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I'm building a little tool to help configuring a Martingale-style laddered trading strategy.

Assuming the following variables:

  • P = Final Position Size
  • S = Number of ladder steps
  • I = Size Increment
  • F = First position size

$$P=\sum_{i=0}^{S-1} F(1+I)^i$$

I'm having difficulties to isolate F (the first position size) if P and I are known.

This needs to be plugged into an Excel spreadsheet and I'm not too sure where to begin to type the formula.

Any help is really appreciated.

Thanks!

thisisbbc
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  • By $*$ you mean multiplication? If so you can just have $F = P(\sum I^i)^{-1}$ – GuPe Jun 22 '21 at 23:25
  • @GuachoPerez - Correct, I removed * for clarity. Thanks for the help. Now I have to figure out how to plug that into excel since sums are only possible on a defined range. Thanks again! – thisisbbc Jun 22 '21 at 23:45
  • If the increment $I$ is fixed, $\sum_{i= 0}^{S-1} (1+I)^i = \frac{(1+I)^S-1}{I}$, so you could just plug this value in. – GuPe Jun 22 '21 at 23:53

1 Answers1

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$\sum_{i = 0}^n ar^n = a\frac{r^{n+1} - 1}{r - 1}$ is the closed form for a geometric series (i.e. a sum of terms that change by a constant multiplicative factor). In your case, $n = S - 1$, $a = F$ and $r = 1 + I$ so you'll find some things simplify even further and you can plug things into Excel very quickly.

ConMan
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  • Removed previous comment, I was confused. Did the simplification again and now got the exact result I wanted. Thanks a lot for help :) – thisisbbc Jun 23 '21 at 01:55
  • Just out of curiosity, do you have any material to suggest to learn more about closed forms for geometric series? Are summation solutions akin to integrals where you have to "memorize" different forms to be able to reduce them? – thisisbbc Jun 23 '21 at 02:00
  • Well the closed forms for arithmetic and geometric series are pretty standard algebra, probably at mid-late high school level? For sequences and series in general, it's a pretty broad topic, but Khan Academy has some resources that could be useful depending on how deep you want to delve. – ConMan Jun 23 '21 at 02:13