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With central banks pegging interest rates to near zero rates, an argument could be made that the future distribution of interest rates and bond returns are not normally distributed. How has modern portfolio theory handled this phenomenon? What are the implications for real money asset allocators, such as pension funds, on their asset allocations? Have the implications (if any) actually been implemented in actual asset allocation shifts for such funds?

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Many pension funds use projected asset class returns (capital market assumptions or CMAs) and backward-looking estimates of volatilities and correlations to set the strategic asset allocation. A 10-year period for the return projection is typical. The determination of actual weights is more or less an exercise in constrained mean-variance optimization.

While projecting future returns is fraught with uncertainty (particularly for equities), CMA estimates for bonds have been historically much more reliable with current yield as a good predictor of future returns, particularly when yields are low.

The graph below shows the outlook for bond returns is not attractive to say the least -- and not to mention the fact that the current low yields are without precedent. Most models would now call for a lower allocation to bonds as most U.S. pension funds have a required rate of return of around 7 - 7.5%.

Unfortunately, diversification in the form of a balanced allocation between stocks and bonds, e.g. 60/40 has been the primary form of risk mitigation at pension funds for many decades. This is problematic for pension funds going forward as (1) bonds are likely to be a large drag on performance -- most assuredly if higher inflation returns -- and, (2) as feared, the negative correlation between stocks and bonds seen over the last two decades reverts to the low positive average seen before 2000, whence bonds provide even less protection when equities decline.

Also, there is an emerging realization that a large allocation to bonds has not even worked well in the past. While it has dampened portfolio volatility across all market environments, i.e., when not needed, it has failed to provide sufficient equity tail-risk protection to justify the performance drag particularly during the record-setting economic expansion from 2009 to 2019. That is perhaps one reason why the average funded ratio at U.S. public pension funds remains at only 70%.

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  • $\begingroup$ Thanks very much for the thoughtful response. $\endgroup$ – AlRacoon Sep 24 '20 at 19:12
  • $\begingroup$ Thanks very much for the regression of 10yr returns vs Initial Yield. The strong relationship seems to hint that asset allocators should take expected returns from bond allocations to almost nothing. $\endgroup$ – AlRacoon Sep 25 '20 at 20:38
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I'll add some comments, recognizing that 1) they are highly opinionated, and 2) they don't actually offer any real solutions. Hopefully more thoughtful and useful answers will emerge.

First of all, purely from a philosophical perspective, I have to admit that I sometimes find these discussions on strategic asset allocation (SAA) "strange." Strategic asset allocation is supposed to give us a portfolio that we'd hold when we have no market views; it's supposed to be the best beta portfolio that could withstand any economic environments and regimes. In practice, as @RRL has mentioned, many institutions' SAA process starts by forming Capital Market Assumptions (CMAs), which really represent "views" on the relative attractiveness of different assets. The question being asked itself embeds a view on future bond returns. I think the first question we should ask ourselves is – how good are we at forming such views and do they really have a role in the SAA process? After all, it is plausible for bonds to continue behaving as they have over the past century and that our belief of bond yields not being able to go down further reflects a lack of imagination... (For the record, I don't believe the concerns are unfounded and I've indeed been rather concerned about the role of nominal bonds in a strategic portfolio.)

Now onto the challenge. As @RRL has mentioned, there is some predictability to long-term returns. Bond returns are well forecast by starting yield levels; equity returns are highly correlated to some proxy of dividend yield, valuation mean reversion, and trend earnings growth. The picture below provides my own estimates of expected returns for a US 60/40 portfolio, which admittedly is more pessimistic than many other people's work:

enter image description here

The challenge is abundantly clear. Based on my estimates, no combination of conventional US assets can get us to a 5% real return that many perpetual institutions require. (Again, I must note that the confidence interval is rather wide and my track record of forecasting the future is rather poor.)

Now let's get back to the bond issue in particular. In recent years, we've had low bond yield. That in itself is actually not that terrible, as long as bonds actually offer a risk premium. For example, if bond yield is 2% and cash is 0%, that's 200 bp in excess returns. You lever it 2x (typical for a risk parity type asset allocation), that's 400 bp of excess returns. The issue today is that bonds and cash are both returning 0%, and there's no risk premium to lever. And I generally think this is true across assets... This has prompted some big changes in how some managers are constructing risk parity portfolios.

So what's the solution? I've been struggling for months. Here are some things I've been reading/thinking about: 1) If you have the view that inflation will be a big deal, increase allocation to real assets and inflation-protected assets; 2) Increase allocation to less liquid assets to capture illiquidity premium (that's assuming illiquidity premium is not mispriced today and that you have the skill to select the best managers in each asset class); 3) Increase allocation to areas where there are still yields and higher equity risk premium (e.g., EM). Other proposals are welcome!

Finally, in terms of quant modeling, the previous link provides some color on what some are thinking about in the risk parity realm. In the more "traditional" space, I almost feel the modeling exercise is the easy part. Many institutions now use a simulation-based approach to creating optimal portfolios. These methods have a lot of degrees of freedom, allowing us to model a wide range of asset behaviors (e.g., it appears that future bond returns will be much more assymmetric with significant tail risk; we can potential draw upon experience from EM with high or even hyperinflationary episodes to anchor extreme outcomes). Inevitably, these models will call for less nominal bond allocation due to a combination of lower expected returns and less diversification benefits. And yes, some institutions are already adjusting nominal bond exposures (whilst increasing allocation to linkers).

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  • $\begingroup$ Thanks very much for your thoughtful response. You have given me some things to think about. $\endgroup$ – AlRacoon Sep 24 '20 at 23:45
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Have the implications (if any) actually been implemented in actual asset allocation shifts for such funds?

Yes - or at least a shift is being considered. See this story https://www.cnbc.com/2020/09/16/singapore-summit-cppib-ceo-on-zero-bound-interest-rates.html

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  • $\begingroup$ Thanks very much for the link to the story. I am wondering how they are incorporating their outlook in any mean variance optimization framework (if any). How are they accounting for skewness and/or kurtosis of the outlook for distribution of bond returns? Is just reduced returns driving it and they are excluding the asset class from any optimization? Is the standard optimization being overridden and a CIO call is made as a tactical bet? $\endgroup$ – AlRacoon Sep 24 '20 at 18:11

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