A Quick Visual of the Anatomy of a 3D 5-Asset Mean-Variance Map

I'll assume you know the principles here and some of the math. I just wanted to run through a step-wise visual of the internal structure of a 3D 5-asset mean variance map the way I've been looking at it lately. I have no idea how easily this might be discredited.  I did this for myself to make sure I understood a previous post and I'm putting it here just for the heck of it;  I'm not so sure there is any practical purpose here, this is more just-for-fun.  The charts use AGG SPY EFA IYR and GLD for the asset classes and the time frame is 34 months in 2014-2016. Returns are annualized total returns. Std dev is annualized from a monthly series. This timeframe (and data) is (are) pretty arbitrary; I happened to have done some other study earlier this year that used this same data and I was too lazy to build something different.


1. Let's start with an efficient frontier of stocks and bonds. This is textbook stuff.  We'll ignore the risk free rate and the tangency line and the optimal portfolio and leverage and all that since I am not getting into theory, just visualization.  Fwiw, I did a 3D version of this line here.

2. Now I'll create an "efficient frontier" (sort of...I suppose that only makes sense in an isolated odd way not related to textbook theory) of 5 asset pairs, including the first one we saw above. I'll chart them in pair-wise combinations.  That means I add 3 other assets and look at the mean-variance line for each of the 10 pair combos using their paired return and std dev(and covar matrix).  The scale changed a bit but the line in #1 above is the same. Again, each line terminus is 100% allocated to that particular asset and in between are various allocations to the pair from 0 to 100%.

3. Now, just for the hell of it, let's look at this in 3D with the Z axis being a function for diversification.  Low means 100 % allocation to one of the pairs and high means 50/50 allocation. The first chart is more or less the same perspective as above just tipped up a bit.  The second chart is the first one rotated clockwise a little more than 90deg.

4.  Then we add a sample of all possible combinations of the 5 assets in a fully allocated portfolio.  If we move in 1% increments there are something like 4.6 million combos so I use about a 1% sample.  Overlay this on the previous chart up in #2.  This below, then, is the mean-var map for five assets. The efficient frontier is still on the upper left and it is the boundary past which I'd like to go...if I can. This snapshot is more or less meaningless because in real life it would be more of a movie; things change every instant. That, and there is no way to forecast this stuff into the future. Would that I could...

  5. Now let's "3D" this beast just for fun.  Actually not just for fun. I think this helps give a sense of what is going on when creating an asset-class-diversified portfolio.  I'm just not sure what to say about it yet and I know I'm looking at this in an odd way. Note that the vertical axis in the next chart is the z-axis diversification function. X is the portfolio standard deviation and Y the return. For orientation the spur coming towards you below happens to be EFA in the chart above.  The red lines are the 10 pair-lines and the blue dots are, well, the blue dots... the many portfolio combinations.

6. Now, because we are here at the end and there is nothing else to say and because my significant other thinks I have lost my mind when I do this kind of stuff, let's add a moving GIF!  The perspective starts the same as #4 and then the chart tips up and away and rotates so that you see the y axis (portfolio return) and the allocation to bonds pass by you.  The important AGG-SPY pair can be seen as the little red arch underneath the mass and to the right at the end of the GIF.