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 volatile minimization 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 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