Nassim Taleb introduced the concept of Wittgenstein’s ruler in the first book of his Incerto series, “Fooled by Randomness: The Hidden Role of Chance in Life and in Markets”. He elaborated on the concept and usage of it in his technical companion to the Incerto series, “Statistical Consequences of Fat Tails: Real World Preasymptotics, Epistemology, and Applications”. He defines it this way:
“Wittgenstein’s ruler: Unless you have confidence in the ruler’s reliability, if you use a ruler to measure a table you may also be using the table to measure the ruler.” Nassim Nicholas Taleb, “Fooled by Randomness”, 2001.
If you have doubts about the efficacy of the ruler, you are probably learning more about the ruler, as well as those utilizing/espousing it, than you are about the table.
Nassim applies this against the obvious flaws of assigning Gaussian/Normal distributions to markets and then making claims of unimaginably large standard deviation outcomes. He uses the simple example of LTCM and the claims by some of their leadership of “10 sigma” events. They obviously had the wrong ruler!
We look at the entirety of Sharpe World through the lens of Wittgenstein’s ruler. We have ample evidence that the rulers applied by the practitioners of modern Finance and Economics are unreliable. Literally, none of the core underlying assumptions of markets and economies, as applied by the denizens of Sharpe World, are accurate representations of reality. We said this 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/.
“In Sharpe World, historical volatilities and correlations always remain constant. Geometric compounding paths are irrelevant. Tails are never fat. Leverage is not risk. Frequency matters more than magnitude. Ensemble averages dominate time averages. Hens lay soft-boiled eggs.”
Any supposed expert, operating under those sorts of assumptions, is using an unreliable ruler, and should certainly be considered an unreliable expert. The application of these flawed tools to markets and economies tells you more about those applying the tools than it does about the markets and economies.
Thus, our Wittgenstein’s ruler antennae perked right up when we heard the news that Ben Bernanke, one of the true high priests of Sharpe World, had been enlisted by some of his devoted followers over at the Bank of England to “lead an independent review into the Bank’s forecasting and related processes during times of significant uncertainty”.
This is another one of those economic notes that we would be loath to recommend anybody to read. In true Wittgenstein’s ruler fashion, it tells you a lot more about the limitations and biases of the review process (and the reviewer) than about the flaws of the underlying problems with the BOE’s forecasting and monetary policy making.
It is not particularly difficult to critique the Bernanke review, just difficult to do so politely. In the review, there really is no criticism of the forecasting models or of those at the BOE charged with generating the forecasts and making policy decisions based upon those forecasts. The review makes twelve recommendations broken down into three broad sections.
- “Building and maintaining a high-quality infrastructure for forecasting and analysis.” This is really the only criticism of significance by the review. The BOE needs to upgrade their software. It was the computer’s fault.
- “Providing a forecast process that better supports the MPC’s decision-making.” Under this section, while “noting the evident strengths of the process”, the reviewers make some fairly obvious suggestions, eg. adjusting the starting point (initial condition) for subsequent forecasts to the reality of the economic circumstance as opposed to using the previous failed forecasts as your starting point for future forecasts. (On the topic of the importance of initial conditions, readers may enjoy referring back to our January 2024 Update – “Butterfly Effect”. https://convex-strategies.com/2024/02/16/risk-update-january-2024-butterfly-effect/). They also suggest that staff should be “encouraged and incentivised to accumulate experience and expertise”. Finally, the review suggests the creation of “alternative scenarios” that reflect possible risks to the forecasts from “unexpected changes in exogenous variables”.
- “Using the forecast to communicate the MPC’s outlook and policy rationale to the public.” The review states it very clearly: “Good communication helps the public understand the rationale and implications of policy choices and can make policy work better by helping to anchor inflation expectations and by influencing asset prices”. This is that grey area, that we so often discuss, between forecasting and forward guidance (aka manipulated expectations). Think about that: the point of forecasting and policy making is to influence expectations and influence asset prices. Masters of the universe.
