“Situations of uncertainty and intractability rule out optimization and, along with it, the usefulness of the theory of maximizing subjective expected utility.” Gerd Gigernzer, November 2024.
The rationality wars: a personal reflection | Behavioural Public Policy | Cambridge Core
We linked to this wonderful paper from Gerd Gigerenzer, and paid homage to it with our choice for the title, in our November 2024 Update – “Rationality Wars” Convex Strategies | Risk Update: November 2024 – “Rationality Wars”. This particular quote, however, is what we devoted the bulk of our thoughts to in our May 2025 Update – “Just Do It” Convex Strategies | Risk Update: May2025 – “Just Do It”.
Back in the May “Just Do It” note, we referenced some of the wonderful research done by Singapore’s Sovereign Wealth Fund (GIC), in collaboration with JP Morgan Asset Management (GIC-ThinkSpace-Building-A-Hedge-Fund-Allocation.pdf), noting how nicely the research aligned with some of the heuristic decision rules championed by Gigerenzer, as opposed to the far more common application of expected utility methodologies. It is a good note, worth a read if you missed it.
We bring it up again here because, conveniently, GIC just came out with their annual disclosures of their long-term returns, giving us a chance to peak in and see if last year’s research epiphany, i.e. use explicit loss mitigation as your key diversification tool freeing more capital to participate in markets, has filtered through into improving results GIC’s 20-year annualised real return dips to 5-year low of 3.8%, warns of volatile returns ahead – CNA. Sadly, that does not seem to be the case.
As ever, GIC give a beautifully produced overall presentation at their website GIC Report on the Management of the Government’s Portfolio for the Year 2024/25. Unfortunately, as nice as it all looks, the overall report is in our opinion really nothing more than an exercise in classic Sharpe World obfuscation.
They provide the below two tables with the Nominal Return and Volatility over 5, 10, and 20-year periods for both their own portfolio, the GIC Portfolio, and their Reference Portfolio, a 65/35 portfolio of global equities and global bonds.
Figure 1: Normal Annualised Return and Volatility of GIC Portfolio (in US$, for periods ending 31 March 2025)
Source: GIC Report on the Management of the Government’s Portfolio for the Year 2024/25
Figure 2: Normal Annualised Return and Volatility of Reference Portfolio (in US$, for periods ending 31 March 2025)
Source: GIC Report on the Management of the Government’s Portfolio for the Year 2024/25
Throughout the Report, anytime they mention the Reference Portfolio, it is always caveated with the point that it is not a “performance benchmark” but, rather, representative of the risk appetite they are mandated to undertake by the “Client” (the Singapore citizens whose wealth they manage).
“The Reference Portfolio is not a performance benchmark for the GIC Portfolio but represents the risk the Client is prepared for GIC to take in generating good long-term investment returns. On occasions when we are more risk-averse than the risk profile of the Reference Portfolio, such as when market exuberance leads to heightened valuations, we may lower our risk exposure. Conversely, we may increase our risk exposure when the opportunity arises.” GIC Report, July 2025.
The number of times they reiterate this point could lead one to think that they are a tad sensitive about performance comparisons between the two. Per the above quote, they spend much of the report justifying why they have been prudently driving slowly, consistently and increasingly undershooting the risk appetite assigned to them by the Client. Over the last 5, 10, 20 years, they have been leaning risk averse.
All very standard Sharpe World behaviour. Drawdowns were unforeseeable events, usually shocks to correlation assumptions and corresponding surprises in volatility, while explicitly foregone upside is explained away as prudent slow driving. In reality, it is all just the inevitable result of targeting the compounding-path-destroying premise of the Sharpe Ratio. The Wittgenstein Ruler of the financial industry.
As some say, you can’t eat Sharpe Ratio.
They stress throughout the report that the GIC Portfolio is even more diversified than the simple 65/35 Reference Portfolio. One might suspect this is something like Risk Parity being more diversified than a simple Balanced Portfolio yet, over time, only contributing greater volatility drag to the compounding path. Much like so many of the advocates of traditional investment practices, the Report, in stressing the challenges of an ever more uncertain and volatile world, exclaims that they are making every effort to diversify better. We, of course, would advocate adding convexity.
