3D Mean-Variance-Diversification Model 2014-2016

This was kind of fun.  This is the mean-variance space for portfolios of SPY AGG EFA GLD IYR ~2014-thru-Nov2016 but with a third dimension added based on a diversification function (e.g., low value is concentrated 100% in one asset class; a high value would mean the allocation is spread evenly across 5 asset classes). This 3d space is an efficient frontier using something like 1% of possible allocations of 5 assets if done in 1% allocation increments (~4500).


Axes:
X = Portfolio standard deviation (w CoVar matrix)
Y = Portfolio weighted return
Z = Function of diversification (concentration vs spread).
                   Z is on the bottom coming towards you

Thoughts:

- While fun, I doubt this has anything directly actionable that will make me any $

- It's hard to see but the meat of the 2D eff frontier, when blown into 3D is made up mostly of allocations up the Z axis, or in other words diversification gives most of the lift to efficiency. But we already knew that. Also if you look closely you can imagine the two asset AGG-SPY frontier in the form of a 3D line; it's the arch from around 4 to around 7 1/2% inside the scatter mass.

- The even-weight portfolio appears to be sub-optimally efficient over that particular timeframe along with a whole bunch of other almost-even-weight allocations.

- Good luck trying to figure out ex-ante which allocation will be the best one in the future.


Postscript...

Here is the 2d version on which this was based:

Here is a full rotation. I figured out how to screen capture and gif it without having an ENORMOUS file.

 
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Done in R with Scatterplot3D.

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Other reading (mostly beyond me, and for which I cannot vouch, but...):

• Solving Markowitz's Inefficiencies through MVD Frontier, Riccardo Brignone and Gianfranco Forte. Università degli Studi di Milano-Bicocca
• Markowitz 3.0: Including Diversification Targets in Portfolio Optimization via Diversification Functions, Heinze, Provinzial Rheinland Versicherung AG