# Maths Question



## Chorlton (10 March 2011)

Hello All,

If there is anyone on here who is relatively good with maths and more specifically maths equations can they please PM me.

I am trying to work out a maths problem with regard to how many shares I need to sell in order to recoup my original money after paying tax.

I will go into more detail if someone can help me out. 

I've been working on it for a while with no luck 


Thanks in advance,
Chorlton


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## zzaaxxss3401 (10 March 2011)

Send me a private message if you like.

It depends on a number of factors including your tax rate (for CGT purposes), length of time held and whether there have been any capital raisings which you have participated in. I have a spread sheet that works it all out for me (well the tax part anyway) for each of my tax years... need to keep good records incase of an audit.


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## howardbandy (10 March 2011)

Hi Chorlton --

Does it help to put all the information you know, estimates for the items you don't know, and formulas that relate the items, in a spreadsheet.  Then change the values of the estimates until the equations balance.  Excel has "Solver" that acts as a goal seeking tool that might do the changing for for you.

Thanks,
Howard


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## Chorlton (10 March 2011)

howardbandy said:


> Hi Chorlton --
> 
> Does it help to put all the information you know, estimates for the items you don't know, and formulas that relate the items, in a spreadsheet.  Then change the values of the estimates until the equations balance.  Excel has "Solver" that acts as a goal seeking tool that might do the changing for for you.
> 
> ...




Hi Howard,

Hope life is treating you well. 

As a quick side note, I recently received your email about your latest book offering. Based of the quality of your last 2 books, I intend to get it ordered online before the weekend. I'm especially interested in your chapter about knowing when a system is broken as that is a question that I have asked before and have never received a satisfactory answer to.

Anyway, back to my problem:

Basically, what I want to do is to input the share price that I want to sell at and for the formula to tell me how many shares to sell so as to recoup my original investment after tax

Normally, if I knew in advance how many shares to sell I would do the following: (As a side note, for this example I am ignoring the reduction in tax rule if I hold the stock for over 1yr)

INPUT: # shares currently held [A]
INPUT: The original cost of purchasing these shares *
INPUT: My Tax Rate [C]
INPUT: The Sell price [D]
INPUT: # Shares to Sell [E]

OUTPUT: Net Return (after Tax)

Calcs:

Cost Base [F] = ( [E] / [A] ) * 

Consideration [G] = [D] * [E]

Tax to Pay [H] = ( [G] - [F] ) * [C]

Net Return  = [G] - [H]

--------------------------------


However, with regard to my particular maths problem I already know what the Net Return  is (as it is meant to equal the amount I original invested  ) but want I want to know is how many shares to sell to achieve this figure.

In other words, my inputs & outputs would be:

INPUT: # shares currently held [A]
INPUT: The original cost of purchasing these shares 
INPUT: My Tax Rate [C]
INPUT: The Sell price [D]
INPUT: Net Return (after Tax)

OUTPUT: # Shares to Sell [E]


I'm trying to create a formula to work this out but am getting stuck. If anyone can help in any way that would be excellent.

Chorlton*


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## burglar (10 March 2011)

Chorlton said:


> Chorlton





He doesn't include CGT, perhaps he is a citizen of the U.S.
http://thepatternsite.com/ZeroCostAverage.html


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## white_crane (10 March 2011)

An easier way is to ignore tax and just work out the number of shares you need to sell in order to cover your costs.  What is left over is all profit and will be taxed accordingly when you sell.

Until you sell for a profit, you don't pay tax.  Since you don't know when you are going to sell the rest of the shares, you won't know how much tax you are going to pay.

To work out the number of shares to sell to cover costs:

sb = shares bought
pp = purchase price per share
br = brokerage

ss = shares to sell
sp = sell price per share

therefore...
ss = (sb * pp + 2br) / sp


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## zzaaxxss3401 (10 March 2011)

Put simply, I'm assuming you're trying to work out the free carry point (correct term?). Meaning, when a share hits a particular price, how many shares can you afford to sell to recoup your initial investment - the remaining shares can continue to gain in price and will be pure profit (before CGT).

