Risk Update: July 2024 – Chaos

“Too often, the potential range of behavior of complex systems had to be guessed from a small set of data. When a system worked normally, staying within a narrow range of parameters, engineers made their observations and hoped that they could extrapolate more or less linearly to less usual behavior.” James Gleick, “Chaos: making a new science”.

It’s not hard to see how the above statement aligns to our criticisms of what we dub “Sharpe World”, the nonsensical assumptions that undergird the consensus models of today’s economics and finance. Put very simply, chaos theory shows us that complex systems, even seemingly simple ones, are nonlinear. Making linear extrapolations with far too small data sets is just plain wrong.

We highly recommend folks getting their hands on a copy of James Gleick’s book “Chaos”. It is very much a layman-accessible telling of the history and evolution of what has become known as Chaos Theory. Gleick manages to pull together the seemingly disparate paths of the climatologists, mathematicians, ecologists, biologists, physicists, engineers, economists, even physicians, that all found their way to the same discovery – the real-world exhibits chaos. So ubiquitous were the implications of the findings of famed physicist Mitchell Feigenbaum that he dubbed it a ‘universal theory’ or “Universality”.

The book has sections that cover many of the stars from our own writings. Edward Lorenz (https://convex-strategies.com/2024/02/16/risk-update-january-2024-butterfly-effect/), Benoit Mandelbrot (https://convex-strategies.com/2021/10/19/risk-update-september-2021/), Doyne Farmer (https://convex-strategies.com/2022/08/16/risk-update-july-2022/) and Claude Shannon (https://convex-strategies.com/2021/05/21/risk-update-april-2021/) to give just a few examples.

Mitchell Feigenbaum, a mathematical physicist, is another of the characters that played a major role in the development of chaos theory. His discovery/development of the logistics map and the scaling of period-doubling bifurcations (known as Feigenbaum’s Constant) in the lead up to chaos, is one of the best visualizations you will ever see as to how complex systems become chaotic and are, thus, unpredictable.

Figure 1: Feigenbaum’s Bifurcation Logistics Map

Source: Wikipedia

The wonderful folks at Veritasium produced this short clip on the logistics map that gives a very clear explanation of how Feigenbaum came to make his discoveries.

This equation will change how you see the world (the logistic map) (youtube.com)

The gist is that Feigenbaum iterated a simple equation on a constrained population growth (eg. rabbits). The population constraint, think if the population gets too large there could be a starvation event, creates a negative feedback loop forcing the iterations to exist within a finite space. The formula is simply:

where x is the population size as a percent of the maximum population constraint and r is the growth rate. To generate the logistic map, he iterates the changes in the growth rate (x-axis) and produces the steady state of the subsequent population rate. A growth rate below 1, and the population goes to zero. Growth rates between 1 and 3, the population as a proportion of maximum slowly grows higher but always eventually settles in on a single steady state. Once the growth rate gets to 3, we get what is known as a period doubling, the population starts to bounce back and forth between two different states. That doubles again to four states at a growth rate that of 3.4283 (the first scale, growth rate of 1 to 3, prior to the initial period doubling, divided by the Feigenbaum Constant 4.6692…. gives the scale to the next period doubling, ie 2/4.6692 = .4283). It then doubles again to a periodicity of 8 at a growth rate around 3.52. Then to 16 at 3.54. Then 32 at 3.544. And very quickly into chaos.

It is pretty straightforward to apply that same simple formula but assume it represents some sort of economic or social system. The growth rate and constraint function could be on an economy, as opposed to a population size. The growth rate could represent nominal growth, or some other factor like the growth of money and credit (classical inflation), or a simplified measure of inflation like a price stability measure (eg. CPI yoy%).

