The Impermanent Portfolio

Besides seeking returns, investors are also keen to limit volatility.  It’s not just about comfort … over most time horizons short of a decade returns are notoriously difficult to predict.  What did well over the last decade sheds almost no light on what will do well over the next.  Even multiple decades of returns have little tendency to repeat in the future.  Moreover, volatility is a measure of the degree of confidence that any particular range of return might be realized.

Asset class volatility – the variability in returns – however does tend to be persistent over time.  For this reason, it’s relatively more useful as a guide to portfolio construction.  Even an investor for whom low volatility isn’t a high priority may carefully weigh volatility just because it’s more predictable.  A bit of a serenity prayer type thing … control the things you can.  

Yet more persistence doesn’t mean perfect persistence.  The relationship between asset classes does drift over time.  In particular, the proportions of asset classes within a given set of classes that produces the lowest volatility, while more persistent and predictable than overall returns, evolves and needs to be occasionally updated to be of the most use.  With that in mind, I’ve run several tests using the latest historical data to model what portfolio mixes are likely to be volatility efficient going forward. 

First a rundown of what went into these tests.  Readers not interested in technical details should feel free to skip ahead to the results.  All of the tests cover sixteen week intervals ending between January 1, 2000 and the end of last week.  The omission of data prior to 2000 is because the economic and financial environment has changed to the extent of making it less relevant and possibly counterproductive in foreshadowing what’s ahead.  I chose sixteen week intervals as a general reflection of what’s apt to be felt by most investors.  Even a long term investor about to make a substantial portfolio withdrawal usually has a few weeks discretion over timing, but may be hard pressed to wait a year.  It’s a bit longer than a calendar quarter and long enough to minimize the effect of noisy fluctuations.  The assets put to the test are short term treasuries, long term treasuries, stocks, copper, gold, silver and platinum.  The significance of these choices will become apparent. 

A word about units.  This a big deal to me because such tests are routinely run by sophisticated analysts who completely disregard their significance.  I’m using US dollars as the unit of account for this analysis.  Anyone who tries to tell you that the volatility of Asset X is Y at some frequency over some time interval is not telling you the truth.  They’re assuming that their unit of account has no volatility of its own … and presenting zero evidence for the assumption.  It is possible for example that a sufficiently broad mix of assets has virtually zero real volatility, yet if measured in a unit that has volatility itself will appear volatile.  Minimizing volatility relative to US dollars is not the same as minimizing volatility period, and we won’t skip over that fact here at Financology.  The dollar is an asset too, and its own fluctuations are merely obscured by measuring its value with itself.

We’ve also constrained the allocation to short term treasuries to zero for this analysis.  This is because they are tightly tethered to US dollars and have by far the lowest volatility – as measured in US dollars – and without this constraint the algorithm will simply default to 100% short term treasuries.  An investor can scale the resulting volatility results to virtually any level simply by varying the allocation to short term treasuries while holding the proportions of the other asset classes constant. 

First let’s look at the set of intervals ending between the beginning of 2000 and the beginning of 2020.  “Mean” refers to the average sixteen week return and standard “Deviation” to root mean square volatility.  The results of minimizing the volatility of the six remaining assets are:

Treasuries:  0.3046
Stocks:  0.4101
Copper:  0.0000
Gold  0.2853
Silver  0.0000
Platinum  0.0000

Mean  0.0231
Deviation  0.0549

The outcome that the allocation all of the commodities except for gold comes out to zero is striking.  Intuitively we might have expected that any fourth asset might have some independent degree of freedom and that some small amount might have at least some diversification value, but this was not the case.  To a portfolio of stocks, bonds and gold, any addition whatsoever of copper, silver or platinum increased the volatility and had zero diversification value from the perspective of volatility.  What’s more, of the four commodities, only gold improved the diversification of a portfolio of stocks and bonds.

Interestingly enough, however, if we constrain the mix to exclude gold, we get

Treasuries:  0.4533
Stocks:  0.4713
Copper:  0.0755
Gold  0.0000
Silver  0.0000
Platinum  0.0000

Mean 0.0227
Deviation 0.0590

Copper was able to pinch hit for gold to a small extent, at the cost of somewhat lower overall return and higher volatility.  A higher Treasury allocation was also required.  Regardless the implication is that the addition of some physical commodity to a portfolio of stocks and bonds can improve portfolio efficiency.  Stocks and bonds alone were never really a complete balanced portfolio.

Next let’s expand our time frame to the end of last week.

Treasuries:  0.2516
Stocks:  0.4371
Copper:  0.0000
Gold  0.3113
Silver  0.0000
Platinum  0.0000

Mean  0.0236
Deviation  0.0569

Hmmm … just by including the period since the beginning of 2020 in our data set, the importance of gold has increased, mostly at the expense of treasuries.  Comparing with the original result above, treasuries have fallen from 0.3046 of the portfolio to 0.2516, while gold has increased from 0.2853 to 0.3113.  Stocks have also risen a bit, and unsurprisingly this comes at the cost of an increase in overall minimum volatility as well.