The review makes specific effort to show that the BOE’s forecasts were not particularly worse than a broad group of other central banks, all using the same basic modelling methodology, whose forecasts were just as bad. Even this is not enough to get Mr. Bernanke to consider that there could be something wrong with the core modelling methodology. The core tenets of the religion forever go unquestioned.
The cynical amongst us might argue, much like the quarterly exchange of letters between the BOE Governor and the Chancellor of the Exchequer for not meeting the price stability mandate (now exchanged for 14 out of the 15 quarters that Andrew Bailey has been the Governor), that the review is just a charade to sidestep any sort of accountability.
Paraphrasing Nassim Taleb – “without accountability, there can be no learning”.
Figure 1: UK CPI yoy% (white). March 2020-March 2024 (Gov Bailey term). Price Stability Target Range (red dash). Quarters Inside Target Range (green circle)
Source: Bloomberg, Convex Strategies
A more honest version of a review was given by the BOE Chief Economist, Huw Pill (amazingly, who never got the slightest mention in the Bernanke review), at last year’s Sintra Conference. We noted this at the time in our June 2023 Update – “One Thing” https://convex-strategies.com/2023/07/13/risk-update-june-2023-one-thing/.
Mr. Pill’s comments, publicly stated for the whole world to hear, touched on both the failings of the Sharpe World modelling methodology as well as the intentional influencing objective of targeted communications.
First off, their models don’t represent reality.
“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 the 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.
And then, the intent to influence outweighs the desire for accuracy.
“The role of CBs and CB forecasts is not necessarily to produce the best forecasts; the role is to support the best monetary policy decision which brings inflation back to target. I think that does lead you to a whole set of issues about how you organize your discussion internally and you allow the role for judgement, that role to have many different models, many different analytical frameworks, to help you have a robust and resilient view. Then ultimately how you convert that into a way of communicating with the public and financial markets. Monetary policy, and indeed economic policy making more generally, can have an effect on behaviour which supports what you are trying to achieve and internalizing that benefit is one that is pretty key to having a framework that just doesn’t put accurate forecasts, in some abstract sense, on a pinnacle above the thing that is the real importance of what the underlying process is.” Huw Pill. ECB Sintra Conference, June 2023.
Mr. Pill is telling you that Wittgenstein’s ruler applies! His ruler has no idea how to measure the table and his task is simply to convince the public to believe what size he wants them to believe. Far more direct than Mr. Bernanke’s Econ 101 failing 80-page term paper.
We aren’t alone in our criticism of central banker “forward guidance”. Investing legend Stanley Druckenmiller shared very similar thoughts in a recent interview on CNBC.
“I don’t know. What I would do is just say nothing and do what Fed Chairs used to do. When you need to raise rates, raise them. When you need to cut them, cut them. Don’t go on 60 Minutes, you’re not a rockstar. You’re the Fed Chairman. You are supposed to be running monetary policy for the good of the country, not to be going on 60 Minutes. Bernanke did a lot of things that, by hindsight, I don’t feel very good about. One of the worst was forward guidance. You’ve got a bunch of academics sending a message to the market. As a practitioner, I’d rather they just get rid of the forward guidance and just do their job. When you need to raise rates, raise rates. When you need to cut them, cut them.” Stanley Druckenmiller, 2024.
Is anybody listening?
We quoted an earlier version of Wittgenstein’s ruler in our February 2022 Update – “The Road to Serfdom & Pascal’s Wager” https://convex-strategies.com/2022/03/18/risk-update-february-2022/.
“It is only prudent never to place complete confidence in that by which we have even once been deceived.” Rene Descartes.
Ludwig Wittgenstein, the namesake of Taleb’s Wittgenstein’s ruler, is a fascinating guy. A philosopher that was a contemporary of John Maynard Keynes at Cambridge and, randomly, a cousin of Friedrich Hayek. https://en.wikipedia.org/wiki/Ludwig_Wittgenstein.
