Sunday 12 August 2018

The art of asset allocation - poor figure 1.5

Darst ends his bombastic preface with a trite lesson on the etymology of the word 'art', being an expression of something beautifully put together, with skill and in adherence to a craft's skill base.  He adds, pompously and wholly inappropriately, "In addition to these senses of the term 'art', an important reason for naming this book .. relates to the use of more than 130 illustrations and charts intended to help investors to quickly grasp and retain important asset allocation and investment concepts".  Big self-praise indeed.  I've already indicated how strongly I disagree in my first blog on this book.

Let's take one of those early charts and dis-articulate it.  Figure 1.5 purports to show something simple and important - namely the effect of inflation on an asset, over various ranges of time and inflation rates.  How does one construct a chart like this.  Step 1 is go into excel, add a formula to a rectangle of cells, then take it into powerpoint, add crude arrows over the headings and hey presto.  This isn't art.  At all.

First of all, look how he's aligned the arrows (the only possible act of  creativity here).  He wants the downward facing arrows to indicate depreciation in real value as a result of inflationary erosion, so he overlays downward facing block arrows to semantically flag to the reader 'going down'.  However, when her comes to represent the effect of inflation, he clearly intends to have this go in the opposite direction (higher inflation after all erodes faster).  But putting the arrow the other way around (his claimed art-innovation here) merely shows an inflation rate reading pointing 'up' but with numbers decreasing.  This is a visualisation mismatch - a semantically jarring chart which, far from adding to clarity, pointlessly detracts away from clarity.

Second, I hear you say, '"but the guy's a finance guy, what matters is the rigour and discipline he applies to the numbers".  Well, wrong again.  I ran 3 versions of this simple table in a spreadsheet, first of all the correct way (with geometric inflation, since the effect of inflation is geometric) and secondly, using annual compounding.  In neither case did I replicate his numbers.  To get his numbers I have to apply simple interest adjustments, a process which at one point intensifies inaccurately the degree of erosion (helping him make his point, but via a mechanism which is unwarranted) and fails to represent any reality for how inflation as an economic phenomenon occurs.  

Here's the chart showing the erosion with geometric compounding $e^{-it}$
years
151020
inflation0.010.990.950.900.82
0.020.980.900.820.67
0.030.970.860.740.55
0.040.960.820.670.45
0.050.950.780.610.37
0.060.940.740.550.30
0.070.930.700.500.25
0.080.920.670.450.20
0.090.910.640.410.17
0.10.900.610.370.14
0.120.890.550.300.09
0.150.860.470.220.05

Taking as a representative point, the 10 year, 15% point, and applying the annualised formula I get 0.25 instead of 0.22.  I.e. you lose less.  Yet for this point he reports 0.20.  The only way to get there is to apply the following algorithm: $0.85^{10}$, which of course doesn't handle compounding at all.

In conclusion, aesthetically and numerically, I am not a fan of figure 1.5.   Also, I note that the western economies will try to position themselves at 2-3% inflation.  Let's assume this will continue to be the case, more or less, until one dies.  This will guarantee a 50% loss in real terms over the first half of the average working person's life.  Over the full 40 years, two thirds of your purchasing power would be eroded by putting your capital under a mattress in these circumstances.

The Art of Asset Allocation

I'm starting to read "The Art of Asset Allocation" by David Darst.  It already possesses the fly cover and typography of a mostly-empty finance book, and I have decided to go hard on it.

I've read the preface and chapter 1 and I can see that he does two things with diagrams.  One, he utterly recapitulates precisely the same message in his largely textual figures in the textual body of the book, in essence doubling up the message, flabbing the book contents out.  Two, he sees it as some form of art, whereas in reality it is largely a power-point mockery of art.

Here's his chapter 1 message.  The first enemy of the capital owner is the oft-present influence of inflation, eating away at capital's purchase power.  This, of course, is a message of returns (real returns being greater than 0 in fact) and not at all specifically directly related to asset allocation.  But it is fine nonetheless to borrow this out of kilter core concern of finance.

A point I really don't like about chapter one, but one which is partly true, is the way the author tries to make too many points of decision in asset allocation to be driven by investor preference.  For example inter-asset correlation isn't really just an investor decision.  There's of course a choice to be made in working out this window upon which you base your correlations, but this isn't simply a function of investor preference.  This,  ideally, is either something the asset allocation adviser can do for you, or if not, then provide guesses which are going to be at least as informed as your own.  

Also, what's going on with figure 1.2, which seemingly gives four fundamental meanings of asset allocation.  If you read these meanings closely, you'll find that they're largely repeats of each other - blending trade offs is really just the same as balancing characteristics and setting constraints on representation is precisely just a re-description of the very act of diversification.  Perhaps an unacknowledged goal for the author is to have a chunky tome. 

In terms of ideas from the book, chapter 1 introduces us to the following: first, there's a sequence of six steps in asset allocation (the diagrammatic 'art' here is a series of six boxes with a horizontal arrow running across the top - so, artless, really would be a better adjective.  He also attributes most of these plodding Powerpoint/Excel efforts as "source: the author").  Second, there's a Maslowian foundations pyramid.  Also, already at this point one asks what the relationship is between the steps and the pyramid, and to what degree these also are overlaps.  Third is a kind of meta-analysis - pros and cons of engaging in asset analysis.  Fourth, Darst reminds us of a pedestrian and widely recognised distinction between asset categories which protect capital and those which grow it.  Lastly, and to continue situating this quotidian distinction, he reminds us of the two elements of the entropic bite of financial reality - inflationary erosion and short term volatility - financially dying of old age and dying young in an accident.