One of their most Sharpe Worldy representations in the report is shown in figure 3, an image of two probability distributions. The intent is to show the benefit in reduced volatility (standard deviation), aka ‘risk’ in Sharpe World, due to the enhancement of diversification. Of course, this is all just hypothetical and is represented in their well-constructed image as though there is no impact on the mean return, and a perfect symmetry in what they are giving up on the upside to reduce the risk on the downside, not to mention the fact that what they represent as the ‘tail’ isn’t really the tail.
Figure 3: GIC Portfolio Diversification Benefit
Source: GIC Report on the Management of the Government’s Portfolio for the Year 2024/25
If, however, we took the actual returns and volatility from the GIC Portfolio and the Reference Portfolio over the last 5 years, the two distributions tell a somewhat different story. Obviously, the rolling average annualised returns do not line up perfectly, as they do in the above image, and what they are, usually explicitly, foregoing to the upside is much greater than what they are, probabilistically, reducing on the downside.
Figure 4: GIC 5yr Portfolio Distribution: Actual vs Reference
Source: GIC Report on the Management of the Government’s Portfolio for the Year 2024/25. Convex Strategies
This visualization shows why those desiring compounded wealth need to steer clear of Sharpe Ratio optimizers. As we stated above, said optimizers are explicitly foregoing the upside to probabilistically reduce the downside. The downside mitigation, in general, is reliant upon assumptions of stable correlations to achieve those ex-post presumed diversification benefits. This is what leads to concave portfolio construction and the accompanying volatility drag. The enemies of compounding.
This is what we discussed in the “Just Do It” note and what GIC’s own research shows GIC-ThinkSpace-Building-A-Hedge-Fund-Allocation.pdf. In their Total Portfolio Approach methodology, when trying to evaluate diversifying strategies based on their benefit to the overall portfolio, 100% of the allotted allocation (they capped the potential allocation at 20%) goes to “Loss Mitigation” strategies, and that gives enough total risk reduction to even reduce somewhat further the bond holdings and allow a small increase in participating assets. Only explicit negative correlation provides a benefit. In other words, all other of the assumed low-correlation diversifying strategies in the chosen Hedge Fund universe (Equity, Credit, Event Driven, Relative Value, Multi-Strategy, Commodity, Macro, Managed Future) that did not qualify as a “Loss Mitigation” strategy (i.e. negatively correlating), would be allotted an allocation of 0%, and you would replace the full 20% limit of your existing bond allocation. Think about that.
Figure 5: GIC/JPMAM Portfolio Optimization to Sharpe Determinant. Jan2005-Dec2023
Source: JPMAM, GIC, HFR, Pivotalpath
An even more telling outcome shows up in our extended version of their analysis when we add what we dubbed “Explicit Loss Mitigation”, in the form of Long Volatility strategies (the EurekaHedge Long Volatility Index) and optimised to Sortino Ratio (downside volatility) instead of Sharpe Ratio (volatility). Our conclusion now shifts the entire 20% allocation over to the Explicit Loss Mitigation and allows for the entire remaining 20% allocation to bonds to be switched over to the participating asset of equities. Greater negative correlation, greater convexity, more reliability, equals greater benefit to the portfolio, again over the same time period used in the GIC / JPMAM paper.
Figure 6: Portfolio Optimization, including Explicit Loss Mitigation, to Sortino Ratio Determinant. Jan2005-Dec2023.
Source: Bloomberg, Convex Strategies
We can also compare where various hypothetical strategies are over a 20-year compounding path. We will set as the target return the realized return, 6.2%, of their 65/35 Reference Portfolio (we have constructed this using the Net MSCI World Total Return Index {NDDUWI Index} and the Global Bond Aggregate Total Return Index {LEGATRUU Index}. For a proxy of the GIC Portfolio we will use a 53/47 weighing of the same global equities and global bonds which aligns to their 20yr rolling return of 5.7%. Taking from our extended version of the GIC Total Portfolio Approach research, we will add a Barbell Portfolio that is 80% in Global Equities and 20% in the EurekaHedge Long Volatility Index (EHFI451 Index).