There is not nearly enough time to elaborate on his works here but, for those willing to dig down a rabbit hole, we highly recommend perusing his works as captured in the “Tractatus Logico-Philosophicus” and “Philosophical Investigations”. The latter work contradicts many of the perspectives of the earlier one. Truly fascinating stuff.
For our purposes, we will simplify Wittgenstein’s relevance around the concept of context-specific language. In essence, the meaning of words, or language, is defined within the specific context of its usage. There is not one predetermined meaning. It is the context-specific divergence from the static mean of a word that drives true meaning.
“The truth shows itself. It is not said or even expressed in thought. What can be said can be said clearly, and whereof we cannot speak, we must remain silent.” Ludwig Wittgenstein, “Tractatus Logico-Philosophicus”, 1921.
“The problems are solved, not by giving new information, but by arranging what we have known since long.” Ludwig Wittgenstein, “Philosophical Investigations”, 1953.
Sounds familiar! It is not the average usage/frequency that matters but, rather, the divergence/entropy that delivers understanding/information. Wittgenstein is the philosophical companion to Claude Shannon’s “A Mathematical Theory of Communication”.
https://people.math.harvard.edu/~ctm/home/text/others/shannon/entropy/entropy.pdf
“The fundamental problem of communication is that of reproducing at one point either exactly or approximately a message selected at another point.” Claude Shannon, 1948.
Both Wittgenstein and Shannon stress that language/information is driven by context/chaos, that which diverges from the expected. Uncertainty reigns.
The linkages here go on and on. Wittgenstein’s work was influential on the concepts of heuristic decision making and the likes of Herbert Simon, whom we referenced in our discussion around Gerd Gigerenzer in the February 2024 Update – “Where’s the Risk?” https://convex-strategies.com/2024/03/15/risk-update-february2024-wheres-the-risk/.
Decision making under uncertainty is best addressed through heuristics, and skin-in-the-game, not through simplified statistical analysis that misses critical context, ie. what could have happened (possibility) not just what did happen (probability). Thus, again, the importance of applying Wittgenstein’s ruler to any expert espousing Gaussian distributions, as an underlying assumption, to an analysis of real-world problems.
We find yet another linkage, as discussed in our aptly titled March 2023 Update – “Probability vs Possibility” https://convex-strategies.com/2023/04/14/risk-update-march-2023-probability-vs-possibility/. In this note we focused on exactly this issue and referenced such acclaimed thought leaders on the issue of uncertainty as Pippa Malmgren, GLS Shackle, and Frank Knight.
“In Knight’s version, our ‘possibility’, Shackle’s ‘imagination’, Pippa’s ‘wet brain’, becomes ‘thought’. Our ‘probability vs possibility’ is Knight’s ‘analysis vs thought’.”
We can add to that list Wittgenstein’s ‘context’, Gigerenzer’s ‘large worlds’, and Shannon’s ‘entropy’.
This brings us full circle and ties perfectly back into the teachings of Taleb and Mandelbrot, of the power law distribution of things, of the non-smooth fractal nature of the real world. Likewise, the work from Per Bak on Self-Organized Criticality and the fact that relevant change in systems comes through significant phase transitions, that evolution jumps along the paths of Punctuated Equilibriums. It is the divergence that matters and ever more so the greater the scale of the variation.
We have long discussed the core fragility in the system, laying it out in the language of Bak’s sandpile analogy back in our infamous August 2021 Update – “Self-Organized Criticality” https://convex-strategies.com/2021/09/22/risk-update-august-2021/.
“At some point, you wonder if the bubbling water will become more convincing than the previous 30-year average when the water didn’t boil? Are they blind to it? Or, as we suspect, are they just even more concerned about the, not to be mentioned, structural fragility of the sandpile? At what point, ala President Biden and his (misplaced) talking up of the capabilities of the Afghan National Security Forces, should we start to expect assurances that, even should the Fed withdraw their unprecedented monetary support, the market will be able to stand up to the pesky residual solvency fingers of instability? Of course, to some extent, we hear this all the time. We hear how, under Basel III, the banks are stronger and better capitalized than ever! Surely, they don’t need central banks to underwrite the values of the assets that they own. We hear of innovative new life rafts like the Standing Repo Facility that will smooth market function when central banks aren’t around to buy assets from over-levered holders. We hear of permanent standing swap-lines around the world. We hear of central clearing, new more sophisticated margining protocols, more and more reams of regulatory reporting and oversight. The financial system is well trained and well equipped to stand up against any of those un-surrendered solvency issues that may have survived the years of artificial support. Keep your ears open.”
