Uncertainty in Equity-Bond Correlation Assumptions

I was just reading this article on equity bond correlations (Challenging Equity-Bond Correlation Assumptions, winton.com). The gist of the piece is roughly this: 

what number should be used? The distribution is fairly flat and so any value between -60% and 60% is almost equally likely. By taking the average, we are simply picking a number close to the middle of the distribution rather than choosing the most frequently observed correlation...Often we assume future correlations will be similar to those experienced in the past. Naively, we may be tempted to represent these correlations with a single number; however, the historical data suggests that we need to include some uncertainty around our estimate at the very least. The equity-bond correlation, in particular, is one of the key estimates used in the asset allocation decisions of an investor but, given its historical variability, it is a relationship which requires careful modelling.

So I thought, as I have done in the past: "hmmm. I wonder what it looks like."  Or in this case: "how much and how wide would the bend in the efficient frontier change using the range of correlation assumptions mentioned in the article."  I'm sure this kind of thing is in chapter one of the textbooks but I wanted to see it myself.  No doubt I could probably come up with a number analytically vs charting it out but that would take me too long and eat into my happy hour.

Arbitrary assumptions:

Asset 1: 3% r, 4% sd
Asset 2: 8% r, 18% sd
Correl: -.6, -.5, -.4, -.3, -.2, -.1, 0, +.6
allocations: 0->100% in 1% increments

Chart:

curves left to right represent -.60 -> +.60 in correl coef.

Conclusion

I usually use for my modeling, as the article warns against,  a single number somewhere between -.1 and 0 as an average over long history. I get his point because it does vary all over the place over time.  But here, at the widest point in the chart using the artificial assumptions above, we have maybe 3 points of variance in the portfolio standard deviation.  That doesn't freak me out too much since I don't personally allocate that heavily to bond funds vs individual bonds nor do I personally have so little equity to put me at exactly that wide point (though it's not all that much better at 50 or 60% eq) nor, I should say, do I usually model like that either. And, I might even accept that kind of correlation uncertainty before I'd take the 100% certainty (not really 100% since future vol is unknown) of super high volatility in the upper right corner[1]. This does bring up the issue of efficiency however and the possible loss of non-correlation when it is needed most (recall march of 2009, aargghh) especially for retirees during a drawdown looks pretty harsh here especially since there are other ways to work this. By that I mean that I personally think we are starting to live (this is opinion, btw, not a supported researched fact) in a golden age of alternative risk that can augment non-correlation at a portfolio level with all sorts of tools other than bonds. Think particularly of "systematic risk" and "strategies" as opposed to "asset classes" as such especially since we are starting to see at least a few more of these hedgefund- and CTA-like things at publicly available and affordable prices and reasonable investment minimums.  We'll see in the next down cycle who's been helpful and who has not.


[1] I should point out here that the topic of parameter uncertainty -- not just correlation but variability and randomness in all of the inputs -- is not a new topic.  This has been touched on often before. In particular I am thinking of things like resampled frontiers covered by R Michaud. But there are others and this has been a common critique when discussing MPT. I guess it is good just to emphasize once again this particular uncertainty in correlations.  But we shouldn't forget the broader topic of uncertainty at all levels.