Last month we titled our Update “Recession. Yay!” in which we said this:
“As we have stated over recent months, the ‘good outcome’ would be to get to the recession, and we see people willingly buy and hold bonds. We would argue this is what happened in what was an epically ‘good outcome’ November 2023. Pauses by central banks, softer CPI and employment numbers, and the firm belief that central banks will follow the same old playbook, saw an aggressive repricing of imminent interest rate declines, ie. a willingness to buy their bonds, and that was GOOD!”
https://convex-strategies.com/2023/12/14/risk-update-november-2023-recession-yay/
December continued, almost precisely, along this same path. Updating some pictures from last month, shows that “Recession. Yay!” carried on with enthusiasm.
Figure 1: Total Return Bond Indices: US Tsy (white), US Corp (yellow), US High Yield (green). 2023. Normalized
Source: Bloomberg
Figure 2: Total Return Equity Indices: SPX (blue), NDX (orange), MSCI World (purple). 2023. Normalized
Source: Bloomberg
Key to this enthusiasm was the December 13th Fed FOMC meeting, updated Dot Plots within the new SEPs (Summary of Economic Projections) and subsequent press conference comments.
Here is the link to Chair Powell’s presser – https://www.federalreserve.gov/mediacenter/files/FOMCpresconf20231213.pdf
Chair Powell put to rest the question that we posed in last month’s update as to ongoing adherence to the August 2020 policy innovation known as ‘Flexible Average Inflation Targeting’.
We posed the question thusly last month; “We know now, with the benefit of hindsight, that the Fed was most certainly willing to “let it run hot”, in line with their FAIT policy, once measures of inflation picked up. Will they now be willing to “let it run cold” to push the average back down to target? It seems very unlikely.”
Chair Powell put the nail in the FAIT coffin in response to a question about whether he would begin cutting rates before his preferred price stability measure declined back to 2%. His response was this:
“I mean, the reason you wouldn’t wait to get to 2 percent to cut rates is that policy would be, it would be too late. I mean you’d want to be reducing restriction on the economy well before 2 percent because — or before you get to 2 percent, so you don’t overshoot, if we think of restrictive policy as weighing on economic activity. You know, it takes a while for policy to get into the economy, affect economic activity, and affect inflation.”
We look forward to the removal of FAIT from the formal policy statement or, alternatively, the reframing as to its asymmetric nature.
On the other side of the dance floor, we still have the Bank of Japan (BOJ), who is adamant about persisting with whatever you would call their version of FAIT. They are two years-ish now above their stated target and still pedal to the metal with stimulative policy settings. BOJ Governor Ueda gave a Christmas day speech where he updated the gathered attendees on his version of how Japan’s economy functions.
Wages and Prices: Past, Present, and Future (boj.or.jp) Kazuo Ueda.
As is too often the case with central bank speeches that we link in these pages, this is not a useful read, other than to further familiarize oneself with the disdain for which central bankers hold the general public and their belief in their ability to manipulate outcomes. We can save folks the time and summarize the presentation with three quick quotes and one picture that on its own says more than the 11-pages of text.
“Japan’s inflation rate, measured in terms of the consumer price index (CPI), has continued to exceed 2%.”
“…in Japan – with the significant increase in the cost of imported raw materials being transmitted with a lag – the inflation rate has continued to exceed 2 percent since spring last year.”
“In order to turn the situation around and achieve sustainable and stable inflation accompanied by wage increases, the Bank of Japan has patiently continued with monetary easing.”
Figure 3: Japan CPI ex-Fresh Food and Energy
Source: Wages and Prices: Past, Present, and Future (boj.or.jp)
We will just leave Japan there, for now.
Eyeballing figures 1and 2 above on the performance of bond and equity markets makes one thing apparent – bonds neither protected through the year nor, to a reasonable extent, did they participate during the recovery in the final two months. To make this easier to see we can show the two key indices, SPX index and the US Treasury index, together.