Just as GIC found in their research, the superior look-back answer was to replace the assumed diversification benefit of all of their diversifying strategies with explicit loss mitigating strategies, then take more participating risk. In our theoretical example, The Barbell Portfolio wins with actual risk measures (eg. Downside Volatility, Max Drawdown, Downside Beta) all in line with the delegated risk appetite of the Reference Portfolio.
Figure 7: 20yr Hypothetical Compounding Paths vs Target Return. Reference Portfolio (light blue). Proxy Portfolio (dark blue). Barbell Portfolio (gold). Preservation Portfolio (Fuchsia). Apr2005-Mar2025
Source: Bloomberg, Convex Strategies
All will have noticed, and we should point out, that we have added a fourth strategy which we have dubbed the “Preservation Portfolio”. Of course, it is easy to do with hindsight but imagine if we could go back in time and advise GIC on their portfolio. Throughout their Report, they stress that their “mission is to preserve and enhance” the capital they have been entrusted with.
An advisor, back at the beginning of this period, might rationally had stressed focusing first on the preservation aspect. Let’s start with really strong defensive allocations. In our hypothetical Preservation Portfolio we have made that part of the allocation 25% to Gold (GLD US Equity) and 25% to Explicit Loss Mitigation, again using the EurekaHedge Long Volatility Index. In our race car analogy, we’ve started by putting really good brakes on the car. Next step is the enhance part, how do we figure out how to drive fast.
Now that the preservation is locked in, the investment team is freed up to stop worrying about all the external exogenous stuff, all the unknowable future events that can be viewed as risk instead of recognizing that risk is the portfolio, the race car. Now that the actual risk is theoretically dealt with by the substantial allocation to actual risk preservation strategies, the investment team can get on with their job of enhancing. The advisors might rightly instruct them to focus on innovation and growth; focus their participating investments on technological and productivity enhancing businesses that will make the world a better place.
We have used as a proxy for this, in the hypothetical Preservation Portfolio, the Nasdaq 100 Total Return Index (XNDX Index) and selected a 50% weighting. This is just a proxy. The point is that an investment team should focus, whether that be publicly listed growth stocks or private and venture capital opportunities of the financial or real nature, on things that really a) have the potential to change the world (new technologies, new productive means, new energy solutions, new demographic solutions) and b) participate convexly in upside value creation. The whole point of the defensive allocation is to free up the right resources to pursue the upside. Stop paying people to drive slowly. Hire really good drivers and give them a car with really good brakes.
The hypothetical Preservation Portfolio lives up to its name. It has far less Downside Volatility, far less Max Drawdown, far less Downside Beta, than not just the Reference Portfolio but even the persistently risk-averse Proxy Portfolio. Yes, the Preservation Portfolio has the benefit of hindsight, however the principal remains true: fit good brakes on your race care so you can, safely, drive faster. Just do it!
Ever so slowly, the investment world is starting to figure some of this out. For example, see the below article referencing recent changes coming out of the University of California system.
UC Dumps Hedge Funds, Ups Public Equity Allocation
“The $190B University of California’s endowment and pension fund is divesting from hedge funds due to its inadequacy in providing risk protection…During its July meeting, the board approved a plan to slash, for both the endowment and the pension plan, its 10% target allocation to its absolute-return portfolio, or hedge funds portfolio…UC’s chief investment officer noted the plan’s hedge fund positions had weakened its overall performance by injecting risk during market tensions in 1999, 2008, and 2020.”
Of course, the problem isn’t hedge funds, per se, but rather absolute return strategies. Strategies spinning low correlation benefits, almost certainly optimizing to Sharpe Ratio metrics. More often than not, their low correlation only sustains in good market environments, again explicitly foregoing upside, only to find out that their correlation rises in bad market environments. Their correlation is concave to the market. They seem to be getting the picture that they need to drive faster and relying on assumptions of stable correlations hasn’t much worked as a risk mitigation strategy in tough times. It is unclear, from the article, if they have figured out the value of good brakes.