Here's a spreadsheet I've modified. It includes brokerage costs, CGT discounts for shares held more than 12 months and using the Goal Seek function should work it out for you... I've plugged in a couple of prices / dates and it seems to work. Let me know.

Just create a new spreadsheet with the labels on the left, the values in the next column and the formulas (where applicable) in column "B" are detailed in the "D" column. Good luck.


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## skc (10 March 2011)

Chorlton said:


> Anyway, back to my problem:
> 
> Basically, what I want to do is to input the share price that I want to sell at and for the formula to tell me how many shares to sell so as to recoup my original investment after tax
> 
> ...



_*

E = [A * B] / [D - (D-B)*C]

To think of it another way... [D - (D-B)*C] is how much per share you can clear after tax. So [E] is simply your total cost base [A * B] over that.

Probably around year 10 algebra level *_


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## Chorlton (10 March 2011)

Thanks to everyone who offered their help. Problem now fixed !!!


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## Gringotts Bank (13 April 2012)

If a system has an average win of 0.5%, and an average loss of 5%, what % of trades need to be winners for the system to break even?


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## skc (13 April 2012)

Gringotts Bank said:


> If a system has an average win of 0.5%, and an average loss of 5%, what % of trades need to be winners for the system to break even?




0 = win% x 0.5 - (1-win%) x 5

Win% = 90.091%.


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## skc (13 April 2012)

skc said:


> 0 = win% x 0.5 - (1-win%) x 5
> 
> Win% = 90.091%.




Sorry. Typo. Should be Win% = 90.91%


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## pixel (13 April 2012)

Gringotts Bank said:


> If a system has an average win of 0.5%, and an average loss of 5%, what % of trades need to be winners for the system to break even?



 you divide the loss rate by the win rate to find out how many wins it takes to make up for one loss.

5 / 0.5 = 10, so you need at least 10 wins to recover one loss. 
Gives you 10 wins in 11 trades, or 90.90909...%

quite a tall order, IMHO.


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## howardbandy (13 April 2012)

Gringotts Bank said:


> If a system has an average win of 0.5%, and an average loss of 5%, what % of trades need to be winners for the system to break even?




Greetings --

For any trading system and a list of trades (real, backtest, or hypothetical), it is possible to compute the percentage of trades that are winners and the average amount or percentage won per trade, and the percentage of trades that are losers and the average amount or percentage lost per trade.  For a first cut estimate, the algebraic relationship can be used to make estimates of profitability as those percentages and amount won or lost change.  

Given a list of trades and static position sizing, the final equity is always the same no matter what order the trades occur.  But the order of the trades has a significant effect on the shape of the equity curve and the amount of the drawdown experienced as those trades occur.  

For many traders, the combination of final equity and maximum drawdown determine the attractiveness of a trading system.  

Monte Carlo analysis can be used to determine the health of a system, the likelihood of drawdown of various magnitude, and the position size that will produce the highest final equity while limiting drawdown to an amount acceptable to the trader.  I have posted several articles describing how this can be done on my blog.  
http://www.blueowlpress.com/WordPress/

The technique uses Microsoft Excel and a free addin available from my website, and does not depend on any specific trading system development platform.

As a general rule, the best trading systems limit both the percentage and magnitude of losing trades.  

A system that has a high percentage of winning trades, but a low ratio of average win to average loss, will have a highly variable equity curve with periods of smooth gains interrupted by large drawdowns.  In order to keep the risk of a wealth-threatening drawdown to a reasonably low level, position size must be kept low, and final equity is correspondingly low.  Traded at full fraction (using all available funds for each trade), systems with these characteristics are very likely to go bankrupt.

Thanks for listening,
Howard


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## pixel (13 April 2012)

Totally agree, Howard: A system with that kind of ratio is a shortcut to bankruptcy.

That's why I added "tall order".

I do however hope (giving GB the benefit of the doubt) that those numbers were examples only and could've been mistakenly transposed.


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## Gringotts Bank (14 April 2012)

Thanks all.  This type of system seems to be popular in competitions and amongst sellers of systems.  Lots of tiny winners, couple of big losers.


