TANGENT AIM ... part 2 of 4
We will use the following symbols in this part:
M = the total market value of our stock before the sale
F = the portfolio control before the sale
X = the amount of market value sold based on Standard AIM
N = the market value of the stock after the sale
G = the portfolio control after the sale
S = the sell resistance or SELL SAFE
Y = the amount of market value sold based on Tangent AIM
First we note that M is greater than F/(1-S) because this is a sale.
We also note that:
N = M - X
G = F
and finally according to Standard AIM
X = (M*(1-S)) - F
where * indicates multiplication
clearly X is greater than zero because M is greater than F/(1-S)
now if we calculate N we get
N = F + M*S
and since M is greater than F/(1-S) we get that
N = F + M*S is greater than F + (F*S)/(1-S) = F/(1-S)
Thus since N is greater than F/(1-S) we in theory have another Standard AIM sell. Of course Standard AIM would have you wait one month (or some other period depending upon your update frequency) before making this next sale (assuming nothing happened in the interim). After this next sell the resulting market value will still be greater than F/(1-S). Thus this implies an infinite number of sells each of which is smaller than the last. This series of sales could be added up because, as Conrad quite correctly observed in his development of Vortex AIM, this series does converge. However we can arrive at the sum in a more direct manner.
Under Tangent AIM I want to sell an amount Y such that the new resulting market value will be exactly equal to F/(1-S) so that no further sale is generated. Therefore let us set
(M-Y)=F/(1-S) and solve for Y giving
Y = (M*(1-S)-F)/(1-S) which is simply
Y = X/(1-S)
Thus the first difference between Standard AIM (from now on SA) and Tangent AIM (from now on TA ... not Technical Analysis) is that even though SA and TA produce a sell at the same time, TA will produce a larger amount of sale. For example if S is 10% then Y is about 111% of X.
Let's look at a specific numerical example. Suppose that the current market value were $12,000 and that the portfolio control were $9,000. Also assume that our sell resistance is 10%. Thus we have:
M = 12,000
F = 9,000
S = 0.1
First we see that F/(1-S) gives 10,000 and M is greater so that we do indeed have a sale.
Either using the above formula or the SA approach (i.e. sell advice plus safe adjustment) we find that
X = 1,800
N = M - X = 12,000 - 1,800 = 10,200 which implies another sale
But 1/(1-S) = 10/9 in SA ... thus
Y = X * 10/9 = 2,000
and
M - Y = 12,000 - 2,000 = 10,000 which implies no sale.
In summary then we can say that to use TA on the sell side simply calculate the sell amount using SA but don't consider minimum transaction size. Now increase this sell amount by multiplying it by 1/(1-S) [or alternatively by dividing by (1-S)]. If you are using standard safe settings of 10% you simply multiply by 10/9. Now of course you can consider minimum size. Of course if the SA amount was already large enough then so will the TA amount be but ... even if the SA amount did not meet your minimum requirement, the TA amount still could.
Let me conclude this section with two observations.
First, I based everything above on F. I could have however used G instead of F. Since G=F however, the results are the same. As we will see in part 3, this is not true of buys. In this case F and G are not the same. Of course we could further modify TA by adding to F a certain multiple of the sale amount (this multiple could be negative) so that F and G were different. Then I would find a third sell amount Z which would be determined in relationship to G. I won't do this here but will do it in part 3 when we consider buys.
Second, in geometry when two objects just touch but do not intersect we say that they are tangent to each other. The sell amount in TA is determined so that the resulting market value is just equal to the top Lichello Band or in other words is tangent to the top Lichello Band. Similarly after a buy TA sets the resulting market value tangent to the bottom Lichello Band. It is for this reason I use the term "Tangent AIM".
Barry