Taking a cue from this, let’s see what happens if we increase the weight of the period since the beginning of 2020.  We could even completely exclude the data prior to 2020, but I’m reticent to do that because it reduces our sample size to an uncomfortably small set.  So instead let’s simply give each data point in the post-2020 range 63 times the weight of each data point in the 2000-2020 range.  This still puts too much weight on a relatively small sample set to extrapolate forward, but will at least give us a qualitative indication of how asset class correlations may have shifted so far in the 2020s.  We have:

Treasuries:  0.1516
Stocks:  0.2896
Copper:  0.1284
Gold  0.3569
Silver  0.0000
Platinum  0.0735

Mean  0.0421
Deviation  0.0584

Let that sink in a moment.  Not only treasuries, but stocks as well, have decreased, and with gold, copper and platinum for the first time have made an appearance.  Given the recent rally in commodities, if we were talking about returns, this might not seem particularly noteworthy.  But this is purely volatility.  Simply to minimize volatility, industrial commodities have taken on a diversification value not seen in the prior two decades.  Astonishing.

Finally, let’s select a weighting that emphasizes the changed environment since the beginning of 2020, but that nevertheless remains broad enough that we can have some confidence in its sustainable relevance.  We choose to weigh each 2020-Present data point at three times the weighting of each 2000-2020 data point.  This gives us the following minimum volatility weighting:

Treasuries:  0.2062
Stocks:  0.4573
Copper:  0.0000
Gold  0.3364
Silver  0.0000
Platinum  0.0000

Mean  0.0253
Deviation  0.0586


7 thoughts on “The Impermanent Portfolio

  1. jk says:

    it might be interesting to look at results before and after the gfc. it feels like the world [or at least the financial part of it] changed a great deal at that time.

    1. Bill Terrell says:

      Interesting suggestion … thanks JK. I’ll follow up with what I find.

    2. Bill Terrell says:

      Here are the results of the test over two periods. Take them with a grain of salt … although they each represent 640 overlapping sixteen week periods, there are only 40 effectively independent sixteen week periods in each sample set. It’s enough though to give a general sense of the changes.

      Over the sixteen week intervals ending from 1996 0928 – 2008 1227:

      Treasuries: 0.5150
      Stocks: 0.2183
      Copper: 0.0361
      Gold 0.2307
      Silver 0.0000
      Platinum 0.0000

      Mean 0.0234
      Deviation 0.0435

      Over the sixteen week intervals ending from 2009 0103 – 2021 0403:

      Treasuries: 0.1923
      Stocks: 0.5455
      Copper: 0.0000
      Gold 0.2622
      Silver 0.0000
      Platinum 0.0000

      Mean 0.0291
      Deviation 0.0520

  2. jk says:

    interesting, thanks. my 2 observations, which i’m sure won’t be news to you, are:
    1. the gold weighting remained relatively constant between the 2 periods
    2. treasuries and stocks traded weightings. makes sense in hindsight, of course. i wonder if there’s a forward looking way to see these things? or is that subsumed by synthetic systems?

    i’m looking forward to your systems update as we enter july.

    1. Bill Terrell says:

      A challenge in interpreting these data is keeping in mind the degrees of abstraction involved. It’s an effort for me even after having worked through the design and construction of the model. Not only are the results not returns; they’re not even volatilities. They’re the proportions of the selected assets that give the lowest overall volatility under the test conditions. This joint volatility is not only a function of the volatilities of the assets individually (generally the higher the volatility the lower the weighting) but also reflects their phase relationships. If for instance you had two assets which moved exactly inversely, an equal mix of the two would always have zero volatility, no matter how volatile the individual assets. Shift the phase 180°, and you can’t reduce the volatility at all.

      And all that’s in addition to the complication of using an asset that has volatility of its own as a unit of measure.

      Extending that to three asset classes reminds me of three phase electrical power, where you have three sinusoids displaced by 120° such that they everywhere sum to zero. One of the big picture takeaways for me is the apparent universality of the three asset portfolio, where three dissimilar assets seem to be required for maximum portfolio efficiency … firstly no less than three but secondly no more … at least the striking rate of diminishing returns past three. That second part was a surprise to me.

      There were two goals in this post. One was to illustrate the evolution of the minimum volatility allocation … a timely issue given the popularity of declarations of the death of the 60-40 portfolio. The other was to get a sense of what the minimum volatility mix might look like for the 2020s as a whole. This latter question was the motivation for the last set of figures in the post.

      That’s of course as much art as science. My sense is that in meaningful ways the 2020s will echo the 2000s. Of course it will be different in other ways, so the idea is to allow for it without forcing it. So that last posted run includes data from the 2000s along with the 2010s and of course the overweighted slice of the developing 2020s. That set of results would be my best estimate so far of what the minimum volatility mix would look like at the end of the decade; that is, a forward looking view of the 2020s as a whole.

      As for how these results might fit in with Synthetic Systems, the latter deals squarely with returns. Generally speaking, in addition to fundamentals and valuations, I use the minimum volatility mix to help inform an overall strategic allocation while using SS to make +/- tactical adjustments along the way.