crescet and titubit

The speed with which one's wealth grows, and its absolute level, are tied to one's life style (one's consumption of one's income).  A useful simplification is to assume one's income derives largely from one's wealth.  Economically, this is almost completely unreasonable, since it applies only to a vanishingly small fraction of humanity.  One then needs to spend to live from this wealth.  There are however minimal quality of life spends which may imply several modalities in the relation between the wealth growth process and the spend process.  I assume for simplicity that wealth is sufficiently large that the income spent can be made in a way which still leaves wealth growing.  Put another way, there is an assumption that the wealth process grows faster than both inflation and the daily consumption of your lifestyle.   A second critical threshold is for now also ignored - as with the case where the lifestyle spend significantly impacts the wealth process, transaction costs also can incur a third hurdle to overcome.  These assumptions clear away much of the thrust of the Darst book on asset allocation.

Next, an implicit starting assumption is that wealth at time $t$ may be considered as residing in one or more currency (short term fixed income) buckets.  One then imagines that the mean value theorem can be applied to the act of taking financial risk above this risk free (globalist) position.  That is to say, in equilibrium, the entirety of the job of strategy allocation and capital deployment can be waved away as solved for now, and modelled as a single 'bet' over an appropriate time frame, whose outcome can be a win or a loss.  One then determines the ideal bet size, per unit of time, based on the mathematics of Gambler's Ruin.  That is to say, that the average bet size can be no bigger than some fraction $\delta$ of wealth at point $t$ if volatility (and long term, ruin) is to be avoided.

Of course, in reality, the complete opposite applies with titubit.  Bet sizing is often ignored and instead one's lifestyle generates the major driving constraint to investment returns variance tolerance.  In short, our lack of funds makes us bet too big - this together with transaction costs, destroys our wealth.

Strategy allocation: a wealth process (crescet), a volatility constraint (titubit) and an expected life (fugit) and a cycle (circuit)

In chapter 2, Darst tries to carve up the space of approaches to 'asset allocation' through dimensions of style, then how strategic the approach is, and finally how quantitative the approach is.  As I mentioned in the last post, I think the 'style' dimension is bogus.  This in the limit can be replaced by owning the market of available strategies in toto), in their market weights, and then by implementing risk appetite purely through levering the in toto portfolio.  Next his seemingly clear quantitative versus qualitative  distinction breaks down too - for an ideal strategy allocation algorithm, the parameterisations are empirically calibrated and the discovery of new strategies are qualitative, whereas ideally the implementation, given a broad parameter set, ought to be quite algorithmic and computationally tractable.  Again ideally, the re-allocation decision might in theory be near-real time.

Finally, the dimension of 'strategic' v 'tactical' is the difference between Kant and Machiavelli. 

I think you want the algorithm to be as autonomous as possible, and to make a call on the strategic/tactical dimension based on the following inputs: where you are on your own expected wealth process and your expected lifespan.  Your spend process ought to follow from these two, and shouldn't count as an input.  Likewise this set of input parameters can be used in the determination of how much leverage to use (how long do we think it will take us to get there).  Your expected spend (and the lumpiness thereof) is really a (time-dependent) constraint on the volatility you desire on your wealth process.

The starting point (the long term equilibrium point) would be based on the maximum likelihood weightings, based on as much data as there is available for the strategies.  If one then subsequently had a model of strategy cycles, then that would be burned in too, to a degree proportional to one's confidence in the cycles model.  The mean value theorem guarantees that your long term equilibrium parameters are a good starting point, in the face of no certainty about cycles at all.

Crescet, titubit and fugit are facts about you.  Curcuit and the long term equilibrium weightings are parameters of the strategies.