“To ensure that a central bank does not prioritise the solvency of the sovereign over its primary mandate of price stability, the European treaties prohibit monetary state financing. In its public sector purchase programme ruling of 5 May 2020, the German constitutional court stated that this prohibition had not been obviously circumvented because ‘acquired debt instruments are to be returned to the market if continued intervention is no longer necessary to achieve the inflation target’. However, that stipulation would not be upheld if central banks continue to maintain government bonds on a large scale over the long term.” Jens Weidmann and Jorg Kramer. January 2024.
Big ECB balance sheet is a source of risk not stability – OMFIF
This short and sweet article from Jens Weidmann (President of the Deutsche Bundesbank 2011-2021) and Jorg Kramer is presumably in response to the ongoing discussions/narrative around the ECB’s ‘Operational Framework’ review, as recently floated by ECB Chief Economist, Philip Lane. We discussed said topic in some depth in our November 2023 Update – “Recession. Yay!”.
https://convex-strategies.com/2023/12/14/risk-update-november-2023-recession-yay/
The opening quote above highlights the proposition that extraordinary balance sheet usage, as a policy accommodation tool, would be temporary and that the bonds/assets would be returned to the market. The actions were not a permanent injection of funds and financing. This argument was made across the global spectrum of asset purchasing central banks, maybe most notably by then Fed Chair, Ben Bernanke. Now, across various ‘framework’ reviews, we see ever increasing efforts to justify forever larger balance sheets.
As we have so often noted; “If it doesn’t work, do more. If it works, do more.”
It is nice to see someone of Mr. Weidmann’s pedigree publicly declaring his objections to the spin coming out from his former colleagues. The authors get right to the crux of the ‘Fiscal Dominance’ issue.
“In an extreme case, the central bank is caught in a near-irresoluble dilemma. Either it disregards its price stability mandate and counters a destabilising increase in government financing costs by further massive government bond buying regardless of the inflation outlook, or it risks a sovereign debt crisis.”
They also touch upon one of our leading pet peeves, being the advocacy of maintaining a policy to offset fragility that is a direct result of said policy. As in, wildfire prevention policies creating so much fire risk that you have no choice but to maintain the pursuit of wildfire prevention policies.
Weidmann and Kramer continue: “Another argument used in favour of large ECB balance sheets is that banks’ demand for central bank reserves allegedly fluctuates more than in the past. High excess reserves could, it is claimed, prevent this instability from affecting money market rates and ultimately destabilising the economy. But this instability is itself largely created by the inoperability of the interbank market – caused by over-abundant central bank balances.”
We showed this picture back in the November 2023 Update.
Figure 1: ECB Assets (blue) and Eurozone HICP Index (white)
Source: Bloomberg
The authors even go right down our own path of advocacy towards central banks acting as risk managers, not as wizards behind the curtain.
“Banks do not have to hold permanent volumes of excess liquidity for reasons of financial stability. In the same way, homeowners do not keep large sums of money in their current accounts to rebuild their houses after a fire. Instead, they take out fire insurance.”
Obviously, the same goes for investment managers!
Lest you think these musings about temporary interventions becoming permanent aspects of the newly revised framework for today’s initial conditions are brand new, we give you Ben Bernanke’s Jackson Hole speech from 2012.
https://www.federalreserve.gov/newsevents/other/o_bernanke20101105a.htm
“Estimates of the effects of nontraditional policies on economic activity and inflation are uncertain, and the use of nontraditional policies involves costs beyond those generally associated with more-standard policies. Consequently, the bar for the use of nontraditional policies is higher than for traditional policies. In addition, in the present context, nontraditional policies share the limitations of monetary policy more generally: Monetary policy cannot achieve by itself what a broader and more balanced set of economic policies might achieve; in particular, it cannot neutralize the fiscal and financial risks that the country faces. It certainly cannot fine-tune economic outcomes.”
Then Chair Bernanke lists out the potential costs of the expansion of their balance sheet through Large-Scale Asset Purchases (LSAPs), aka QE.
- “One possible cost of conducting additional LSAPs is that these operations could impair the functioning of securities markets.”
- “A second potential cost of additional securities purchases is that substantial further expansions of the balance sheet could reduce public confidence in the Fed’s ability to exit smoothly from its accommodative policies at the appropriate time.”
- “A third cost to be weighed is that of risk to financial stability.”
- “A fourth potential cost of balance sheet policies is the possibility that the Federal Reserve could incur financial losses should interest rates rise to an unexpected extent.”