We long ago coined the catchphrase – “What about the 40?” aka “Who’s gonna buy the bonds?” – as our simplified version of what has been popularized under the framework of “fiscal dominance”. The IMF has climbed on the wagon and produced a lengthy note titled “Fiscal Policy in the Great Election Year”.
Fiscal Policy in the Great Election Year (imf.org)
“Nevertheless, four years after the onset of the pandemic, public debts and deficits are higher and debts are projected to remain high. Chapter 1 of the Fiscal Monitor documents divergences in fiscal policies around the world. First, the projected rise in global public debts is mainly driven by China and the United States, where public debt is now higher and expected to grow faster than prepandemic projections. Fiscal policy developments in these major economies, notably in the United States, have implications for global financing conditions.”
Definitely some echoes of our own Hunger Games analogy in the IMF’s analysis! https://convex-strategies.com/2023/11/17/risk-update-october-2023-the-hunger-games/.
The concept of “fiscal dominance” is easily captured in the below image. This is simply the issuance size for the regular auctions of the 5yr US Treasury. We have labelled each of the three obvious spikes in issuance size with the justification for the needed increase in federal funding. The current spike, labelled as “Interest Cost”, is self-evident as to its relevance in the “fiscal dominance” framework.
Figure 2: US 5yr Treasury Auction Allotment. 2004-April2024
Source: Bloomberg, Convex Strategies
We have written at length over recent months on the various efforts to shore up the ‘Afghan National Security Forces’ and, thus, secure ongoing buying of the bonds. We discussed much of this at some length in our February 2024 Update – “Where’s the Risk” https://convex-strategies.com/2024/03/15/risk-update-february2024-wheres-the-risk/. A quick listing of various efforts that are in the hopper:
- ISDA letter on behalf of banks for US Treasury holdings to be given a permanent exemption from the SLR (supplementary leverage ratio), ie. the post GFC implementation of a gross leverage constraint. (Wittgenstein’s ruler alert: the same folks who told you the SLR would make the system safer are now telling you its removal will make the system safer)
- The Federal Reserve brushing aside the transition to so-called Basel III Endgame that would have required more capital to be held by banks. (Wittgenstein’s ruler alert: the same folks that told you banks would be made safer with higher capital requirements are now telling you banks don’t need higher capital requirements)
- As they did at the end of October, the US Treasury announces a continuation of unprecedented weighting of short-term issuance. TBACRecommendedFinancingTableByRefundingQuarter-05012024.pdf (treasury.gov)
- As we have discussed for months now, the premature end of QT has commenced with the Fed announcing QT tapering at their most recent meeting. https://www.federalreserve.gov/newsevents/pressreleases/monetary20240501a.htm (Wittgenstein’s ruler alert: the same guys that didn’t taper QE stimulus until March 2022, when Core CPI was 6.5%, already 450bp above their target, are now telling you they will commence tapering of QT, removal of stimulus, as Core CPI is at 3.8%, still 180bp above their target)
We now have a couple of new ones to add to that list.
First up, a proposal by Freddie Mac to the FHFA (Federal Housing Finance Association) to start purchasing single-family closed-end second mortgages https://www.fhfa.gov/SupervisionRegulation/Rules/RuleDocuments/FRE%20Closed-End%20Second%20Liens%20Notice%20for%20Web.pdf.
There was a wonderful article, published by the FT, from Meridith Whitney rather effusively praising this proposal. Ms. Whitney closed the article with this beauty of a quote:
“Rarely have I seen such a true win-win scenario for the government, Wall Street and the US consumer.”