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## cynic (14 April 2012)

Gringotts Bank said:


> Thanks all.  This type of system seems to be popular in competitions and amongst sellers of systems.  Lots of tiny winners, couple of big losers.




Have you considered the impact of profit erosion from slippage?

I'd envisage that many of those tiny winners could potentially be transmuted into small losers subsequent to a mere few points/pips slippage when trading a real market.


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## MACCA350 (15 April 2012)

white_crane said:


> An easier way is to ignore tax and just work out the number of shares you need to sell in order to cover your costs.  What is left over is all profit and will be taxed accordingly when you sell.
> 
> Until you sell for a profit, you don't pay tax.  Since you don't know when you are going to sell the rest of the shares, you won't know how much tax you are going to pay.



If you are an investor for tax purposes the CGT event is calculated on a per share basis. In other words if you sell a portion of your parcel to recoup your investment you have made a profit on those individual shares and will be taxed on them accordingly.

For example say you invested $10k(ignoring brokerage for simplicity):
Buy 10,000 shares @ $1
Sell 5,000 shares @ $2
You've recouped you're investment of $10k BUT you've made a profit of $5k on those 5,000 shares which will be subject to CGT. Whether or not you actually pay the CGT on those shares is dependent on you're individual tax liability.

I'm guessing the way you described it relates to being taxed as a trader not an investor.

Cheers


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## ishakeel (29 April 2012)

share trading... a mathematical problem...


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## Spongle (25 June 2012)

I have a maths question:

A physical mass-spring system is modelled by the second-order differential equation
M
d2y
dt2 + 2

dy
dt
+ ky = 0
where k is the spring constant, 
 is the damping coefficient, and M is the mass.
(i) Show that, if 
2 < kM, the general solution to this system is
y(t) = e−t (Acos(t) + B sin(t))
and find expressions for  and  in terms of 
, k, and M.
(ii) Graph the motion of the system for the initial conditions y(0) = 1, y′(0) = 0.
(iii) What is the period of the oscillation? In the limit that 
 ! 0, what happens
to the period if the mass M is doubled?


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## bellenuit (25 June 2012)

Spongle said:


> I have a maths question:
> 
> A physical mass-spring system is modelled by the second-order differential equation
> M
> ...




I suggest you try http://www.wolframalpha.com

You will have to play with it a bit so that you can express the equation in a manner that Wolfram Alpha understands. But it should be able to solve most of what you are asking as well as graph the equation.

Check some of the examples on that website to find out its capabilities.


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## mazzatelli (25 June 2012)

Spongle said:


> I have a maths question:
> 
> ...




It's pretty involved to set it all out, and especially on this forum with no latex capabilities.
Where exactly are you getting stuck?


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## CanOz (25 June 2012)

mazzatelli said:


> It's pretty involved to set it all out, and especially on this forum with no latex capabilities.
> Where exactly are you getting stuck?



 Must be lacking some ky somewhere...

CanOz


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## cynic (25 June 2012)

When I read Spongle's post, I thought that it was intended in jest.

Correct me if I'm wrong Spongle, but I currently feel quite certain that you already have the answers to your math questions.


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## mazzatelli (25 June 2012)

CanOz said:


> Must be lacking some ky somewhere...
> 
> CanOz




hehe - I'll give you that


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## Spongle (25 June 2012)

cynic said:


> When I read Spongle's post, I thought that it was intended in jest.
> 
> Correct me if I'm wrong Spongle, but I currently feel quite certain that you already have the answers to your math questions.




Yeah I was just being an idiot for a change 

I am in the process of learning how to answer such questions as I'm a 30 year old 1st year spaz and have to cover general calculus.

Chemistry is my bag oooooh I love it!


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## Judd (26 June 2012)

Spongle said:


> Yeah I was just being an idiot for a change
> 
> I am in the process of learning how to answer such questions as I'm a 30 year old 1st year spaz and have to cover general calculus.
> 
> Chemistry is my bag oooooh I love it!




Another site for calculations

http://www.martindalecenter.com/Calculators4_2_MechSZ.html#MECH-SPRING


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