Impressively on the mark. Unfortunately, none of the potential costs are deemed worthy of much concern. The responses to the four listed concerns:
- “…to this point we have seen few if any problems in the markets for Treasury or agency securities…”
- “The FOMC has spent considerable effort planning and testing our exit strategy and will act decisively to execute it at the appropriate time.”
- “We have seen little evidence thus far of unsafe buildups of risk or leverage…”
- “…monetary policy can achieve the most for the country by focusing generally on improving economic performance…”
All of the above concerns have materialized, over time, and we might conjecture continue to warrant somewhat greater consideration than Chair Bernanke soft-shoed around in 2012. Notably, he did not mention a particular risk around foregone price stability.
Indeed, much consideration has been given to the eventual unintended outcomes as gently foreseen by Chair Bernanke. For a quick summary, we would suggest you click into our September 2022 Update – “Is Sharpe World Closing”. In this Update we link to five of our other past Updates where we specifically noted and discussed regulatory efforts around many of the above listed concerns.
https://convex-strategies.com/2022/10/18/risk-update-september-2022-is-sharpe-world-closing/
This brings us back to our regular refrain – they don’t know what the impact of their interventions will end up being. More accurately, they can’t know.
We wonder if those in the Ivory Towers, undertaking economic forecasts and manipulations, are familiar with the premises of Chaos Theory and the Butterfly Effect?
Chaos: The Science of the Butterfly Effect (youtube.com)
This is another short video from the folks at Veritasium. It touches on the works of two legends in the world of the mathematics around uncertainty, Henri Poincaré and Ed Lorenz. The video poses the simple question – “How well can we predict the future?”
Poincaré is often considered one of the originators of the mathematics underlying chaos theory, specifically evidenced by his 1890s work on what is known as the “three-body problem” https://en.wikipedia.org/wiki/Three-body_problem. Years later, in 1962, mathematician and meteorologist, Ed Lorenz conducted the now famous experiment where he changed the initial conditions ever so slightly (to three decimal places instead of 6 decimal places) and generated massively different weather scenarios, despite using the precise same model and assumptions. This leads to the concept underlying complex systems and non-linear dynamics.
In his 1993 book, “The Essence of Chaos”, Lorenz defined the butterfly effect thusly: “The phenomenon that a small alteration in the state of a dynamical system will cause subsequent states to differ greatly from the states that would have followed without the alteration.” https://en.wikipedia.org/wiki/Butterfly_effect
Note, these two clever chaps came to their, mathematically robust, conclusions in 3 variable states of a deterministic physical realm. The seers in the faux-science realm of economic forecasting are dealing with a much more complex environment than that. The economy, the markets, are multi-variate, non-deterministic, non-linear, social systems dominated by pesky critters with free will. This is why, as we noted in November’s Update, the likes of ECB Chief Economist, Philip Lane, couches so many of his proclamations of future outcomes as being predicated “in the steady state” with “all else equal”. If only the world was so simple!
We quoted Mr. Lane’s compadre, Huw Pill of the Bank of England, in our June 2023 Update – “One Thing”. https://convex-strategies.com/2023/07/13/risk-update-june-2023-one-thing/
“As inflation moves away from target, the everything-else-equal assumption that allows us to break down the contributions to the drivers of inflation in a linear way tends to become unworkable. The likelihood of second round effects is much stronger when there is a tight labour market. The impact of shocks is not additive to one another but has an important multiplicative moment. Which means linear models are not very successful.” Huw Pill. ECB Sintra Conference, June 2023.
As Poincaré and Lorenz would put it – “sensitive to initial conditions”.
Going back to last month’s Update, “It’s Just Math” https://convex-strategies.com/2024/01/15/risk-update-december-2023-its-just-math/ and the wonderful quote from Nobel Prize-winning mathematical physicist, Eugene Wigner.
“The world around us is of baffling complexity and the most obvious fact about it is that we cannot predict the future.”
Case in point, we received the quarterly updates from the Bank of Japan (BOJ) on the Outlook for Economic Activity and Prices (January 2024). For the first time in two years, the forecast for 2023 Fiscal Year y/y% change for CPI ex-Fresh Food and Energy was not shifted higher. They held it steady to the previous October projection of 3.8%.
Figure 2: BOJ forecasts for GDP, CPI ex-Fresh Food, and CPI ex-Fresh Food and Energy. YoY% Change
Source: https://www.boj.or.jp/en/mopo/outlook/gor2401a.pdf
We can update our view of the history of their forecasts. (Note, we stick to CPI ex-Fresh Food and Energy as it does not include the one-off 1% impact of the government fuel subsidy from February 2023. Funny how the BOJ never mentions the impact of that.)