We are going to throw out another Wittgenstein’s ruler alert on that one!
And finally, the always reliable interaction between the folks at the Treasury and their TBAC (Treasury Borrowing Advisory Committee) brings us the latest “TBAC Charge”, where the TBAC has been tasked with providing proposals for new product solutions to “expand the investor base in Treasury securities”. TBACCharge2Q22024.pdf (treasury.gov)
The stating of the purpose for the “Charge” in the first two lines of the Executive Summary page is a masterclass in deadpanning.
- “The borrowing needs of the Treasury over the coming years are expected to drive an increase in issuance”.
- “The share of outstanding Treasuries held by its two largest investor types (foreign investors and the Federal Reserve) has been decreasing in recent years”.
In other words, “whose gonna buy the bonds?”
Of the various proposals, one stands out and garners more attention than the others. Callable Bonds!
Figure 3: US TBAC Charge Presentation April 2023. Callable Bonds New Product Proposal
Source: TBACCharge2Q22024.pdf (treasury.gov)
That’s right, the TBAC, predominantly made up of banks, is recommending the US Treasury to issue a structured product. The logic behind this is straightforward. If the buyers of the Callable Bonds can account for them the same way they account for ordinary treasury bonds and, as such, recognize the benefit of the higher coupon created by the embedded selling of optionality, but not hold additional capital against the risk of said sold optionality, well then regulated entities will gobble them right up.
This presentation is definitely worth digging through. There are a couple of extra pages on the Callable Bonds in an appendix that are not to be missed. For those that spent time in banks that are active in the structuring of Callable Bonds, and the management of the Bermudan Swaptions/Interest Rate Swaptions they spin out, this will be a very familiar presentation. The Hunger Games implications of the US Treasury entering the Callable Bonds octagon is something worth contemplating.
Meanwhile, fragility builds. In the perspective of Self-Organized Criticality, what causes the avalanche? The last snowflake.
The below picture, just a simple chart of the EUR/USD 25delta butterfly (the difference between ATM Implied Volatility and the 25delta Implied Volatility), is a great example of how Sharpe World considers risk versus what is actually risk. Sharpe World defines the risk, after the fact, as some unforeseeable exogenous event. We’ve written in red lettering how Sharpe World would explain the major “risk shocks” of recent years. We are all familiar with these unpredictable, hindsight-labelled, events.
Figure 4: EUR/USD 25delta 9mth Butterfly
Source: Bloomberg, Convex Strategies
We would, of course, argue that the actual risk is indicated by the red circles. It is the fragility in the accumulation of snow ahead of the avalanche. It is the fragility in the buildup of combustible material on the forest floor ahead of the wildfire. It is the compression of risk premium through the application of leverage in the procyclical risk and accounting ecosystem of Sharpe World. The unwinds, while arguably triggered by or at least explained away by an exogenous spark, are the results of the reflexivity potential that has built up as the combustible material agglomerates in the system.
We love this picture. It is such a clear visualization of what risk actually is. Overlaying it with something like the 1st VIX future gives a further useful visual of our point that the risk to investment portfolios is truly correlation.
Figure 5: EUR/USD 25delta 9mth Butterfly (white) vs VIX 1st Future Contract. May2007-April2024. Normalized
Source: Bloomberg, Convex Strategies
While we are not in the business of predicting triggers, rather just owning efficient negatively-correlating asymmetry, we do occasionally ponder over the fragilities and familiarities that we see.
If any readers were around for the wonders of the mid to late ‘90s, you might recall a little something that came to be known as the Asian Crisis. One of the telling issues, though not often commented upon, in the buildup to and subsequent unraveling of the currency policies in EM Asia was the strength of USD/JPY from its lows in April 1995 (79.80 where the Fed stepped in to provide a helping hand in intervention) through to the highs in August 1998 (circa 147.50). This USD/JPY strength played a not insignificant role in tearing up managed/pegged currency policies from Thailand in July 1997 through to Malaysia and Russia in Q3 1998 (with shockwaves leading to the downfall of LTCM).