Figure 4: US Total Return Indices: SPX (blue) vs US Tsy (white). 2023. Normalized
Source: Bloomberg
Bonds, even with the significant recovery off the lows in October, were not an attractive portfolio complement again this year. Visually, it is easy to see this has been the case for at least the last three calendar years in figure 5.
Figure 5: US Total Return Indices: SPX (blue) vs US Tsy (white). 2021-2023. Normalized
Source: Bloomberg
Everybody knows the problem here. Correlation between bonds and equities has turned positive as the long-suppressed level and volatility of price stability measures has risen. Folks also know that we question whether the recent history of this correlation being negative is a naturally occurring phenomenon or if it was something orchestrated by inflation targeting central banks in the Greenspan Put era of central banking.
Figure 6: US 5yr Equity-Bond Correlation vs 5yr Annual Inflation %
Source: Meketa, Convex Strategies
The above red dots indicate, through the high and volatile inflation regime of the ‘70s and ’80, that key correlation was consistently positive. Now, as measures of inflation have moved higher once again (the light blue dots culminating in the bright blue triangle), that pesky positive correlation has returned.
We, of course, don’t know any better than anyone else if it is here to stay. Figure 7, gamed with our drawing of the yellow ovals over the current period and the beginning of the last major regime shift into higher and more volatile inflation measures, certainly warrants the question.
Figure 7: US PCE Core yoy% (white) and Moving Averages 3yr (purple), 5yr (red), 7yr (green). 1960-2023
Source: Bloomberg, Convex Strategies
That question is most simply summed up with our most favourite of visual representations – the Bank of England scattergram of eight hundred years of their CPI measure’s 20yr average and volatility. What is a return to normalcy?
Figure 8: UK 20-year Average Inflation vs Inflation Volatility (1217-2023) – Return to Normalcy
Source: https://personal.lse.ac.uk/reisr/papers/22-whypi.pdf /Millenium dataset of the Bank of England, Convex Strategies
Was the period of peak volatility suppression of this price stability measure, 1997-2016 in this representation, that aligned/led to the beneficial environment of negative equity-bond correlation, the normal/natural state of things? Or, as we regularly state, will it eventually be taken as an example of Minsky’s famous claim, “stability begets instability”.
Will the current state of play, ‘Recession. Yay’, lead us straight back to a post-Volcker-esque world of low and stable inflation measures? Or, as indicated by our mind-manipulating yellow ovals above, are we merely in the early stages, as was the case in the late ‘60s/early ‘70s, of paying the piper for the attempt at “managing” nature?
While this is a wonderful discussion at cocktail parties and on podcasts, the more relevant issue is what it means from an investment and risk management standpoint. The answer to that is that it both doesn’t matter and that it is absolutely critical. It doesn’t matter because the solution to the investment and risk management challenge is the same either way – be convex. Yet it is critical because if you get it wrong, in either direction, not being convex could be a disaster.
This, as always, brings us back around to our raison d’être. The purpose of investment and risk management is to compound capital through time. It is about geometric averages, not arithmetic averages. It is about time averages along distinct, non-ergodic, paths, not ensemble averages of parallel universes under assumptions that there are no ergodic breaks through time. It is about force, not momentum. It is about acceleration and deceleration, not average lap speed. We said it yet again to close out last month’s Update:
“As always, we come back to the same things. Shannon’s Entropy. Jensen’s Inequality. Time averages over ensemble averages. Geometric returns over arithmetic returns. Sortino ratios over Sharpe ratios. Control over predictions. If your objective is improved terminal compounded capital, the answers are very straightforward. It is just math….”
Those who know us well, know that this is what we love digging into in our spare time. There is an obvious common sense to the benefit of positive convexity in an investment portfolio. The taking on of non-recourse leverage, through efficient long volatility/convexity strategies, is easy to see as being beneficial to the compounding path in its role of mitigating downside pain while allowing upside participation. The actual mathematics, however, of what we sometimes term as the ‘magic dust of convexity’, is not that straightforward and far from fully resolved.
