Given low, and in some countries negative sovereign rates, are sovereign bonds still the best portfolio diversifier in the long run? 

Yes

Because the portfolio optimization function has also changed. We are moving away from a world of profit maximization to a world of loss minimization.

Given persistent and large output gaps and surplus capital in the developed world, the expected return on future capital investment should be negative.

If Japan, Switzerland, Sweden and Denmark are any guide, their respective stock markets are down or flat since rates hit 0%. US is still a massive outlier (buybacks) but that is also fading (SPX buyback index is down YTD).

From a long-term point of view, I would still own sovereign debt as it has superior risk-adjusted returns even at these low yields. For example, in the last bear market for bonds, 10yr UST went from 1.95% in 1941 to 14.6% in 1982. Annual real total return for the period was 0.4% (annual nominal return was 5% with Sharpe ratio of 0.54). There were 10 years of negative returns (24% of the time) with the largest drawdown of 5% in 1969. In the bull market that followed, annual real returns were much higher but that was only because of disinflation (nominal returns were only marginally higher – around 6%). We still had 6 years of negative returns, but the largest drawdown was 11%.

‘Bond bubble’ is an oxymoron. The best value on the curve now: T-Bills. If you could be bothered to roll them, they would have a similar return to the long end but much lower volatility. The Fed just announced it is in the market buying T-Bills (as it ‘should’: the Fed is massively underweight T-Bills vs both history and the market). Despite heavy Treasury issuance net supply of T-Bills is expected to be negative next year.

US retail is massively underweight USTs: about 3-5% of all financial assets and about 2% of their overall assets.

Is gold a better portfolio diversifier when sovereigns yields are negative? Perhaps, in the short term and only for retail. Long-term, expected return on gold should also be negative (as long as sovereign yields are negative). For institutional investor gold is an inferior option from a liquidity and regulations point of view.

Is there a better portfolio diversifier at the moment, short-term? Perhaps soft commodities which trade below production costs (for some, like cotton, wheat – substantially below) – compare to precious metals which trade 50% above marginal cost of production. 

Soft commodities might be the exception among the major asset classes, whereby expected return is actually positive in a negative sovereign yield world, given that they already experienced negative returns in the past 10 years and their zero (negative?) weights in institutional or retail portfolios (mean reversion).

One can go even fancier here, up the risk curve, and allocate to hard currency emerging market debt, which has had even better risk-adjusted returns than USTs over the last 3 years. And, depending on currency views, go even further into local currency (unhedged) emerging market debt. USTs do not need to be negative, just to hover around 0%, for emerging market debt to really outperform, assuming no major market dislocation.

Finally, on the equity side, some allocation to emerging markets equity is also probably warranted given their massive under-performance specifically to US equities and my projected negative returns of the latter going forward. Unlike their developed market counterparts, emerging markets are not running negative output gaps and therefore, capital is still expected to earn a premium there.

Bottom line: if we are indeed in a loss-minimization type of world when it comes to investment returns (note, this does not assume any kind of market crash) one is still better off staying in sovereign debt, even when it yields negative as every other liquid asset is bound to return even more negative on any reasonable time scenario.