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
		1	5	10	20
inflation	0.01	0.99	0.95	0.90	0.82
	0.02	0.98	0.90	0.82	0.67
	0.03	0.97	0.86	0.74	0.55
	0.04	0.96	0.82	0.67	0.45
	0.05	0.95	0.78	0.61	0.37
	0.06	0.94	0.74	0.55	0.30
	0.07	0.93	0.70	0.50	0.25
	0.08	0.92	0.67	0.45	0.20
	0.09	0.91	0.64	0.41	0.17
	0.1	0.90	0.61	0.37	0.14
	0.12	0.89	0.55	0.30	0.09
	0.15	0.86	0.47	0.22	0.05

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.