One of our most revered forefathers on the topic, famed mathematician Benoit Mandelbrot, (his book “The (Mis)Behavior of Markets” is compulsory reading) proposed the field of Fractal Geometry as holding the magic key to unlocking the mathematical complexity of the beneficial nature of convexity in investment strategies.
We don’t know if it is even remotely true but, in our minds, we like to believe that Benoit was working on this project (what we internally refer to as the search for the “God Particle”) when he discovered the extraordinary Mandelbrot Set.
Figure 9: The Mandelbrot Set
Source: Wikipedia
You can go online and find all sorts of presentations that, like the one we have linked here, use computers to show the infinite magnificence of the Mandelbrot Set. We like this particular lecture because it aligns with some of our own metaphysical views on the topic to hand. If you have not yet had the opportunity to explore the Mandelbrot Set, we really recommend you find time to watch this.
The Secret Code of Creation – Dr. Jason Lisle (youtube.com)
Professor Lisle has all sorts of wonderful quotes as he leads us through his presentation. Some of which are really quite grand but hard to argue with, for example:
“Gives you a little window into the mind of God.”
One quote, in particular, that encapsulates our view on the mysteries of convexity and its relationship to compounding along non-ergodic paths, ie. it is all there just waiting for us to find it.
“This is all built into numbers and has been waiting for us to discover it.”
Near the end of the lecture, Professor Lisle references a paper by Nobel Prize-winning mathematical physicist, Eugene Wigner. Professor Lisle provides us with this quote from that paper.
“The miracle of the appropriateness of the language of mathematics for the formulation of laws of physics is a wonderful gift which we neither understand nor deserve.”
Beautiful.
The Wigner paper is truly fantastic and chock-full of gems.
Eugene Wigner. “The Unreasonable Effectiveness of Mathematics in the Natural Sciences.”
“The world around us is of baffling complexity and the most obvious fact about it is that we cannot predict the future.”
This might reflect the reasoning around the fact that the so-called Nobel Prize in Economic Sciences is not in fact one of the original Nobel Prizes established by Alfred Nobel. Here is another comment from Wigner that could have come as a direct rebuke of Sharpe World, perfectly along the lines of our (and Hayek’s) criticism of the desire to be ‘precisely wrong’.
“Considered from this point of view, the fact that some of the theories which we know to be false give such amazingly accurate results is an adverse factor.”
Wigner, unlike the armies of Sharpe World, is well aware that the nice closed mathematical solutions of the physical sciences don’t apply when you loop humans into the situation.
“A much more difficult and confusing situation would arise if we could, someday, establish a theory of the phenomena of consciousness, or of biology, which would be as coherent and convincing as our present theories of the inanimate world.”
We highlighted the word ‘consciousness’ in bold as it is a term that often comes up when we discuss the inherent sense of the value of positive convexity, of the reality of non-ergodic paths, when one has skin-in-the-game. Our often-analogized race car driver innately knows the importance of brakes to the task of winning the multi-lap race. Heck, even the importance of the brakes in testing the car to see if engine, transmission, aerodynamics, whatever, can improve its speed. The driver, in the car, with skin-in-the-game, has ‘consciousness’. We discussed the implications of just this in our June 2023 Update – “One Thing”.
https://convex-strategies.com/2023/07/13/risk-update-june-2023-one-thing/
This train of thought naturally takes us back to our March 2023 Update – “Probability vs Possibility”. The concept of ‘consciousness’ aligns to our representation of ‘possibility’. Pippa Malmgren’s ‘wet brain’. GLS Shackle’s ‘imagination’. Frank Knight’s ‘thought’. All the things that innately exist in accountable humans yet are ignored in the consensus of science applied by Sharpe World followers to human driven endeavours like economies and markets.
https://convex-strategies.com/2023/04/14/risk-update-march-2023-probability-vs-possibility/
All the same thing, in essence. All representations of the ‘god particle’, the gap between the ‘probability distribution’ and the ‘possibility distribution’ and the relationship that positive/negative convexity has within that gap. On both sides of the market. Fragility vs antifragility.