Figure 3: History of BOJ Quarterly Forecasts for CPI ex-Fresh Food and Energy
Source: Bank of Japan, Convex Strategies
What stands out is the persistent revisions higher to the projections for FY 2022 and 2023, yet the unwavering return to just below 2% for FY 2024 and 2025. No matter the circumstances, it comes back below target. As we constantly note, they have great confidence that their extraordinarily accommodative policy settings, WILL NOT WORK! Thus, they firmly intend on continuing with them. Does make one wonder who exactly is making the most effort at instilling the so-called ‘deflationary mindset’. The current implied path of CPI ex-Fresh Food and Energy for the remaining three months of FY 2023 is shown below.
Figure 4: Japan CPI ex-Fresh Food and Energy YoY% (white) and Estimate Future Path to Achieve BOJ Jan 2024 FY’23 Forecast (multi-colored)
Source: Bloomberg, Convex Strategies
We look forward to receiving the revised projections in April and commencing our efforts to track the BOJ’s inferred path to their (current) FY’24 projection of 1.9%.
Japan is a fantastic case study to let the mind wander as to the implications of all the long history of interventions and the ongoing string of Butterfly Effects that have been, and yet will be. The path matters, a lot and this loops us back, yet again, to the concept of Ergodicity; ergodic versus non-ergodic processes, nsemble averages versus time averages.
The leading voice as to the implications of ergodicity on the worlds of finance and economics is a wonderful chap by the name of Ole Peters. We often reference notes from and link to Ole’s website – Ergodicity economics – Formal economics without parallel universes.
The most recent article from Ole is an absolutely spectacular telling of the history of the key contributors to the field. It is well worth a read, well worth bookmarking.
Ergodicity economics — a history – Ergodicity economics
In his telling through history, Ole eventually touches on a piece of his own work. A piece that we hold at the very core of our own efforts to understand the complexity of time and the flaws at the absolute centre of Sharpe World.
“In 2011 I published a solution of the St. Petersburg paradox, arguing that because of the broken ergodicity in multiplicative random growth the optimal behavior of an individual gambler would not optimize expected wealth but time-average growth. Like in Kelly’s and Whitworth’s case, the result can be mapped to using expected logarithmic utility. I’m explicit about the broken ergodicity and its consequences: we don’t need utility to solve the St. Petersburg paradox; properly accounting for broken ergodicity is enough.”
The paper he is referring to is his note – “The time resolution of the St. Petersburg paradox”.
https://arxiv.org/pdf/1011.4404.pdf
The two key conceptualizations that Ole makes to come up with his resolution of the paradox, and thus counter the Sharpe World orthodoxy going back to Bernoulli’s work on probability and statistics, are simply set forth for all to see:
- “Rejection of parallel universes: To the individual who decides whether to purchase a ticket in the lottery, it is irrelevant how he may fare in a parallel universe. Huygens’ (or Fermat’s) ensemble average is thus not immediately relevant to the problem.”
- “Acceptance of continuation of time: The individual regularly encounters situations similar to the St. Petersburg lottery. What matters to his financial well-being is whether he makes decisions under uncertain conditions in such a way as to accumulate wealth over time.”
Some, us included, might claim ‘common sense’. Or, as Ole puts it, the paper “concludes that the prominence in economics of Bernoulli’s early arguments may have contributed to poor risk assessments of modern financial products, with consequences for market stability through the effect of credit and leverage, as foreseen by writers as early as Adam Smith.” We are in good company!
“Excessive risk is to be avoided primarily because we cannot go back in time. Behavioural aspects and personal circumstances are relevant on a different level – they can change and do not immediately follow from the laws of physics.”
Risk is subjective. The Arrow of Time is asymmetric. The Butterfly Effect.
We used the St. Petersburg paradox as an allegory to peel back the curtain a little bit on what actually goes on in the construction of convex payouts, way back in our March 2019 Update – “St. Petersburg Paradox”. https://convex-strategies.com/2019/05/06/risk-update-q1-2019/. To the point about market stability, we put it like this back then:
“This is precisely how crises materialise. Too many wannabe casino operators get too complacent in competing to sell infinite expected loss games at ever-lower upfront prices due to an overly short term, probability based, no personal accountability, business model.”