One could almost imagine that this concept was the very foundation behind the move towards central bank decisions to become inflation targeting institutions and to choose a target around 2%. Ignoring the Goodhart’s Law implications of turning a measure into a target, and whether or not the various chosen targets (different in every regime) are appropriate representatives of what you are truly trying to target (inevitably they will start ‘gaming’ the target), you can imagine the decision, much like the rabbit population, that too low a growth rate of inflation (realistically the growth of money and credit as represented by a chosen price stability measure) won’t support sustained economic growth, while too high a growth rate of inflation leads to chaos. Probably quite true!

Any central bankers (and we doubt there are any) that might have applied the principles of chaos to their concept of inflation targeting obviously threw them out of the window when they adopted ideas like Flexible Average Inflation Targeting (FAIT). Determining that it was a good idea to “let it run hot” shows a pretty severe lack of chaos theory understanding.

Mr. Feigenbaum describes the pretension of the High Priests of Sharpe World succinctly in this very clear paper on his theory of Universality.

“This general mechanism gives a system highly sensitive dependence upon its initial conditions and a truly statistical character: since very small differences in initial conditions are magnified quickly, unless the initial conditions are known to infinite precision, all known knowledge is eroded rapidly to future ignorance.” Mitchell Feigenbaum, 1980.

PII: 0167-2789(83)90112-4 (ttu.ee) Mitchell Feigenbaum – “Universal Behavior in Nonlinear Systems”

Regular followers will have heard it from us time and time again: “Without price stability, there can be no stability.”

Or, as we quoted Margaret Thatcher back in our September 2022 Update – “Is Sharpe World Closing?” https://convex-strategies.com/2022/10/18/risk-update-september-2022-is-sharpe-world-closing/

“Inflation destroys nations and societies as surely as invading armies do. Inflation is the parent of unemployment. It is the unseen robber of those who have saved”

There is plenty of that to be seen at the moment.

‘And so it begins to be real instead of just possible: US prepares for “all scenarios”. “The Pentagon has ordered the deployment of Navy destroyers and cruisers, both with offensive and defensive ballistic missile capabilities, and an additional squadron of fighter jets to the Middle East as Tehran vows to avenge the killing of militant leaders, officials said Friday.”

Geopolitics has unravelled because nobody cared about it until it was underway. The warning signals have been building for a decade.’ Pippa Malmgren.

  • Violent overthrow of the government in Bangladesh https://www.nbcnews.com/news/world/bangladesh-prime-minister-reportedly-ousted-student-led-protests-rcna165110. “Bangladesh Prime Minister Sheikh Hasina resigned and left the country Monday, the army chief said, a day after almost 100 people were killed in clashes with the police as student-led protesters demanded she step down.
  • To the world of good old-fashioned politics. Chaos.
  • In France’s recently held Parliamentary elections, the previous ruling party, Renaissance party, of President Emmanuel Macron, having come a distant third to the right-wing National Rally (RN) party of Marine Le Pen in the first round of elections, forged an election pact with the amalgamated left-wing parties led by Jean-Luc Mélenchon, the New Popular Front (NFP), for the second round of votes (it is the quirky way it works in France), to block RN from gaining power. France’s messy elections, explained | Vox. RN still managed to garner 33.15% of the second-round votes, but only ended up capturing 24.6% of the seats. Anybody paying close enough attention might feel a slightly ominous chill around the similarities to the Spanish elections of 1936, where an alliance of left-wing parties, dubbing themselves the Popular Front, defeated a collection of right-wing parties known as the National Front. Popular Front (Spain) – Wikipedia. Just saying. As it is France, the streets filled with rioters after both rounds of the election.
  • In the UK, the ruling Conservatives were ousted in the Parliamentary elections with the further shame of receiving just 24% of the vote share, the worst showing ever for an outgoing government. On the other hand, the winning Labour party gets the esteem of coming to power while receiving just 34% of the votes, the lowest ever for any incoming government. That 34%, not far different from RN’s 33.15%, however, earned Labour 70% of the Parliamentary seats. Behind the UK Election: What the Vote Count Means for the Labour Government | Wilson Center. Riots continue to ensue as we type.
  • In the US, the campaign for the November elections really started to heat up. The Republican nominee had an assassination attempt on his life, with bullets flying past and one clipping his ear, all on live TV. Meanwhile, the Democrat nominee, the incumbent sitting President, withdrew from the race (but not from the presidency) for no real stated reason. The power-behind-the-curtain of the Democrat party selected the current Vice President to step in as the appointed nominee for the upcoming election. Somehow, the campaigns carry on, business as usual.