From an investment/risk management perspective, the solution to our inability to know what the future holds, to the dilemma of the question as to whether central banks will return us to the anomaly of the previously unseen stable inflation, is simply to be convex. Build risk portfolios that protect and/or benefit from the unforeseen outcome, from the divergences from expectations. Unlike Sharpe World methodologies, not only is this theoretically robust but it is also empirically supported. Even if we can’t quite come up with a closed loop solution to be precise (and wrong) about the future. Build portfolios that are optimized to the divergences from the mean of the expectation, not the other way around. As Nassim Taleb puts it in his wonderful book, “Antifragile” – “The volatility of an exposure matters more than its average – the difference is the ‘convexity bias.’”
We can show plenty of simple examples. Many may have heard, as of the end of the market’s 2023 calendar year, what a tough year it was for long volatility strategies, particularly those focused on the S&P and VIX space. You may have even heard of the stellar performance of various volatility selling strategies, proxies, indices. As we have done before, below we show the simple comparison of the CBOE’s mirror image S&P Put indices – Put Write and Put Protect. The Put Write Index (PUT Index) systematically sells (and rolls) 5% Out-of-the-Money (OTM) S&P500 puts. The Put Protect Index (PPUT Index) follows the same systematic rules but buys (and rolls) 5% OTM S&P500puts while owning the underlying S&P500 index. Put Write provides non-recourse leverage/insurance. Put Protect takes on the non-recourse leverage/insurance and owns the underlying risk. Put Write earns a premium and underwrites the downside risk. Put Protect pays a premium, maintains the upside and foregoes the downside. Turns out, in this simple comparison, option buying was more profitable than option selling in 2023.
Figure 10: CBOE Put Protect Index (blue) vs CBOE Put Write Index (white). Normalized. 2023
Source: Bloomberg
Lest you think that 2023 was an anomaly in the risk reward benefit of the two sides of non-recourse leverage, here is the view since January 2019.
Figure 11: CBOE Put Protect Index (blue) vs CBOE Put Write Index (white). Normalized. 2019-2023
Source: Bloomberg
Here it is since January 2013.
Figure 12: CBOE Put Protect Index (blue) vs CBOE Put Write Index (white). Normalized. 2013-2023
Source: Bloomberg
We can see with the naked eye that in the big shock event of March 2020, as we would expect, the Put Protect strategy had far less risk. We can also see, during the periods of outsized market gains, late 2023 for example, the Put Protect strategy had better upside participation. What we don’t see is that, throughout the entire period, the Put Protect strategy always had better potential protection against what could have gone wrong and always had better potential participation in what could have gone right. It was, and is, much more resilient to the ‘possibility distribution’. It has good ‘convexity bias’ and that good bias pays off as divergences from the mean of the expectation expand.
What we are referring to here as the ‘convexity bias’, we are using as a positive framing of the benefit of good/positive convexity against divergences from the mean. Mr. Taleb’s Tail Risk collaborator, Mark Spitznagel, has coined the phrase “volatility tax” as the negative framing of the cost of bad/negative convexity in an investment portfolio as realizations diverge from the mean of the expectation. It is very easy to understand. Our above friend, the Put Write Index, is harmed by ever greater divergences below the expected outcome yet does not benefit from divergences above the expected outcome. On the compounding path, the simple math around geometric returns makes it clear that negative compounds are more negatively impactful than the equivalent positive compounds are beneficial (down 50% requires a subsequent 100% positive return to recover it, while up 50% needs but a subsequent 33% loss to wipe it out). For a fee, good old Put Protect turns that around, foregoing the worst of the potential downside, while maintaining exposure to the potential upside, making it difficult to see where supposed ‘the cost’ is.
We talk all the time of the standard concept of risk mitigation in traditional Sharpe World investment strategies, forego upside to probabilistically reduce downside. We can throw a few of the stalwarts into the same picture.
Figure 13: CBOE Put Protect Index (blue) vs CBOE Put Write Index (white). Bloomberg 60/40 Index (orange). S&P Risk Parity Index 105Vol (purple). Eurekahedge Hedge Fund Index (yellow). Normalized. 2019-2023
Source: Bloomberg
Easy enough to see that 60/40, Risk Parity, and traditional Hedge Funds are just another version of Put Write; bounded/limited upside with correlated downside. In other words, no real diversification value, no real complement, to growth assets in a portfolio.