We focused on Ergodicity in our so titled September 2020 Update – “Ergodicity”. https://convex-strategies.com/2020/10/21/risk-update-september-2020/. Our comments in this note, not surprisingly, echo the language of Ole’s paper above.
“As usual, it simply comes back to math. It is the flawed practice, throughout the industry, of applying ensemble averaging as though wealth were an ergodic progression, and therefore using simplistic short term, probabilistic, expected returns as a decision-making tool. Properly evaluated, investment returns must be evaluated as non-ergodic
and evaluated with time averages. Each of us can only get the results that we get, we can’t get the average of results of a large group and cannot go back in time to change the results once received!”
Today’s initial conditions are the results of decades of non-ergodic path dependencies. The Butterfly Effect of the past sets up the Butterfly Effect of the future. The policy measures of central bankers and government officials, aligned with the flawed-math and regulatory practices of unaccountable fiduciary organizations, has led to precisely the sort of stability issues that Adam Smith foresaw.
The stability concern is most obviously in the reliance on an anomaly of recent historical market behaviour and an application of the flawed mathematics and supporting regulation of Sharpe World fiduciary entities. As we have discussed so often, we can simplify this as the unprecedented ownership of uncapitalized risk in the form of bonds. For the basic core sample, we use the traditional balanced 60/40 portfolio as the poster child in this dilemma. For 20-30 years, policy makers, intentionally or otherwise, perpetrated an environment where bonds provided a positive return, low volatility, negative correlation and portfolio benefit to investors.
In the decade ending December 2020, bonds were a beneficial balancing component to an otherwise equity-based investment portfolio. The bonds themselves were a positive returning, low volatility, asset that provided a modicum of negative correlation to equities when needed. In the below hypothetical worked examples we will use the Bloomberg US Treasury Total Return Index (LUATTRUU Index), as our fixed income proxy, and the S&P 500 Total Return Index (SPXT Index), as our equity proxy.
Figure 5: US Tsy 100% (blue) vs SPX 60% and US Tsy 40% (red). 2011-2020. Scattergram and Return Distribution
Source: Bloomberg, Convex Strategies
Figure 6: US Tsy 100% (blue) vs SPX 60% and US Tsy 40% (red). 2011-2020. Compounding view
Source: Bloomberg, Convex Strategies
Figure 7: US Tsy 100% (blue) vs SPX 60% and US Tsy 40% (red). 2011-2020. Portfolio Statistics
Source: Bloomberg, Convex Strategies
Switching the bonds for an outright holding of S&P shows that, while foregoing far better upside of the equities, there was a definite portfolio risk benefit to holding 40% in bonds.
Figure 8: S&P 100% (blue) vs SPX 60% and US Tsy 40% (red). 2011-2020. Scattergram and Return Distribution
Source: Bloomberg, Convex Strategies
Figure 9: S&P 100% (blue) vs SPX 60% and US Tsy 40% (red). 2011-2020. Compounding view
Source: Bloomberg. Convex Strategies.
Figure 10: S&P 100% (blue) vs SPX 60% and US Tsy 40% (red). 2011-2020. Portfolio Statistics
Source: Bloomberg, Convex Strategies
You can see that over the period 2011-2020 the 60/40 portfolio essentially cuts in half the key risk measures of Downside Volatility and Max Drawdown. Thus, generating a much superior Sortino Ratio of 2.0, versus a Sortino Ratio of 1.4 for the S&P on its own.
Unfortunately, when we run the same analysis over just the last three years, all that (moderate) benefit from owning bonds disappears.
Figure 11: US Tsy 100% (blue) vs SPX 60% and US Tsy 40% (red). 2021-Jan2024. Scattergram and Return Distribution
Source: Bloomberg, Convex Strategies
Figure 12: US Tsy 100% (blue) vs SPX 60% and US Tsy 40% (red). 2021-Jan2024. Compounding view
Source: Bloomberg, Convex Strategies
Figure 13: US Tsy 100% (blue) vs SPX 60% and US Tsy 40% (red). 2021-Jan2024. Portfolio Statistics
Source: Bloomberg, Convex Strategies
Now, bonds no longer provide a positive return on a standalone basis. The bonds no longer have exceptionally low Downside Volatility and low Max Drawdowns. Comparing the 60/40 to the standalone equities shows the bonds have lost all of their previous benefit.