Finally, bringing it back to where our focus lies, to the world of economics and markets. Chaos.

In the last week of July, alone, we got a policy rate hike from the Bank of Japan (BOJ), a policy rate hold from the Federal Reserve (Fed), a first policy rate cut since commencing the recent hiking cycle in December 2021 from the Bank of England (BOE), and the eighth consecutive cut, dating to November 2019, from the People’s Bank of China (PBOC). Very much as we discussed in our March 2024 Update – “Divergence” https://convex-strategies.com/2024/04/16/risk-update-march-2024-divergence/.

Japan, as the last major provider of liquidity into what we have coined as the global Hunger Games, has long stood out as the likely trigger for future shocks to the sandpile. We touched on this yet again in last month’s Update – “Hunger Games II” https://convex-strategies.com/2024/07/16/risk-update-jun2024-hunger-games-ii/.

With BOJ’s decision to, ever so slightly, further reduce the level of monetary accommodation at their July 31st policy meeting, they did not disappoint. As we discussed last month, whispers were already out ahead of the meeting that there could be a double whammy of policy rate increase and reduction of JGB purchases. Both came to fruition, with a mere 0.15% increase in the policy rate and a tiny JPY400bn quarterly reduction in bond purchases.

As has become customary by BOJ with recent policy announcements, they provided a couple of nice pictorial slides to explain it all.

Decisions at the July 2024 Monetary Policy Meeting (boj.or.jp)

Figure 2: Bank of Japan July 2024 MPM Slide on Policy Rate Increase

Source: Bank of Japan

Figure 3: Bank of Japan July 2024 MPM Slide on Bond Purchase Reduction

Source: Bank of Japan

While small in absolute terms, the impact on the margins, given the accumulated fragility built in the run up to their policies working, ie. their measure of price stability (Core CPI) exceeding target since Q2 2022 and forecast to do so through Fiscal 2025, USD/JPY reaching 162.00, Financial Conditions achieving all-time extremes of looseness, caused just the sort of shock to the system that those familiar with major market dislocations have become familiar with over the years. The final paragraph in their official statement, finally, gets to the question we have so often asked: “What if it works?”

k240731a.pdf (boj.or.jp)

“As for the future conduct of monetary policy, while it will depend on developments in economic activity and prices as well as financial conditions going forward, given that real interest rates are at significantly low levels, if the outlook for economic activity and prices presented in the July Outlook Report will be realized, the Bank will accordingly continue to raise the policy interest rate and adjust the degree of monetary accommodation.”            Bank of Japan, July 2024.

The implications of it “working” are easily visualized, as we have shown many times before, with a financial conditions index and the value of their currency.

Figure 4: GS Japan Financial Conditions Index (white) vs USD/JPY (green-inverted). 1994 – July 2024

Source: Bloomberg, Convex Strategies

The red circles, our quick and easy visual to help spot where risk is lurking, coincide with the past notable contributions that Japan Inc. has played in global risk build ups. The four circles capture the expansion of liquidity coming out of Japan that respectively culminated in 1997, 2007, 2015, and last month. Anybody that doesn’t think a reversal of Japan financial conditions has played a role in past de-liquefications of global markets wasn’t paying attention.

Japan has done their part, and more, in the current cycle of building imbalances and we have little doubt, given the extremes of the recent cycle, that they will play their role in any future chaos.

