 4,995 instead? Where would the extra collateral come from? I've tried making a high short order with my entire wallet balance, and it seems to go to market ok. Sorry if I'm making any of this harder than it should be...

Offline arhag

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Re: Newbie Shorting Questions
« Reply #4 on: September 19, 2014, 07:42:06 PM »
Math time! Let's generalize this with algebra rather than using specific numbers. Note that this may not be super accurate with the recent changes to the market rules regarding shorts prioritized by collateral.

I want to short x BitUSD at a price of p1 BTSX per BitUSD. I provide m BTSX margin as part of the collateral. This means if my short is fully matched, there will be c = (p1 * x + m) BTSX held in collateral in the short position which owes the network x BitUSD. Now let's say the price of BTSX changes and I want to cover. I purchase x BitUSD at a new price of p2 BTSX per BitUSD (meaning I pay p2 * x BTSX). I use the x BitUSD to cover my short position and that gives me the c BTSX held in collateral. I originally had (m + p2 * x) BTSX in my possession, now I have (p1 * x + m) BTSX in my possession. The net change in BTSX through this process is (p1 - p2) * x BTSX.

I had to keep some amount of BTSX sitting around in order to do this short. I had m BTSX locked up in collateral that I could not touch. But I also had to keep some amount of BTSX around to buy BitUSD to cover; I will define this amount to be s * p1 * x BTSX. Let us say I was fairly confident in the value of BTSX rising with respect to BitUSD. In that case I would be fine with s = 1 since it would be more than the p2 * x BTSX needed to buy the BitUSD to cover. If I want to be more conservative, I should choose s > 1, so that I can afford to cover if the value of BTSX with respect to BitUSD falls. The largest value of s should be (1 + m/(p1*x))/1.5, since if p2 rises high enough that I would need even more BTSX than that to buy BitUSD it would already be too late (the network would do a margin call since the collateral would become less than 150% of the value of the BitUSD debt owed). If BitShares X was modified to allow shorts to cover by bidding for BitUSD on the exchange, I wouldn't need to hold any extra BTSX (meaning s = 0). Whatever my choice, we can claim that I have (m + s * p1 * x) sitting around for the purposes of gaining from my short position. If the value of BTSX does rise with respect to BitUSD (meaning p2 < p1), then in terms of the fractional gain relative to the amount of BTSX I had to hold I gain f = [(p1-p2)*x]/[m + s*p1*x] = [1 - p2/p1]/[m/(p1*x) + s].

Let's define r to be the fractional increase over this period in the price of BTSX in terms of BitUSD. The price of BTSX was first 1/p1 BitUSD and then later became 1/p2 BitUSD. Therefore, r = (1/p2 - 1/p1)/(1/p1) = p1/p2 - 1. I can use this to simplify f above: f = r/[(1+r) * (s + m/(p1*x)]. Let's take the very conservative estimate for s, just to simplify the variables a little more: f = r/[(1+r) * ((2/3) + (5/3) * (m/(p1*x)))]. Finally, let us assume that you can get your short matched at the bare minimum collateral so that we can replace m/(p1*x) with 1. Then f = (3*r)/(7*(1+r)).

And there you have it. Under the above assumptions, if I short and the price of BTSX goes up by 10%, I can cover and increase my BTSX holdings by up to 3.9% (f = (3*0.1)/(7*(1+0.1)) = 0.03896). Notice that even if the value of the dollar drops to zero (meaning r approaches infinity), I can still only increase my BTSX holdings by up to 43% (again assuming I am using the more conservative assumption above).


I would really appreciate it if someone checks my math for errors.

Exercise for the reader :): Given an average steady rate of increase, a, in the price of BTSX with respect to BitUSD (or USD), what is my return on investment with compounding (meaning I short, cover, use gained BTSX to short again, repeat) as a function of a regular short-cover time period T (assuming the price at the moment of each short/cover instance falls on the average steady increase curve)? Solve for both linear and exponential growth curves.
« Last Edit: September 19, 2014, 08:08:24 PM by arhag »

Offline bytemaster

Re: Newbie Shorting Questions
« Reply #5 on: September 19, 2014, 09:53:08 PM »
If you cover and re short you can compound your gains.  In theory you should do this as often as possible. 
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Anything said on these forums does not constitute an intent to create a legal obligation or contract between myself and anyone else.   These are merely my opinions and I reserve the right to change them at any time.

