LC, Interesting Issue you raised.
Constant Value, also known as the constant dollar plan. If you start out with half in stock and half in bonds, you should be able to have cash for investing up to a -70% drop. With AIM you run out of cash around 50%.
This issue, earlier referred to as a high cash burning rate for AIM, is only a feature if an AIM is set and then left without any overriding management techniques. This acceleration of cash burning, I conclude, is a direct result of the Residual Buy Signal as prices keep dropping and which results from the fact that at every buy the PC is raised after a Buy so that the difference (PC-V) increases rapidly as prices drop. This means that the Buy Signal increases more rapidly that the price difference it self. This is, of course, already known and a recognized drawback of AIM. It would require the investor to look for other rational means to ignore the strong Buy Signals is a lower cash burning is desired. For example using filters or “gut feeling” buy-delays so that the investment of the cash is only carried to the point that the AIMer is comfortable with. One could do this for example with ever increasing values of SAFE
In this sense I would be even more inclined to call the Residual Buy Signal a FLAW rather than a feature: it requires more and more the investor to ignore the Buy Advice as prices drop. For the inexperienced AIMer this could become a disaster. . rather than the general advice that he should follow the “instructions” if his AIM System(to take away the emotions of the investing) he should us his "higher" management system to ignore the buying. That does not appear very logical(or automatic) as he must ignore the AIM Advice all the time if prices drop sharply and he is to conserve the Reserve. . .this because the Buy Advice has a FLAW. . .of course this is still only my opinion.
One way to avoid this with AIM is to decrease the buying systematically when prices drop. With SAFE=s and prices keep dropping one could do this
Buy 1=(PC1-V1*(1-s))*1
Buy =0
Buy 2=(PC2-V2*(1-s))*(1-s)
Buy=0
Buy 3=(PC3-V3*(1-s))*(1-s)*(1-s)
Buy=0
Buy n=(PCn-Vn*(1-s))*(1-s)^(n-1)
Buy= 0
To make it logical I have introduced the optional Buy=0 for the case that the price does not change, so eliminating the Residual Buy Signal. In this it is obvious the the source of the Residual Buy Signal remains in the algorithm and is the very reason that the buy signals increase so rapidly with dropping prices.
As you can see that as the number of buys increase the Buy Signal gets weaker as you go. . applying the brakes. Furthermore, as you buy less the value of the PC rises less sharply but because of the dropping prices itself the value of V drops more rapidly as well. . . somewhat counteracting the Brake with the factor (1-s)^(n-1). If in the opinion of the investor the brake needs to be applied more then one can in increase s by a bit till the brake works as desired. That way one can decide exactly how great or how small the Cash Burn Rate should be, or one can calculate at what point the Reserve should be used up, for a certain value of s:
SUM B = B1 + B2 B3 . . .+ Bn = Reserve.
This way one can maintain the basis AIM characters and have an automatic Buying Brake added to it.
In contrast when I contemplate a pure ratio Advice System.
Buy= M*(PC-V)
the Buy Rate does not increase as prices drop (for a fixed price difference as trade trigger). So, relative to AIM the Ratio Buy System has a more severe braking system than AIM. Also here one can simply decrease the value of M if it is desirable to stretch out the Reserve by adjusting a single parameter.
One can set either system to behave exactly as one wants it to behave.
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