Figure 5: Japan CPI ex-Fresh Food and Energy Index (white), USD/JPY (blue), JPY 10yr Swap (purple), NKY Index (papaya) vs BOJ Policy Rate (yellow). Mar2016-July2024

Source: Bloomberg

The Hunger Games now proceed with the contemplation that the final provider of liquidity, and one of the largest, is starting to dial that back and, potentially, preparing for the role where, at 260% of debt/GDP, they could become an aggressive competitor for capital. You don’t need much of this, at the margin, to shake the world. Just for a little perspective, below is the latest from Japan’s Government Pension Investment Fund (GPIF) (Japan’s and one of the world’s largest pension funds). This little visual shows their target benchmark allocation, 25% each in domestic bonds, domestic equities, foreign bonds and foreign equities. It is not difficult to imagine, in a world where the BOJ is not buying circa 100% of net government issuance, that this sort of allocation could evolve towards slightly more support of the home market.

Figure 6: GPIF Portfolio Allocation

Source: annual_report_summary_2023_en.pdf (gpif.go.jp)

The early implications are already clear in the recent realized volatility in JPY FX pairs.

Figure 7: 1mth Realized Volatility USD/JPY (blue), EUR/JPY (orange), EUR/USD (white)

Source: Bloomberg

There has been a significant pickup in realized volatility in all JPY crosses, above are just examples of USD/JPY and EUR/JPY. For perspective, we show EUR/USD which, to date, has hardly budged. We suggest you point to this chart if anybody tries to convince you that, in terms of recent market fragility, Japan isn’t relevant, and it is all just a matter of changing US economic sentiment. Japan is the trigger.

Don’t get us wrong, there are plenty of indications of risk buildup in the US, and indeed elsewhere. Here are a couple simple representations of endogenous concerns.

First up, the implicit leverage of index volatility selling, driven both by outright selling as well as the highly leveraged activity known as dispersion trading. This has driven the implied correlation of S&P constituents down to unprecedented levels. Always a good candidate for a red circle and, as such, highly likely to be reflexive in an unwind.

Figure 8: CBOE 3mth Implied Correlation Index SPX Index top 50 Components

Source: Bloomberg, Convex Strategies

Another something worth paying attention to, something that is far too often naively considered ‘safe’, is the continued disfunction of the US Treasury market. The supposed world’s most liquid market isn’t performing all that well, by at least this measure of liquidity.

Figure 9: US Govt Securities Liquidity Index. Aug2011 – July2024

Source: Bloomberg

It was the brilliant Jim Bianco that brought this version to our attention. The fuller timescale in figure 10, we might argue, is even more telling. This one, as the world entered what became known as the Great Financial Crisis, gives a good impression of what Feigenbaum’s bifurcations leading to chaos might just look like. We have resisted the drawing of our red circle over the current period, thus far.

Figure 10: US Govt Securities Liquidity Index. Aug2007 – July2024

Source: Bloomberg, Convex Strategies

In a note that garnered a lot of attention, the team over at Hudson Bay Capital (Stephen Miran and Nouriel Roubini) put out an interesting piece of work on what they have dubbed Activist Treasury Issuance (ATI), that touches on how Secretary Yellen and team are trying to address the Hunger Games issue of “who’s going to buy the 40?”.

635102_Activist_Treasury_Issuance_-_Hudson_Bay_Capital_Research.pdf (hudsonbaycapital.com)

The note leads off with this:

“By adjusting the maturity profile of its debt issuance, Treasury is dynamically managing financial conditions and through them, the economy, usurping core functions of the Federal Reserve. We dub this novel tool “activist Treasury issuance,” or ATI. By manipulating the amount of interest rate risk owned by investors, ATI works through the same channels as the Fed’s quantitative easing programs.”

The gist of the note is that the Treasury, by reducing the duration of their issuance, is effectively enacting QE (we might compare it more to Operation Twist) and, thus, offsetting the Fed’s efforts to tighten through its own QT. The authors make the case that the intention behind this activity is to explicitly prop up the economy. We, again, might argue that, while that is an outcome of the reduced duration issuance, the primary intent is to protect the Sharpe World holders of the past duration issuance and their mammoth sized unrealized losses.  Tomato, tomahto.