Offline tonyk

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Re: Newbie Shorting Questions
« Reply #6 on: September 19, 2014, 10:23:03 PM »
@arhag
I can complicate your math if you want me to:
1. What BM said
2.Add transaction cost in point 1.
3.'Let us say I was fairly confident in the value of BTSX rising with respect to BitUSD. In that case I would be fine with s = 1 since it would be more than the p2 * x BTSX needed to buy the BitUSD to cover'
You can do just fine with S<1; Question for you - why?
Lack of arbitrage is the problem, isn't it. And this 'should' solves it.

Offline arhag

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Re: Newbie Shorting Questions
« Reply #7 on: September 19, 2014, 10:38:40 PM »
@arhag
I can complicate your math if you want me to:
1. What BM said
2.Add transaction cost in point 1.
Sounds fun. So... where is the work?  :)

3.'Let us say I was fairly confident in the value of BTSX rising with respect to BitUSD. In that case I would be fine with s = 1 since it would be more than the p2 * x BTSX needed to buy the BitUSD to cover'
You can do just fine with S<1; Question for you - why?
Yes, you can get away with s < 1, I was just still being conservative. You would have to predict not only that the value will go up but by how much it will go up to determine what value of s < 1 is acceptable. If you undershoot on s, you gotta liquidate other investments, get a loan, beg people for money, etc. to be able to cover the short. The math would be simpler if BitShares X just let us cover with a bid (s = 0). Then again, in my opinion it is already pretty damn gutsy to short more than half of your BTSX stake.

Edit: BTW, I named the variable s for sanity. Because if your s goes to 0, then you must have lost your sanity. :D
« Last Edit: September 19, 2014, 10:49:55 PM by arhag »

Offline tonyk

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Re: Newbie Shorting Questions
« Reply #8 on: September 19, 2014, 10:52:21 PM »
@arhag
I can complicate your math if you want me to:
1. What BM said
2.Add transaction cost in point 1.
Sounds fun. So... where is the work?  :)

You are the math guy - give us the formula! - best investment strategy with fee f and increase I

3.'Let us say I was fairly confident in the value of BTSX rising with respect to BitUSD. In that case I would be fine with s = 1 since it would be more than the p2 * x BTSX needed to buy the BitUSD to cover'
You can do just fine with S<1; Question for you - why?
Yes, you can get away with s < 1, I was just still being conservative. You would have to predict not only that the value will go up but by how much it will go up to determine what value of s < 1 is acceptable. If you undershoot on s, you gotta liquidate other investments, get a loan, beg people for money, etc. to be able to cover the short. The math would be simpler if BitShares X just let us cover with a bid (s = 0). Then again, in my opinion it is already pretty damn gutsy to short more than half of your BTSX stake.
No, the value of BTSX (USD) stays the same...and you do not put extra money (from other sources) in.
« Last Edit: September 19, 2014, 10:55:29 PM by tonyk »
Lack of arbitrage is the problem, isn't it. And this 'should' solves it.

Offline Riverhead

Re: Newbie Shorting Questions
« Reply #9 on: September 19, 2014, 11:12:04 PM »
I like this one better : https://bitsharestalk.org/index.php?topic=8390.msg115336#msg115336
i.e. leave the profit calculation out of it. Especially in, this case, as one can argue how/what is the correct way to do it.
.0002BTSX


Ya, it was clearer. I deleted the profit stuff (still a gray area for me).

Offline Riverhead

Re: Newbie Shorting Questions
« Reply #10 on: September 19, 2014, 11:13:17 PM »
I think I'm starting to understand a bit better...so in that case, the best you can really do is increase your BTSX holding by close to 50%? The part that's really confusing me is the double amount needed as collateral. If I were to short with say 2495 worth of BTSX in the original example, when the short is sold does that mean the other 2495 I'm still holding will immediately get locked as collateral? And if that's the case, what if I put a short order worth 4,995 instead? Where would the extra collateral come from? I've tried making a high short order with my entire wallet balance, and it seems to go to market ok. Sorry if I'm making any of this harder than it should be...


That's exactly what it means.


Offline nomoreheroes7

Re: Newbie Shorting Questions
« Reply #11 on: September 20, 2014, 12:50:57 AM »
If you cover and re short you can compound your gains.  In theory you should do this as often as possible.

Wow bm, I never would've thought of that! So it's like buying low and selling high...only in reverse: shorting high then covering low, right? That's pretty awesome.

Arhag: I appreciate the math lesson, but I'll be damned if I understand a word you're saying lol. Appreciate the input; hopefully it helps others who are more math inclined.