We can’t help but feel a certain amount of nostalgia given the current move of USD/JPY from near 110.00 just 4yrs ago to now touching 160.00 as FX market players continue to revel in the interest rate differential driven incentive to short the JPY. Meanwhile, the more ‘controlled’ currencies in the region have been much steadier against the USD in their respective markets.
Figure 6: USD Spot FX against JPY (white), CNH (blue), KRW (papaya), THB (purple), IDR (yellow), PHP (light blue), TWD (orange). April2020-April2024. Normalized
Source: Bloomberg, Convex Strategies
The one that we have discussed the most, the obvious standout, is China. We represent this below with the USD/CNH FX rate, normalized and compared to USD/JPY.
Figure 7: USD Spot FX against JPY (white) and CNH (blue). April2020-April2024. Normalized
Source: Bloomberg, Convex Strategies
The similarities to what we saw back in the ’95 to ’98 USD/JPY run are hard to ignore. For simplicity sake, we just show the comparison below from the initial part of that period to USD/KRW but could, of course, do the same for THB, IDR, PHP, MYR, etc.
Figure 8: USD Spot against JPY (white) and KRW (papaya). May 1995-20Oct 1997. Normalized
Source: Bloomberg, Convex Strategies
If we extend that chart by just a few months, we get the result (just one example of many) that led to the subsequent labelling of the “Asian Crisis”. We remind readers of one of our core axioms: “Pegs end badly. All pegs end”.
Figure 9: USD Spot against JPY (white) and KRW (papaya). May 1995-Feb 1998. Normalized
Source: Bloomberg, Convex Strategies
Don’t get us wrong. We aren’t predicting an imminent end to the current peg being imposed by the Chinese authorities. We are simply stating the fact that pegs are inherently fragility-building and prone to reflexivity if/when they become unsustainable, whether voluntarily or otherwise.
From an investment and risk management perspective, it comes down to the same thing. Be convex. Contrary to the singular advocacy of Sharpe World, that driving slowly is the only solution to risk mitigation, we are certain that the answer is to put good brakes on your car so that you can, safely and confidently, drive faster.
One of our like-minded friends, Ronald Lagnado, over at Universa Investments wrote a nice note on the topic of slow driving. Mr. Lagnado was formerly a part of the team over at US behemoth pension plan CalPERS. He leads his note off with the clear unkept secret of the pension industry.
Universa Research – 60/40 with Leverage
“Most investors recognize that diversified portfolios, such as the traditional 60/40 (equity/bond) allocation, are very likely to underperform all-equity portfolios in the long run. Additionally, the recent bond-market rout starkly illustrates that bonds may not only fail to hedge but can exacerbate portfolio losses. Yet, because of aversion to large equity drawdowns, investors have clung to the 60/40 approach despite the drag on performance. I experienced this firsthand while managing asset allocation at CalPERS where (along with many other pension funds) significant underfunding persisted, despite one of the largest stock-market rallies in history over the past 15 years.” Ronald Lagnado, Universa Investments, April 2024.
We would add, even during the portion of that period when bonds were also in the midst of a multi-year bull market, those pensions were also still underfunded.
The crux of the paper is to show that levering up a 60/40 portfolio to something that has the equivalent volatility of 100% equity, while generating moderately more return over the backward testing period, isn’t really worth the extra risk that you were taking and would be taking going forward. It is, obviously, highly dependent on the trend declines in interest rates, historically low bond market volatility and somewhat anomalous negative correlation of bonds with equities during a significant portion of the back test period. This has not been the case during large blocks of the back testing period and particularly not the case in the most recent years. There is no certainty that it would be the case going forward.
The paper concludes with the same point that we relentlessly make.
“The levered 60/40 portfolio is in effect just an exercise in raising the equity allocation towards or back to 100% and overlaying a bloated financed position in bonds as an inefficient and unreliable hedge against equity drawdown.