Fortunately, we can get the whole thing straight (with spin) from the horse’s mouth in the latest Quarterly Refunding Announcement documents. Below we’ve linked the responses from the Treasury Borrowing and Advisory Committee to the two “Charges” assigned to them for this recent meeting.

TBACCharge1Q32024.pdf (treasury.gov)

TBACCharge2Q32024.pdf (treasury.gov)

We can simplify the two Charges into:

  1. How many Bills, as an overall proportion, can we issue?
  2. Who’s going to buy the 40?

Figure 11: TBAC Q3 2024 Charge 1

Source: TBACCharge1Q32024.pdf (treasury.gov)

Figure 12: TBAC Q# 2024 Charge 2

Source: TBACCharge2Q32024.pdf (treasury.gov)

“May the odds be ever in your favor!”

We came across a wonderful Substack note discussing complex systems and the challenges of unintended consequences in a nonlinear world.

The problem with problem-solving is slowly destroying the world (wholebraininvesting.com)

We just had to share the little embedded comic strip from this note that perfectly echoes our own frequent description of the challenges of fire wardens in the ivory towers of economic central planning that have done such a good job of preventing fires, thus creating so much fire risk, that they feel they have no choice but to prevent fires.

That’s a beauty!

In the world of complex systems, and none are so complex as economies, we know that nonlinearity and chaos lurk beyond our ability to foresee it. How does one function in such environments of uncertainty? A simple answer, where it is available, is to buy insurance. Sadly, the flawed mathematics and assumptions of Sharpe World, eg. things like utility functions, cannot make sense of insurance because they do not reflect the non-ergodic path through time.

Fortunately, we have Ole Peters to make it right. Ole joins up with Alexander Adamou and provides this wonderful piece of clarity, “Insurance makes wealth grow faster”.

1507.04655 (arxiv.org)

Ole makes the simple point that, in the unrealistic world of utility/expectations/ensemble averages/parallel universes, insurance is looked at as a time-irrelevant zero-sum bet. Time, however, is clearly not irrelevant in the path to long-term wealth. In each of our own individual paths, we don’t get the expected value of a 5% probability of 100% wipe out. For us it is a binary event and ends our path with no hope of recovery. Similarly, we do not buy insurance as a bet but, rather, as a protection against uncertainty for an activity that is, for us, far more profitable than the cost of the insurance. This is how we accumulate actual wealth, not period by period rate of change of expected wealth.

Under traditional Sharpe World (“the expected wealth paradigm”) views of a holding of ergodicity, there is no logic for insurance contracts to exist. And yet they do.

“The problem with the expected-wealth paradigm: No price exists that makes an insurance contract beneficial to both parties, and yet insurance contracts exist.”

As we say so often, mean expectation targeting strategies, like Modern Portfolio Theory, are explicitly based around optimizing to single period expected returns. Time-aware strategies targeting divergences from the expected mean, those with convexity, are optimizing to actual accumulation of wealth.

In Ole’s terminology, the utility paradigm is the realm of the fiduciary. The time paradigm is where end capital owners actually exist.

“The utility paradigm is another model of human behaviour. It posits that humans act to maximise the rate of change of the expectation value of their utility.”

“The time paradigm is another model of human behaviour. It posits that humans act to maximise the long-time rate of change of their wealth.”

We have discussed it many times before. The like for like comparison is not selling insurance versus buying insurance, as though it were some single period bet. The correct comparison is between selling insurance (providing non-recourse leverage) versus buying insurance (taking on non-recourse leverage) and taking the risk you are protecting against.

We have shown the simple comparison of this concept several times before, using the cleanly constructed S&P indices from the CBOE. The Put Write Index (PUT Index), which systematically sells and rolls 95% 1-month puts. The Put Protect Index (PPUT Index), which owns the S&P and systematically buys and rolls 1 month puts. We can also add in the Buy Write Index (BXM Index), which owns the S&P and systematically sells and rolls 105% calls. Below we show these indices, as well at the SPX Index on a 2024 YTD view, a 5-year view, and a 12-year view.