We aren’t the only ones that have noticed that traditional Sharpe World strategies, those that rely upon flawed assumptions of Gaussian distributions along with stable volatilities and correlation, have delivered exceedingly poor results over recent years. The team over at Markov Process International has run some analysis on a range of Risk Parity strategies.
Risk Parity Not Performing? Blame The Weather. | Markov Processes International
This is a useful evaluation but be warned, it all comes from a Sharpe World framework. No mention of the impact on compounding, everything is annual arithmetic returns. No Sortino ratios, just Sharpe ratios. Still, without showing just what the true negative impact has been on what really matters, compounding, they do make some good points about the core flaws/challenges of the strategy and the extent to which it have failed to deliver. Despite only showing the last two years of annual returns, it is easy enough to see that none of the presented Risk Parity strategies have managed a positive geometric average over that short period.
Figure 14: Annual Arithmetic Returns for 2022 and 2023 (YTD as of Nov) Risk Parity Strategies
Source: Morningstar. eVestment. HFR. Markov Process International
“With one exception, the current volatility levels of funds in the peer group are the highest ever, or on par with the highest on record.”
Figure 15: 24-Month Rolling Volatility of Risk Parity Strategies
Source: Markov Process International
“No one has perfect foresight on correlations and volatilities across all asset classes.”
Figure 16: 24-Month Rolling Correlations with Equities
Source: S&P. Bloomberg. ICE. BofA. Markov Process International.
“The Risk Parity approach has its roots in a simple idea that shorting and leveraging inevitably “lifts” Markowitz’ efficient frontier to allow for more optimal [read “higher Sharpe Ratio] portfolios.”
Figure 17: Sharpe Ratios for Risk Parity Strategies over 3yr, 5yr, 10yr, 15yr periods
Source: Morningstar. eVestment. HFR.
Really, this is a good piece of work, but would it kill them to show a compounding line, or rolling CAGRs, or Sortino Ratios? It would give a much more honest representation of the damage that has been, and is continuing to be, done.
Fortunately, we can help out. We use Risk Parity, in the form of the S&P Risk Parity Index 10 Target Volatility (SPRP10T Index), as our regular champion of a Sharpe World strategy that is perpetually assessed the “volatility tax”. It is the perfect example of the Balanced Racer in our Formula 1 analogy, managing risk by driving slowly, without brakes, on the belief that they can predict future volatility and correlation (sharp curves in the track) and probabilistically survive them while targeting an average lap speed that is ‘right for all seasons’. It is worth noting that this index has significantly outperformed the real-world applications shown in the above analysis.
We compare that against our various Barbell Racers, most generally the tongue-in-cheek-named Always Good Weather (AGW) strategy. This is our convexity enhanced hypothetical version of 60/40 where we replace the ‘supposed’ portfolio benefits of fixed income by putting half its weighting into the explicit negative correlation and asymmetry of the CBOE Eurekahedge Long Volatility Index (EHFI451 Index), 2x levered because of the efficiency in the portfolio risk reduction, and then dial up the equity exposure by a) carrying more equity risk and b) seeking more upside beta convexity with a high beta allocation to Nasdaq (just what we use as ‘high beta’). That ends up with our theoretical AGW 40/40/40 portfolio of 40% S&P Total Return (SPXT Index), 40% Nasdaq100 Total Return (XNDX Index), and 40% CBOE Long Vol.
Over the period 2020-2023, the 4-years when the volatility of inflation measures broke from the grasp of the controlling central banks, comparing the strategies gives you a pretty good idea of which one has the superior ‘convexity bias’.