Figure 14: S&P 100% (blue) vs SPX 60% and US Tsy 40% (red). 2021-Jan2024. Scattergram and Return Distribution
Source: Bloomberg, Convex Strategies
Figure 15: S&P 100% (blue) vs SPX 60% and US Tsy 40% (red). 2021-Jan2024. Compounding view
Source: Bloomberg, Convex Strategies
Figure 16: S&P 100% (blue) vs SPX 60% and US Treasury 40% (red). 2021-Jan2024. Portfolio Statistics
Source: Bloomberg, Convex Strategies
In the recent three years, the bond component no longer provides a meaningful benefit. In fact, based on Sortino Ratio as a measure, the bonds are now a disbenefit. The 60/40 chimes in with a Sortino Ratio for this most recent period of 0.7 versus 1.1 for S&P standalone. There are now but small reductions in Downside Volatility and Max Drawdown from stashing a 40% weighting into bonds and a significant reduction in portfolio return.
As a good visualization of the decline in the beneficial nature of bonds, we show below the rolling 3yr Sortino Ratios of the above proxies. What stands out is a) the decline of the bond standalone performance since its peak just prior to the regime shift in 2021, and b) the reversal of the relative Sortino Ratios with the 60/40 performance dipping below S&P on a standalone basis.
Figure 17: 3yr Rolling Sortino Ratios for S&P (blue), 60/40 (red), US Treasury (gold). 2011-Jan2024
Source: Bloomberg. Convex Strategies.
The reasoning is not difficult to fathom. Since the end of 2020, interest rates went up and interest rate volatility went up.
Figure 18: US Treasury 10yr Yield (blue) and MOVE Index (white). 2011-Jan2024
Source: Bloomberg, Convex Strategies
Also important, maybe even more so, is the correlation between equities and bonds that we keep harping on about.
Figure 19: US 5yr Equity-Bond Correlation vs 5yr Annual Inflation %
Source: Meketa,, Convex Strategies
Regular readers will know that we have some suspicion that an underlying cause of this change in the regimes of bond volatility and correlation, from the Goldilocks period of recent times, could have something to do with the foregone suppression of the volatility of price stability measures by central banks.
Figure 20: UK 20-year Average Inflation vs Inflation Volatility, 1217-2023
Source: https://personal.lse.ac.uk/reisr/papers/22-whypi.pdf, Millenium dataset of the Bank of England, Convex Strategies
Simple question; is the 1997-2016 dot in figure 20 the norm? Or, as it looks like in the chart, is it the clearest anomaly? The answer to that question is probably the key to any consideration as to bond’s likelihood of recovering their status as a worthwhile portfolio component.
Meanwhile, the ‘system’, inevitably, got itself to its highest level of dependence (and leverage) on the imposed belief of the portfolio risk benefit of bonds just as the regime shifted. As long as we do not return to something like the old regime, something with acceptably low levels of volatility and sufficiently beneficial correlations, there will persist pressure to reduce, or at least not increase, holdings of bonds on the basis of some past portfolio benefit. Who is going to own the 40%?
The good news, for risk and investment managers, is that all along, even during the glory days of fixed income, in the hypothetical worked examples we look at here we think that you could have been better off pairing your equity risk with the much more efficient, explicit, risk mitigation of long volatility.
In just the simplest of portfolio transformations, split your bond allocation equally between Long Vol, as usual, we will use the CBOE Eurekahedge Long Volatility Index (EHFI451 Index) as our Long Vol proxy, and more equities. This gives you a simple 80/20 barbell. Over the combined time horizon of our above examples, theoretically it gives you this clean result.
Figure 21: S&P 80% / LongVol 20% (blue) vs S&P 60% / US Tsy 40% (red) 2011-Jan2024 Scattergram and Return Distribution
Source: Bloomberg, Convex Strategies
Figure 22: S&P 80% and LongVol 20% (blue) vs S&P 60% and US Tsy 40% (red). 2011-Jan2024 Compounding View
Source: Bloomberg, Convex Strategies
Figure 23: S&P 80% and LongVol 20% (blue) vs S&P 60% and US Treasury 40% (red). 2011-Jan2024 Portfolio Statistics
Source: Bloomberg, Convex Strategies
As we discussed last month, a regime change in the stable volatilities and correlations of the key portfolio components that make up the core of Sharpe World investment strategies could be an ongoing headwind to traditional investment strategies. Regardless of whether we go back to the ‘good old days’ of suppressed volatility of inflation measures or not, the answer to superior compounding of portfolios will be convexity. In each investor’s own individual Butterfly Effect path, there is no more important initial condition than the addition of positive convexity to your portfolio.
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