I'm keen to re-describe this more concisely and in an order which makes more logical sense, but I'm sticking with the criticism of chapter 1 as I see it.

So, these steps of his.  First, specify assumptions about future expected behaviour of asset classes.  This pretty much is a task he assigns jointly to the capital owner and the allocation specialist.  I challenge this.  And will challenge it at later points in this book - he's making this a joint responsibility of the capital owner.  This ought to be the job of the allocation specialist.  Making it the capital owner's job feels like pre-preemptive blame sharing.  By this step, Darst doesn't mean the classic portfolio optimisation step of deciding where the capital owner wants to be on the efficient frontier - this happens in step two.  No, by step one he means listing the future expected returns, associated risk (vol) and inter-asset correlations.  This is a largely empirical exercise.  Yes, there's implicitly a model behind it and yes there needs to be parameter selection (which to repeat comes on step two).  Step one, as far as I can see, is the running of a mean-variance-correlation analysis on asset categorisations observed universally.  This could be a singular input data set for all capital owners.  Nor does Darst hint at the monumental and incomplete effort this entails for the whole of humanity.    Describing this as the capital owner spelling out his assumptions on future returns, volatility and correlation is akin to the maths teacher asking his pupils to explain calculus to him before he starts that lesson.  Part of the motivation of this blame-sharing move is that the models which are used are rear-view mirror models masquerading as future-seeing  machines.  But the financial world of tomorrow is always somewhat surprising.  The best these models can do is to empirically adopt some form of maximum likelihood estimation principle or, through sheer random luck or through prescient and incredibly rare analysis, make statements about the financial future not observable in the empirical data.  Claiming that instead it ought to come printed on a page under the arm of a capital owner in that first series of meetings with his well-paid allocation analyst is quite improper.

I notice in passing that books like this, and certainly this book, relies heavily on the adjectival space of 'discipline'.  This is probably for two reasons.  First, the finance industry takes so much money off capital owners that it must be repeatedly made clear to them that nothing is being wasted here.  Second, books like this are a form of management consultancy brochure, exploiting and dumbing down academic research yet also papering over the found reality of what way money managers actually work.  There's frequently little concern for asset allocation precision and, believe it or not, for empirical analysis.  Thus 'discipline' is a marketing utopia.

Step two.  The selection of the right set of assets which "match the investor's profile and objectives", and pick the appropriate point on the risk/return profile.  I imagine that, in the limit, this is largely answering the same question for everyone everywhere.  Imagine a book which had a chapter for each of the currencies of the world.  In each chapter, a section for the capital owner's age, and within each section, some relevant data.  This singular book should answer most of these questions for most investors.  Also I think the idea of hiring an allocation analyst to deal with only a subset of your capital, and perhaps for a specific objective, is less optimal (though of course it happens) that a singular view of the person and their hopes for their capital through their whole life, and permeating across all levels of capital from a single dollar to many billions.  You'd then only need to pick a new chapter or section if your base currency jurisdiction or capital level changes significantly.  I'd also assume that all assets would be owned, even in fractional weightings.  That way, the act is not one of selection but one of allocating a weight - of deciding where to slice the pie up (or more generally, you're re-slicing an already sliced pie).

Another slight digression.  A capital owner already has implicitly or explicitly made an allocation decision.  Even if they hold their capital in US dollars under a bed, this is an allocation decision.  So the asset allocation industry is always in the game of making a series of re-allocations  across time.  The act of reallocating, however, in any discussion I've seen about it, is implicitly described as a singular, complete act of re-slicing a pie of capital.  However, there's a way of adjusting the slices which may be more efficient, and more in tune with how capital arrives with capital owners.  And that is to allocate any new incremental capital in such a way that the slices move to the weights you desire, without touching the current set of capital allocations.  This would work if the re-balancing occurred in line with the arrival of new capital.  For the sake of giving this a name, I will call it marginal re-balancing.  In the limit, ignoring costs, the marginal re-balancing process is continuous.  Related to marginal re-balancing is the idea that, for all reasonable sets of allocation decisions given the multifarious behaviours of world economies, it might be that there are certain low or high values for these re-balancing weights such that one can say that each asset class can have a fixed core allocation.  This is, of course, a popular and well understood allocation idea (core allocations and peripheral adjustments).   An advantage of recognising this point lies in the likely reduced transaction costs associated with permanently holding a large fraction (in aggregate more than e.g. 50%) of one's capital in the respective asset classes.  I will refer to this as the core allocation stability thesis.  It is either true at meaningful allocation levels or it isn't.  It is mathematically true that you're always going to get some non-0 threshold weighting for each asset.  The empirical question is whether these cores are in fact large enough in magnitude.  In answering this question, we need first to answer a different question, which is how dynamic is the theoretically perfect allocation algorithm likely to be?  A highly dynamic algorithm might require 0% in US equities at some point.  A conservative one perhaps looks for a set of long term fixed (or, in the limit, actually fixed) set of allocations.

Going back to the idea of continuous, theoretically ideal re-balancing.  The other element of a general modelling of this is a description of how the marginal fractional unit of capital arrives at the pool of extant capital which the capital owner possesses, and at what point in the capital owner's existence.  If capital arrives steadily (net capital grows steadily), this lines up well with the theoretical idea of continuous allocation decisions.  If net capital grows in a more volatile way over a person's life, then that phenomenon too might itself be an input to the ideal capital allocation process.  This process can be referred to as the net capital growth process, and it can have a (stochastic) volatility.