Figure 18: AGW 40/40/40 (blue) vs S&P Risk Parity 10Vol Index (red). Jan2020-Dec2023. Scattergram and Return Distribution
Source: Bloomberg, Convex Strategies
Figure 19: AGW 40/40/40 (blue) vs S&P Risk Parity 10Vol Index (red). Jan2020-Dec2023. Compounding View
Source: Bloomberg, Convex Strategies
Figure 20: AGW 40/40/40 (blue) vs S&P Risk Parity 10Vol Index (red). Jan2020-Dec2023. NAV Ratio
Source: Bloomberg, Convex Strategies
The portfolio statistics affirm what our eyes already tell us – the ‘convexity bias’ is real! Less risk, more return and, most importantly, significantly better geometric compounding/terminal capital. The Barbell Racer is optimized to divergences from the mean of the expectation with significant reduction in Downside Volatility and, thus, a squelching of the ‘volatility tax’ that Risk Parity carries like deadweight around the racetrack.
To match the period that we showed up above when comparing with Put Protect, we can drag the start date back to the beginning of 2013.
Figure 21: AGW 40/40/40 (blue) vs S&P Risk Parity 10Vol Index (red). Jan2013-Dec2023. Scattergram and Return Distribution
Source: Bloomberg, Convex Strategies
Figure 22: AGW 40/40/40 (blue) vs S&P Risk Parity 10Vol Index (red). Jan2013-Dec2023. Compounding View
Source: Bloomberg, Convex Strategies
Figure 23: AGW 40/40/40 (blue) vs S&P Risk Parity 10Vol Index (red). Jan2013-Dec2023. NAV Ratio
Source: Bloomberg, Convex Strategies
Again, less risk, more return and even more compounding benefit through time. And, all the while, the AGW racer, whether we can measure it ex-post/ex-ante or not, had/has more potential braking capacity (less potential downside risk) and more potential acceleration to call upon (more potential upside participation). Every day. Every curve. Every straightway. Every lap.
One last quote from the Markov Process note:
“With a heightened likelihood of longer-term changes in correlations, calls for continued ‘higher-than-Fed-target’ inflation and more elevated volatility in rates as the market vacillates between a future that sees “immaculate disinflation” and a soft landing, stagflation or a hard landing, investors would be wise to realize that a striking disparity in risk parity managers’ approach to balancing portfolio risk remains – and is likely to persist.”
The implications from this final quote, of the ongoing challenges faced by those that have adopted it (as stated in the note, “A less highlighted casualty of the changing stock/bond relationship, however, has been risk parity – and the pension funds that adopted such institutional-oriented strategies and products en masse.”), takes us back to our ‘bad outcome’ scenario. In the ‘bad outcome’, nobody wants to buy the bonds, because they no longer provide the faux portfolio benefit that was hardcoded into the practice and regulation of Sharpe World entities. This is what underpins what we dubbed “The Great Stop Loss” in our October 2023 Update – “The Hunger Games”.
https://convex-strategies.com/2023/11/17/risk-update-october-2023-the-hunger-games/
The restructuring of investment portfolios that have been built on this fundamental dependence on the false assumptions of Gaussian distributions, stable volatilities and correlations, and end capital owners that won’t notice the opportunity loss of the ‘volatility tax’ on geometric returns, will only make the ongoing performance worse for those that hold onto their beliefs in the myths of Sharpe World. Compounding is driven by time and variance. The sooner you start improving your portfolios ‘convexity bias, the sooner you can stop bleeding away the ‘volatility tax’, and the less likely you are to get trampled in a mass-exodus from Sharpe World.
If you manage a sovereign wealth fund, pension fund, insurance portfolio, family office or wealth management strategy that adheres to these Modern Portfolio Theory principles, something like or similar to Risk Parity, please get in touch with us. If you know somebody who manages wealth, yours or others, following a Modern Portfolio Theory/Risk Parity sort of framework, please share this with them and ask them to give us a call. As we said, the question of whether central banks can put the genie back in the bottle both doesn’t matter and matters a whole lot. Either way, investment and risk managers will be better served through an improved ‘convexity bias’ in their portfolio construction. In many of the scenarios that could fall into the ‘possibility distribution’ of these outcomes, it could be absolutely critical.
It’s just math.
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