Figure 13: SPX Index (white), Put Protect Index (blue), Put Write Index (papaya), Buy Write Index (purple) YTD 2024 (normalized and log-scale)

Source: Bloomberg

Figure 14: SPX Index (white), Put Protect Index (blue), Put Write Index (papaya), Buy Write Index (purple). 5 years (normalized and logged scale)

Source: Bloomberg

Figure 15: SPX Index (white), Put Protect Index (blue), Put Write Index (papaya), Buy Write Index (purple). 12 years (normalized and logged scale)

Source: Bloomberg

All time frames support Ole’s premise. Over time, buying insurance and taking on the risk can clearly be a winning proposition. Meanwhile, selling insurance/can also be ‘profitable’, just clearly not as sensible on any sort of risk adjusted basis. The thing that is often missed, as we like to stress, are that the benefits of taking on the non-recourse leverage and owning the risk, as shown in the look back periods, only shows what did happen. It doesn’t show what could have happened. Throughout the entire period, relative to the volatility selling strategies, the Put Protect Index always had more potential upside participation and less potential downside risk.

The legendary Howard Marks made just this point in his recent memo, a note that echoes perfectly the same philosophy that we endlessly espouse.

https://www.oaktreecapital.com/insights/memo/the-folly-of-certainty

“Sometimes things go as people expected, and they conclude that they knew what was going to happen. And sometimes events diverge from people’s expectations, and they say they would have been right if only some unexpected event hadn’t transpired. But, in either case, the chance for the unexpected – and thus for forecasting error – was present. In the latter instance, the unexpected materialized, and in the former, it didn’t. But that doesn’t say anything about the likelihood of the unexpected taking place.” Howard Marks, July 2024.

While we are on this topic, we are going to add just a quick postscript that came to our attention after we had pulled our thoughts together for this July Update. The below note that appeared on the Financial Times, post the market happenings of August 5th, so perfectly aligned with our above discussion on the premise of option selling, that we couldn’t miss sharing it.

Funds offering protection from volatility fail to deliver in sell-off (ft.com)

Anybody, including the authors of the article, that are spinning the impression that such option selling strategies (eg. Covered Calls) are risk reducing should be getting a visit from the mis-selling police. Let us put it very bluntly, contrary to what the Sharpe Ratio tells you, foregoing upside, while retaining the downside, is not risk reducing. It is difficult to detail just how scathing we are of this article.

We quickly punched up the below, comparing one of the referenced Covered Call ETFs from the story, JEPI ETF, with one that we found that appears to try to track the Put Protect Index, XTR ETF.

Figure 16: Put Protect Index (white). XTR ETF (blue). JEPI ETF (papaya). YTD through Aug 5th

Source: Bloomberg

Figure 17: Put Protect Index (white). XTR ETF (blue). JEPI ETF (papaya). Aug 26th 2021 through Aug 5th 2024

Source: Bloomberg

A little perspective that ought to make anybody cringe.

JEPI ETF Market Cap = $33.44 billion. “JPMorgan Equity Premium Income ETF”

XTR ETF Market Cap = $2.4 million. “Global X S&P 500 Tail Risk ETF”

Why do fiduciary wealth managers, financial academics, financial regulators, continue to advocate for things that are destructive to the compounding paths of their clients?

James Gleik goes to Leo Tolstoy for the answer.

“I know that most men, including those at ease with problems of the greatest complexity, can seldom accept even the simplest and most obvious truth if it be such as would oblige them to admit the falsity of conclusions which they have delighted in explaining to colleagues, which they have proudly taught to others, and which they have woven, thread by thread, into the fabric of their lives.” From James Gleik’s “Chaos” as attributed to Joseph Ford quoting Leo Tolstoy.

No doubt, we will come back to this point in future musings.

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by ehpteoh Categories: Risk Update