Shares break-even point question

Dec 2018
3
0
UK
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.
 
May 2016
1,310
551
USA
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.
$p = \text {break even price.}.$

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

$2p = 6305 - 3753 = 2552 \implies p = 1276.$
 
Dec 2018
3
0
UK
$p = \text {break even price.}.$

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

$2p = 6305 - 3753 = 2552 \implies p = 1276.$
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 [email protected] and [email protected] using this calculation does not work out:

2p = 10088 - 6225 = p = 1931.5
 
May 2016
1,310
551
USA
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 [email protected] and [email protected] 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:

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

$p =\dfrac{mq - nr}{m - n}.$
 
Dec 2018
3
0
UK
Ah of course. I feel so stupid. Thank you so much for this.

Sent you a PM.
 
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