Investors would be better served to increase their equity allocation and instead add a small allocation to a more capital efficient and effective tail-risk hedging strategy. This would actually raise the compound returns while reducing drawdown risk.” Ronald Lagnado, Universa Investment, April 2024.
Sadly, the paper ends there without providing any analysis on the benefits of the explicit hedging, plus more participating risk, strategies. Fortunately, it is easy enough for us to jump in and help out on that front.
In the below chart we have created various hypothetical portfolios and represented them in a grid based upon the upside beta (X-axis) vs the downside beta (Y-axis), ie their relative participation to the upside/downside of S&P Equity Index and used bubble size to represent terminal capital. You can see the examples from the Universa paper, of 60/40 (equities/bonds), 100% equities, and the 100/60 (1.60x levered 60/40), all line up almost perfectly on the 45degree line where the upside beta and downside beta are more or less equal. This is what we mean by driving slowly. To reduce the downside beta, you forego upside beta. You take power out of the engine and merely slide up and down the 45degree line.
Figure 10: Hypothetical Investment Strategy Performance. Upside Beta (X-axis). Downside Beta (Y-axis). Terminal Capital = Bubble Size. Jan 2005 – April 2024
Source: Convex Strategies, Bloomberg
What we would dub a “good” risk managed strategy would appear below the 45degree line, indicating that for a given amount of upside beta the strategy has relatively less downside beta, or vice versa, eg for a given amount of downside beta the strategy has more upside beta. This, in a nutshell, is positive convexity.
Hypothetical strategies, for example like the S&P Risk Parity 10%Vol Index and the Endowment Index, that rely on Sharpe World tenets of stable correlations and leverage, end up above the line, with relatively small terminal capital outcomes. They are foregoing upside beta to get less than the equivalent side-stepping of downside beta.
Using the CBOE Eurekahedge Long Volatility Index, an index of active long volatility managers, as our LongVol proxy for explicit hedging, we can construct some simple convexity-superior hypothetical investment strategies.
Our old friend the Dream Portfolio, in the above example, consists of 60% S&P equities, 20% Gold, and 20% Long Volatility Index. Simply imagine replacing the 40% in bonds from a 60/40 portfolio with equal 20% weights in Gold and LongVol. This hypothetical portfolio drops below the line, almost directly below the 60/40 bubble, indicating that for roughly the same amount of upside beta the hypothetical Dream Portfolio has less downside beta, and a noticeably larger bubble.
On the lines of a similar reconfiguration of the traditional 60/40, we could reallocate the 40% in bonds equally across more S&P equities and the LongVol proxy. This gives us what we have dubbed the 80/20 Barbell. The bubble for this one shows roughly the same downside beta as the Risk Parity Index but with quite a bit more upside beta. Similarly, when compared to the Endowment Index, the 80/20 Barbell has very similar upside beta but far lower downside beta. Not surprisingly, 80/20 Barbell has superior terminal capital.
Finally, what about the 1.6x levered version of 60/40 from the Universa example, the 100/60 equities/bond portfolio? As you can see from its position on the 45degree line, there hasn’t been any risk-benefit from the levered bond position, and only marginal compounding benefit despite the significant leverage deployed. We can apply a similar amount of leverage to a convex investment strategy along the lines of our old favourite, the Always Good Weather (AGW) Portfolio. In this hypothetical example, we have matched the 60% bond allocation with a 60% allocation to the LongVol Index and taken advantage of the large explicit risk reduction by dialing up theoretical our upside beta by moving 50% of the equity allocation into Nasdaq100 Index. This moves, what is a noticeably larger bubble, significantly below the 45degree line.
One more axiom – “when you are convex, more risk is less risk”.
Proper risk mitigation/brakes allow one to, safely and confidently, take on more upside participation/drive faster. Of all the multitude examples of Wittgenstein’s ruler, few stand out as obviously as anybody advocating the Sharpe Ratio as a metric for investment performance. If you hear Sharpe Ratio, it is telling you more about the ruler than about the table.
Read our Disclaimer by clicking here