All of this ties back to one of our most repeated refrains – “history alone is a poor measure of risk”. Historical returns only tell you what did happen, not what could have happened. And really nothing about what could happen going forward. A a simple representation of this is the picture we show regularly of various CBOE volatility indices.
Figure 8: CBOE Volatility Indices. PutProtect (blue). Buffer (papaya). PutWrite (yellow). BuyWrite (red). Compounding Paths. Jan2013-July2025. (Normalized and log-scaled)
Source: Bloomberg, Convex Strategies
We always make two key points when showing this picture. 1) Selling volatility (providing non-recourse leverage) is risky but can be profitable. Despite the visible sharp drawdowns, all three strategies that are net volatility sellers (Buffer, PutWrite, BuyWrite) have been profitable over the period. However, buying volatility, taking on non-recourse leverage, and assuming the risk you are protecting against (PutProtect), at least over the above noted period, is more profitable. 2) Even on an historical performance basis, the what-did-happen perspective, the PutProtect had less risk and more return than the other strategies. But, on a what-could-have-happened perspective, it was even better. It always had more potential upside participation, if markets had performed even better, and always had more potential downside protection, if downside shocks had been even more severe. Put simply, it had the best risk/reward in all other parallel universes. It optimizes, relatively speaking, to possibility distribution, as opposed to the mean of the probability distribution.
For one of the all-time classic notes on the concept of multiple universes, written in the sphere of quantum mechanics, we would refer interested readers to peruse this note from Eugene Wigner, “The Problem of Measurement”. It is a masterpiece.
This is a real head spinner of a paper and was/is very controversial in the world of Physics. It proclaims that there are, in reality, multiple universes and the act of measurement merely produces one instantaneous version and that is a version that itself has been impacted by the act of measurement.
“The problem of a measurement on the object is thereby transformed into the problem of an observation on the apparatus…the fundamental point remains unchanged and a full description of an observation must remain impossible since the quantum-mechanical equations of motion are causal and contain no statistical element, whereas the measurement does.” Eugene Wigner, 1962.
This ties back to our core premise on risk management. Risk isn’t what you think, probabilistically, is likely to happen. Risk is what hurts, if it happens. Quoting our friend Hari Krishnan; “Risk is about vulnerability, not predictability”. Risk is your balance sheet, your portfolio, your car, your house, your health. Manage those, don’t pretend to be Rational Economic Man with some mythical ability to calculate the probability of future outcomes in a world of uncertainty, intractability, and ambiguity.
Regular readers may recognize that we borrowed from the Wigner title in our own September 2021 Update – “The Challenge of Measurement” Convex Strategies | Risk Update: September 2021 – The Challenge of Measurement., a piece that is in essence our ode to Benoit Mandelbrot. We also linked to Wigner’s beautiful note, “The Unreasonable Effectiveness of Mathematics in the Natural Science”, also while discussing Mr. Mandelbrot, in our December 2023 Update – “It’s Just Math” Convex Strategies | Risk Update: December 2023 – “It’s Just Math”. Both are very worthwhile reads, we believe.
In the latter of those two notes, we referenced this quote from Wigner:
“The world around us is of baffling complexity and the most obvious fact about it is that we cannot predict the future.” Eugene Wigner, 1960.
We cannot know the future. The best we can hope for is to understand where we are, the now, the current state of initial conditions. This is why we call ourselves observers, not predictors.
Following up on some of the observations that we have been tracking, as relates to challenges in global imbalances, things that we think are key drivers to how we’ve arrived at the current state of initial conditions, leads us to these two recurring, and related, themes. First, the implications of what we have analogised as the “Hunger Games”. The competition to fund existing and growing debt, along with domestic investment priorities, leading to what our friend Russell Napier has dubbed “Capital Nationalism”. Second, and we think it is what undergirds everything that is challenging in the world, we will touch on some further thoughts on population demographics.
