crescet pool

The traditional 'asset allocation' industry typically makes 'investor risk appetite' your problem, not theirs.  They then perform this outdated pre-MPT analysis of the kinds of asset your risk profile might need.  In reality, you need them all, in toto, and your risk appetite only drives the degree of leverage on that total portfolio.  Secondly, using some nineteenth century maths on annuities and perpetuities, they take your requirement of needing a fixed amount at a date in the future, run the formula, and work out what your monthly premium ought to be to achieve that future cashflow.  Note this too works only by eliminating all asset types and strategies except relatively safe loans/bonds, together with a hope that inflation doesn't destroy the real future value.  However, if you're willing to accept uncertainty in the primary return stream (which becomes increasingly OK  the longer your relevant time horizon is), then you can replace a safe (close to risk free) return with increasingly risky returns.

But I think one should try to build a model of the risk appetite, which is to say  a model of the wealth process.  This would be a rather complex process.  Stochastic no doubt, and with feedback from the actual experienced output of your core investment model.  It is much grander (much more destined to failure too) than knocking off a perpetuity to pay for your children's university bill.

Before doing that, it might be worth thinking if there are any macro or qualitative insights which might be gleaned by thinking about a world where everyone, rich and poor, operated a wealth process.  Are there implicit biases in the behaviour of investors based on how wealthy they are?  Secondly, how distributed is wealth?  How does that matter?

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.

The anti-FOMO movement

There are n strategies, each with returns $r_i$.  Ranked top to bottom, so $r_1$ is the strategy with the highest return (long term).  Why not just put your wealth all in strategy 1?  Putting only a fraction of it in 1 and fractions in 2,3,...n leaves one with a feeling of missing out.  I suspect if you live to be 640, then this would be the effective result of the ideal allocation strategy.  Indeed if you have a 60 year perspective, this might also be the case.  But history doesn't always repeat itself.  So you can never be sure the future will continue sufficiently to be like the past.  Hence you'll want to diversify.  For example if you are Russian, living at the turn of the twentieth century and happened to note in 1901 that the St Petersburg stock exchange was your $r_1$, and decided to put all your wealth in there, then you'd be in for a shock when the Russian revolution came and wiped your wealth to zero.  If you were an ultra risk-adverse German post WW1 and thought you'd keep your money in nice liquid deutsche-marks, then the hyper-inflation would have likewise wiped you to effectively zero.

The degree to which you trust the institutions which underpin the strategy returns you feel you have access to is the degree to which larger and larger fractions of your wealth will go into strategies 1, 2 etc. rather than into tail end strategies.  Conversely, the degree to which you are uncertain of the future of those enabling institutions (and this, to be sure, is an uncertain act of political tea-leaf-reading) determines how distributed your wealth will be.  Your degree of confidence in strategies 1, 2 also grow to the extent that your future wealth-investment time horizon is long.

Besides the above unknown unknown, is the idea of correlation.  If all strategies 1,...,n are fully correlated with each other, then each of n is as good, in this one respect, as all the others.  But the degree to which any two (or more) strategies are uncorrelated or lowly correlated, opens the possibility that there was a combination of these strategies which was ideal, in some wider, as yet to be defined sense.  

So a world with a lot of serious unknown unknowns presents a difficult environment for the ideal strategy allocation algorithm, as does a world with cross strategy high correlation.  Thankfully so far the world we live in is somewhat known, somewhat predictable .  And this is the space that the theory of the ideal strategy allocation algorithm can work within, where the past can tell us something about the future, and where strategies have less than perfect correlation.