crescet: waste and pine

"..man in short that man in brief in spite of the strides of alimentation and defecation is seen to waste and pine waste and pine.."  Lucky

The relationship between wealth and income is clearly strong.  There's an argument in economics that we do in fact consume based on our expectation on our lifetime income (under either a simplifying assumption of untrammelled friction-less borrowing from one time period to another or given a borrowing constraint as a function of wealth).  A (real) wealth process is in general replenished by the remnants of income minus consumption, per unit time.  It is also replenished by a rate of return on savings, and there's probably a jump process (in the sense quants use when modelling price action in derivatives pricing) on wealth - unexpected increases and decreases in wealth due to either an inheritance, an unexpected and large cost, etc.

In practice, the relative proportion of wealth over income (or expected income, or average income, smoothed over a lifetime) determines how much one can borrow, and one's consumption response function during times of economic hardship.  In other words, crescet drives your current (and expected future personal credit spread). If the amount you can borrow is always expressed to you as a percentage of your wealth,  then the associated borrowing cap and associated credit spread for loans are both functions of crescet.  Clearly it works well in a theorist's modelling of crescet if one can reasonably assume that there's a stable pattern of consumption based on a lifetime income  model.  It takes the variance out of the expected income process and allows for the possibility for doing a simpler lifetime crescet model.

The natural initial assumption, I think, is that consumption is based on a lifetime wealth process (which has embedded in it a lifetime income model).  It is also natural to assume that lending to consumers will always have a budget constraint based on some simple measurable proxy for the lifetime wealth process.  Current income appears to be the provable, easy to calculate proxy of choice, certainly in the western world.  

In the western world, it is a decent first approximation certainly for the last 70 years, to assume that the average person's wealth is held jointly in the property they live in, and in their pension.  However, when you look at this closely in the context of consumption smoothing and lifetime income, it becomes harder to make a distinction between wealth and sensible foregone consumption for future times.

Needless to say, the general flow of theory on consumption modelling goes like this: classical period economists model consumption largely as a function of interest rates.  Fisher introduces inter-temporal consumption and a budget constraint. Keynes in effect operates on the assumption that the average consumer is very much bound by the limit to borrow (i.e. he theoretically honours a real constraint on borrowing not present in theoretically pure models with frictionless borrowing).  He also, like lenders, approximates income as this year's income, and has no model for income to be shifted from one time to another (saving).  Modigliani added this element in the 1950s.  By far the biggest discontinuity in the lifetime income model is the fact of retirement, so in a sense, Modigliani introduces retirement to the model, and brings with that an ability to save and borrow.  I think this probably is a sign of the times.  In the early 20th century of Keynes, only about 10% of homes were privately owned.  By the 1950s of Modigliani's time, the US already had 50% home ownership.  So having a model which accounted for this significant fact of lumpy consumption in a person's life was an advance.

Friedman further made a sub-distinction between that fraction of 'reliable' and 'windfall' income, and considered the former more determinant in the consumer's life.  Windfall income adjustments (a legacy from a rich relative, a lottery win, a sudden hospital bill, a windfall tax) ought to have a net effect on one's wealth, depending on how that is consumed or saved.

One final chronological piece of background - the 1930s of course foregrounded the problem of persistent unemployment - a phenomenon not 'solved' by adjusting the real interest rate.  This leads Keynes to pursue aggregate consumption, including the less controversial personal consumption function (my current focus) and the much more variable investment function.

Lastly the rational expectations mob arrive on the scene to point out that if the consumer is doing all this good modelling and smoothing of lifetime consumption, then any actual changes to consumption would therefore have to be random (meaning unpredictable).  There's something quite beautiful about that step, even though the assumption made in it is initially hard to believe.

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.