On "Growth Optimal Portfolios" by Corey Hoffstein and Newfound Research

Here is a great post to which I was tipped by an internet-blog friend:

Growth Optimal Portfolios, Corey Hoffstein.  "… we explore geometric mean maximization, an alternative to the traditional Sharpe ratio maximization that seeks to maximize the long-term growth rate of a portfolio. Due to compounding effects, volatility plays a critical role in the growth of wealth. Seemingly lower return portfolios may actually lead to higher expected terminal wealth if volatility is low enough. Maximizing for long-term growth rates may be incompatible with short-term investor needs. More explicit accounting for horizon risk may be prudent." 

This was of interest because I have put so much amateur-hack effort into understanding this subject area.  Past posts include:  

• Asset Allocation, Ruin and Geometric Return 3/14/17
• Some Thoughts on a Geometric Mean Frontier 3/15/17
• Adding a Third Asset Class (Systematic Alt Risk) to the Utility of Simulated Terminal Wealth 3/23/2017
• Another Lesson in Geometric Returns Over Multiple Periods 3/24/2017
• One more extension to my asset allocation optimization journey
• Playing the Geometric Return "Game" with Some Real Data and My Systematic Alt-risk Strategy 3/26/2017
• Revisiting the Geometric Mean Frontier 4/3/2017
• Another obvious reason to put the squeeze on vol 4/11/17
• Time Effects of Geometric Returns, Now With Spending 4/17/17
• One more geo game - sensitivity to volatility 4/18/17
• A Practical Application of Geometric Return Analysis: Retiring My Alt Risk Strategy 5/19/17

There might be a couple others.  These are not perfect because it's been 40 years since a real math class and I am not a PhD. in anything.  On the other hand I decided earlier this year it was important for me to at least try figure out how this all works. I thought it was especially important for retirees like me who have neither infinite-multi-period nor one-period time frames.  It all started with this article  "A Practical Framework for Portfolio Choice" by Richard Michaud.  Either Hoffstein or Michaud are great introductions though there are other papers by Hakansson, Kelly, Estrada, Mindlin, Meucci and a bunch others that attack this topic as well. For me it was worth the effort though it can be some rough sledding at times without a strong math background.  Read the Hoffstein paper.  Here is a modified version of my comments to the "tipper:"

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To xxx:

...

I count four of the better non-family things I've added to my world over the last 5 years as: 1. learning to program in R, 2. settling on a consistent strategy to short options, 3. successfully managing an efficient systematic alt risk program, and  4. understanding the behavior of multi-period geometric returns.  I think this paper is a useful addition to the lit.  Re geometric returns or gmm [geometric mean maximization]: 

- While it is true that gmm investors never get ruined, it needs a little more nuance as they correctly and usefully point out because being ruined only means going to zero while there are indeed other considerations.  And I also think it's also not just all about utility (Samuelson) or the number of years it takes to get to some state reliably better than an alternative (Rubinstein). If I understand it, in the years between now and 208+ (or maybe 4700) years from now (say 10 years) wealth can get so low that it squeezes so much fear out of you that you are left as a whimpering puddle.  Maybe that's the same as utility math.  So, it (gmm) might not be a "reasonable" criterion even though in 208 years it might actually turn out the better bet.  

- The other thing that often gets missed is that even though the multi-period perspective is awesome and proper and underappreciated, papers like this still feel like (properly no doubt) the perspective of an institutional investor or maybe an "accumulator" with a really long time frame.  But there is no consumption! Retirees consume, endowments consume.  I guess that's where either simulation comes in or maybe some kind of complex and semi-deterministic math (Milevsky has thrown out his SPV approach -- profiled by Dirk Cotton in the RMJ in 2015 -- or in his book he uses Kolmogorov equations; Blanchett presented a simple regression formula based on simulation, etc....  The coolest semi-approachable math I've seen lately was that stuff from earlyretirementnow.com that combines geo returns and consumption in one formula.  It's really a form of sim even though it doesn't look like it at first.  

- As the authors and others (e.g., Michaud) have pointed out, the near term time effects of geo returns in our real non-infinite-horizon world seem important to me.  For example, for me, my "horizon" could be 30-40 years (death?) or 15-20 years (an optimal annuitization age?) or even 3-5 years (call it a probability horizon for some crisis that I'll need to survive in order to make it to the next time frame or the next crisis).  Understanding geometric returns over short runs of multi-periods is a relatively untouched area these days that seems like it should be a bigger deal than it is.  

- Corey's paper directly addresses a question I've always had re the low-vol anomaly.  After learning some rudimentary geo math I always wondered if the low vol anomaly thing could be explained by more things than leverage constraints and/or lottery seeking and whether it was partly due to the nature of geometric returns.  I assumed that since lower vol/same return strategies were under-appreciated when one is stuck in single-period world and can beat higher vol strategies there had to be some relationship.  Also since the geometric efficient frontier can in some cases bend down at higher allocations to risk that there might be some explanatory power there too.  I'd love to see more on this some day. 

Newfound continues to be a must-read for me. I appreciate the tip. It's now printed, read, and in a growing pile by my desk that is my new "geometric-return lirbrary" a phrase at which my gf would roll her eyes.  The articulation of the mean-median thing was helpful.  I've read about it before but didn't get it. His was a perfect way to articulate it. 

WS