Thanks all for your input! But I'm still curious what would happen if I were to try shorting my entire wallet balance...the order goes to market, but there wouldn't be enough collateral to support it...would the order just not place or something?

Offline jernau

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Re: Newbie Shorting Questions
« Reply #12 on: September 20, 2014, 06:05:41 AM »
Math time! Let's generalize this with algebra rather than using specific numbers. Note that this may not be super accurate with the recent changes to the market rules regarding shorts prioritized by collateral.

I want to short x BitUSD at a price of p1 BTSX per BitUSD. I provide m BTSX margin as part of the collateral. This means if my short is fully matched, there will be c = (p1 * x + m) BTSX held in collateral in the short position which owes the network x BitUSD. Now let's say the price of BTSX changes and I want to cover. I purchase x BitUSD at a new price of p2 BTSX per BitUSD (meaning I pay p2 * x BTSX). I use the x BitUSD to cover my short position and that gives me the c BTSX held in collateral. I originally had (m + p2 * x) BTSX in my possession, now I have (p1 * x + m) BTSX in my possession. The net change in BTSX through this process is (p1 - p2) * x BTSX.

I had to keep some amount of BTSX sitting around in order to do this short. I had m BTSX locked up in collateral that I could not touch. But I also had to keep some amount of BTSX around to buy BitUSD to cover; I will define this amount to be s * p1 * x BTSX. Let us say I was fairly confident in the value of BTSX rising with respect to BitUSD. In that case I would be fine with s = 1 since it would be more than the p2 * x BTSX needed to buy the BitUSD to cover. If I want to be more conservative, I should choose s > 1, so that I can afford to cover if the value of BTSX with respect to BitUSD falls. The largest value of s should be (1 + m/(p1*x))/1.5, since if p2 rises high enough that I would need even more BTSX than that to buy BitUSD it would already be too late (the network would do a margin call since the collateral would become less than 150% of the value of the BitUSD debt owed). If BitShares X was modified to allow shorts to cover by bidding for BitUSD on the exchange, I wouldn't need to hold any extra BTSX (meaning s = 0). Whatever my choice, we can claim that I have (m + s * p1 * x) sitting around for the purposes of gaining from my short position. If the value of BTSX does rise with respect to BitUSD (meaning p2 < p1), then in terms of the fractional gain relative to the amount of BTSX I had to hold I gain f = [(p1-p2)*x]/[m + s*p1*x] = [1 - p2/p1]/[m/(p1*x) + s].

Let's define r to be the fractional increase over this period in the price of BTSX in terms of BitUSD. The price of BTSX was first 1/p1 BitUSD and then later became 1/p2 BitUSD. Therefore, r = (1/p2 - 1/p1)/(1/p1) = p1/p2 - 1. I can use this to simplify f above: f = r/[(1+r) * (s + m/(p1*x)]. Let's take the very conservative estimate for s, just to simplify the variables a little more: f = r/[(1+r) * ((2/3) + (5/3) * (m/(p1*x)))]. Finally, let us assume that you can get your short matched at the bare minimum collateral so that we can replace m/(p1*x) with 1. Then f = (3*r)/(7*(1+r)).

And there you have it. Under the above assumptions, if I short and the price of BTSX goes up by 10%, I can cover and increase my BTSX holdings by up to 3.9% (f = (3*0.1)/(7*(1+0.1)) = 0.03896). Notice that even if the value of the dollar drops to zero (meaning r approaches infinity), I can still only increase my BTSX holdings by up to 43% (again assuming I am using the more conservative assumption above).


I would really appreciate it if someone checks my math for errors.

Exercise for the reader :): Given an average steady rate of increase, a, in the price of BTSX with respect to BitUSD (or USD), what is my return on investment with compounding (meaning I short, cover, use gained BTSX to short again, repeat) as a function of a regular short-cover time period T (assuming the price at the moment of each short/cover instance falls on the average steady increase curve)? Solve for both linear and exponential growth curves.
This is really good. Thank you. I've been looking for a more rigour. I appreciate the generality. You should put this on the wiki. I'm sure I'm not the only one looking for this.
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Tuck Fheman

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Re: Newbie Shorting Questions
« Reply #13 on: September 20, 2014, 06:34:56 AM »
ELI5 version ...


Offline tonyk

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Re: Newbie Shorting Questions
« Reply #14 on: September 20, 2014, 06:51:07 AM »
Lack of arbitrage is the problem, isn't it. And this 'should' solves it.

 

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