My Math Forum  

Go Back   My Math Forum > High School Math Forum > Algebra

Algebra Pre-Algebra and Basic Algebra Math Forum


Reply
 
LinkBack Thread Tools Display Modes
December 28th, 2018, 08:08 AM   #1
Newbie
 
Joined: Dec 2018
From: UK

Posts: 3
Thanks: 0

Shares break-even point question

I’ve posted this here as I’m sure it’s an algebra problem and it's driving me nuts.

I want to calculate the break-even point of 2 positions via a formula.

For example if I have a long position of (+ 5) @ 1261 and a short position of (- 3) @ 1251

What is the easiest way of calculating break-even point if the market keeps trending up?
I know the answer is 1276 ,as I’ve plotted it manually, but just can figure it out via calculation.
It has to do with the ratio of the size which is 1.66

Any insight would be much appreciated.
Anton Chigurh is offline  
 
December 28th, 2018, 02:15 PM   #2
Senior Member
 
Joined: May 2016
From: USA

Posts: 1,310
Thanks: 551

Quote:
Originally Posted by Anton Chigurh View Post
I’ve posted this here as I’m sure it’s an algebra problem and it's driving me nuts.

I want to calculate the break-even point of 2 positions via a formula.

For example if I have a long position of (+ 5) @ 1261 and a short position of (- 3) @ 1251

What is the easiest way of calculating break-even point if the market keeps trending up?
I know the answer is 1276 ,as I’ve plotted it manually, but just can figure it out via calculation.
It has to do with the ratio of the size which is 1.66

Any insight would be much appreciated.
$p = \text {break even price.}.$

$5(p - 1261) + 3(1251 - p) = 0 \implies 5p - 6305 + 3753 - 3p = 0 \implies$

$2p = 6305 - 3753 = 2552 \implies p = 1276.$
JeffM1 is offline  
December 29th, 2018, 02:04 AM   #3
Newbie
 
Joined: Dec 2018
From: UK

Posts: 3
Thanks: 0

Quote:
Originally Posted by JeffM1 View Post
$p = \text {break even price.}.$

$5(p - 1261) + 3(1251 - p) = 0 \implies 5p - 6305 + 3753 - 3p = 0 \implies$

$2p = 6305 - 3753 = 2552 \implies p = 1276.$
Thank you so much for your time JeffM1

This is great and does solve that problem, but there seems to be a variable missing.

For example, if I have +8@1261 and -5@1251 using this calculation does not work out:

2p = 10088 - 6225 = p = 1931.5
Anton Chigurh is offline  
December 29th, 2018, 05:39 AM   #4
Senior Member
 
Joined: May 2016
From: USA

Posts: 1,310
Thanks: 551

Quote:
Originally Posted by Anton Chigurh View Post
Thank you so much for your time JeffM1

This is great and does solve that problem, but there seems to be a variable missing.

For example, if I have +8@1261 and -5@1251 using this calculation does not work out:

2p = 10088 - 6225 = p = 1931.5
That is because, in your second case, the difference in shares long and shares short is 3, not 2. That is why I worked out your first example: understanding the logic behind a formula is far more important than memorizing a formula. Formulas that are not understood are dangerous because they frequently are misused.

$8(p - 1261) = \text { realized gain (or loss) on } 8 \text { shares long.}$

$5(1251 - p) = \text { realized gain (or loss) on } 5 \text { shares short.}$

$\therefore 8(p - 1261) + 5(1251 - p) = 0 \implies 8p - 10088 + 6255 - 5p = 0 \implies$

$8p - 5p = 10088 - 6255 \implies 3p = 3833 \implies p =1277 \text { and } \dfrac{2}{3}.$

Does that work out?

$8 \left ( 1277 + \dfrac{2}{3} - 1261 \right ) = 8 * \left ( 16 + \dfrac{2}{3} \right ) = 128 + \dfrac{16}{3} = 133 + \dfrac{1}{3}.$

$5 \left ( 1251 - \left \{ 1277 + \dfrac{2}{3} \right \} \right ) = -\ 5 * \left ( 26 + \dfrac{2}{3} \right ) = -\ \left ( 130 + \dfrac{10}{3} \right ) = -\ \left ( 133 + \dfrac{1}{3} \right ).$

Yes, that works exactly. In practice, of course, it may not be possible to achieve the exact breakeven price due to fractions.

The general formula is as follows:

$q = \text { purchase price on long transaction;}$

$r = \text { sales price on short transaction;}$

$m = \text { number of shares long;}$

$n = \text { number of shares short; and}$

$p = \text { breakeven price.}$

$m = n \text { and } q \ne r \implies p \text { does not exist.}$

$m = n \text { and } q = r \implies p \text { is anything.}$

$m \ne n \implies p = \dfrac{mq - nr}{m - n}.$

To derive the last:

$m(p - q) + n(r - p) = 0 \implies mp - mq + nr - np = 0 \implies mp - np = mq - nr \implies$

$p =\dfrac{mq - nr}{m - n}.$
JeffM1 is offline  
December 30th, 2018, 08:48 AM   #5
Newbie
 
Joined: Dec 2018
From: UK

Posts: 3
Thanks: 0

Ah of course. I feel so stupid. Thank you so much for this.

Sent you a PM.

Last edited by skipjack; February 4th, 2019 at 12:02 AM.
Anton Chigurh is offline  
Reply

  My Math Forum > High School Math Forum > Algebra

Tags
breakeven, point, question, shares



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
optimal number of shares get42n8 Algebra 6 January 5th, 2015 11:21 AM
Break Even Point Calculation sarathpillai Applied Math 0 July 24th, 2013 04:37 AM
Selling shares tintin00 Algebra 1 April 15th, 2011 11:04 PM
Break Even point... gr3gg0r Applied Math 6 December 14th, 2007 05:56 AM





Copyright © 2019 My Math Forum. All rights reserved.