Clive, forgive me for being a bit dense for now. . .I have read the text at the bottom twice and my brain is cooking because of information overload. I get the drift up to the ladder definition from 2 to 10.1 in terms of average portfolio yield percentages. . .at 2 I would be at 100% equity and on the top with the yield at 10% I would be 100% in cash.
Also I get the portfolio steps of PV/17 at there are 17 levels between the extreme points 1 to 18. I take a portfolio value at the value of 1700 so each step is 100. . as I start out. . .without thinking about the question as what I should do when I start a new portfolio. . I am already investing(let's assume that) at some point in between, at say 4.506% yield. . . exactly in the middle at equity value =1700 and I have 170 shares so that the share price X=10 and I have 1700 Reserve at that point.
Error correction
In the calculations below I have erroneously assumed that I had 100 shares so the share price = 17 instead of 10, as I used. The numbers in the calculation are wrong but that doesn't matter. . .the methodology of what I did is the key to my attempt to understand you. Forget the numbers and try to follow my interpretation of your method.
When the price rises to the 10th level at 4.715 % yield the value had risen 4,638260098 % and the equity value is now 1778,850422 and the step-value has risen to 104,6382601 so that I will Sell that amount:
PVn is PVnew
PVn = 1778,850422 - 104,6382601= 1674,212162
STEPn Size = 98,48306833
Nxdel = 104,6382601/(10*1674,212162/1778,850422) = 11,11781514
Xn = 100* - 11,11781514 = 88,88218486** shares
*should be 170
**should be 158,8821849
On the way to the top the equity grows but each time the equity is turned into cash.
On the way down I do the same but then I buy 2 step-units instead of 1. . . .then I think I should use the Reserve for calculating step sizes. . .a little Fuzzy on this. . .
This seems an interesting approach but I am not sure if that is your interpretation.
The way I see it is that the step levels on the ladder remain at the indicated yield points but the step size should not be calculated by dividing by 17 BUT by the remaining 8 steps. . . in 8 steps I have to get rid of all the shares!
PVn = 1778,850422 - 222,3563027= 1556,494119
STEPn Size = 194,5617649
Nxdel = 222,3563027/(10*1556,494119/1778,850422) = 25,41214888
Xn = 100 - 25,41214888 = 74,58785112 shares.
(ignore the calculation errors)
Aha, this looks better! As the 11th level is reached on the way up there are only 7 steps left are left, etc., etc. so that at the 17th level the remaining equity is sold---> 100% cash.
On the way down from the start point the same generic calculation process is used at each level but I now have to look at the Reserve of 1700 I started out with and have to divide that up into 8 steps all the way down to the bottom level.
If I use the d'Alembert principle of increasing the stake at each "betting round": 1,2,3,4,5,6,7,8 x the base unit X then I must divide the 1700 Reserve ahead of time into base stake units:
Step#StepSize
10:X: (X=Basic Stake for the loss . . . 8 steps & 1700-X left)
11:2X: 1700-2X left, etc.
12:3X
13:4X
14:5X
15:6X
16:7X
17:8X
18:9X. . .Cash = 0 ---> 45X = 1700 X = 37,78
Every time the price trend reverses after a step down to a higher level the equity value is again divided by 17 and the the process starts again, but possibly from another level on the ladder, and the calculations start from there in an identical way so that each time the 10% level is reached there is 100% cash. This a beautiful mechanism as each time the trend changes from a low point to a higher level the process follows and identical algorithm. As long as the extreme points 1 and 18 are fixed the trading cycles up & down each time on the way down using the 1,2,3,4. . . principle one will gain strongly on the dip-investing on the rebound almost in the same generic fashion as my Vortex Method with aggressive buying, but more structured to create a progressively greater Buy Multiplier to the Dip Bottom.
If my interpretation is not exactly in line with what you tried to teach me then at least this way would be an interesting alternative betting strategy using the remaining Reserve at any point in the cycling of the Y-Z probability distribution of the price cycling.
Supposing my interpretation is taken as a basic technique for a 50-50 price cycle distribution then the the 1,2,3,4, . . .stake investment could be modified to a particular type of investment for which the behavior deviates from the 50-50 behavior. . . for example 1,0,4,0,6,0,8,0. . .skipping a level each time to concentrate the buying more strongly to the bottom of the dip. Actually I have worked on developing this progressive type of investing in the past by using an exponential increment model . . it was triggered by a method used/proposed by Don Carlson: to use the middle of the trading range to calculate increasing trade sizes as the price reached the upper and lower boundaries. . .using something like Bollinger(??) Lines but I have not developed that exponential trade size idea to a final model for actual operation. . .the mathematical problems for doing this were somewhat complex and I abandoned the development. The idea was to use this exponential trade size also for selling. . . concentrating getting out mostly close to the top. My principle difficulty was to automate the floating character of the idea in Excel. Maybe you have "handed" me the solution to my problem with the d'Alembert version: As I see it the Ladder Construction is (or could be) a Floating system. . as the average price moves steadily upwards while the +/- cycling remains the midpoint of the ladder can be moved up as well. . . as the conditions may dictate.
Thanks Clive for providing the input for me to grasp the significance of the attempts I made years ago during my discussions with Don Carson. . . this makes me realize something:
"Because I was able to stand on the shoulders of Giants I was able to see a great distance". . .supposedly Isaac Newt had said that or something to that effect.
I feel a little bit like that now, even of the things I see are not the same as you wanted to show me.
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