We have taken to capturing articles, speeches, announcements that we classify under “repression watch”, keeping an eye out for the proliferating instances of governments hinting at ways to capture/trap domestic savings and institutions to fund national priorities.
As Keynes put it in 1933; “let goods be homespun and above all, let finance be primarily national”.
Here is a recent slate of things that fit that list.
From Scott Bessent, US Treasury Secretary, on relaxed capital requirements for US banks.
“… I intend for Treasury to drive financial regulatory policy that puts American workers first, prioritizes growth, safeguards financial stability, and protects our national security.” Scott Bessent, July 2025.
From Rachel Reeves, UK Chancellor of the Exchequer at her Mansion House speech.
Rachel Reeves Mansion House 2025 speech – GOV.UK
“… since last year, funds covering the majority of the Defined Contribution market have committed to the Mansion House Accord…pledging to invest 10% of their main funds into private assets such as infrastructure and growth markets…with at least half of that going into UK projects.” Rachel Reeves, July 2025.
From a superannuation lending roundtable, attended by Australian Treasurer Jim Chalmers.
Productivity summit: Super lending for corporate debt part of Jim Chalmers’ challenge
“Tapping the super funds’ pools of capital to unlock business investment and unleash productivity growth is an idea whose time may have come.” Australian Financial Review, July 2025.
Maybe most notably from Germany and Chancellor Friedrich Merz.
German firms launch ‘Made for Germany’ investment initiative | Reuters
“The investment tasks we are facing cannot be achieved by public budgets alone. On the contrary, the lion’s share must be provided by private investors.”
If you have the good fortune of subscribing to the unparalleled work of Russell Napier, you will likely have seen his most recent note focusing on the “Made for Germany” initiative and tying in the implications across the rest of Europe, in particular France, as well as the likes of China and Japan. He sums up our premise on the Hunger Games with his usual succinct clarity.
“Capital Nationalism is a force for the repatriation of capital that will be prolonged and play a key role in the breakdown in the current global monetary system and ‘Made for Germany’ is Capital Nationalism.” Russell Napier, August 2025.
Finally, on the topic that occupies more and more of our thinking and research – population demographics. We are forever amazed that this is not issue #1 on all discussions on economic and market challenges of our times. It is reasonably easy to make the case that is the very underlying issue that has a been the dominant driver of today’s economic and financial fragilities. We have taken to proclaiming that “financial repression and fiscal dominance aren’t merely the tools of the future, they are how we got to where we are now”.
We have touched on this many times in past writings, but the one that should really have caught everybody’s eye was the UN chart that we pulled out from Mario Draghi’s European competitiveness review back in our September 2024 Update – “Emergence” Convex Strategies | Risk Update: September 2024 – “Emergence”.
Figure 9: Long-term population developments and projections
Source: United Nations Population Prospects 2022.
We said this in that note: “As interesting as the blue European line is, it is hard to ignore the implications of what is to come in China.”
We can simplify our thoughts down to this very basic premise, as relates to the countries doomed to fight this challenge, every year, for the foreseeable future; there are going to be fewer taxpayers, significantly fewer cohorts in the critical group dubbed working-age population. As population pyramids invert, as dependency ratios (more non-workers, e.g. retirees, relative to workers) increase, the need to subsidize ever more non-workers, while collecting taxes from ever fewer workers, has some pretty obvious implications. Not least of which might be exactly the kind of financial repression that we have seen for the last couple of decades, give or take, for much of the world.
Figure 10: US Nominal GDP yoy% (white) vs Fed Funds Rate (blue) and US 10yr Treasury Yield (purple). US Federal Debt/GDP (papaya). Since 2001
Source: Bloomberg
If you gave as a simple definition of financial repression, holding interest rates (r) below nominal growth rates (g), commonly written as (r < g), you would have to say we have been under financial repression for most of the last 25 years. Yet, the generally stated purpose of reducing government debt to GDP has resulted in quite the opposite, with the US going from sub 60% to now in excess of 120%. Is it possible that financial repression, which many point to as a successful post-WWII policy in the US, doesn’t work at the other end of the population demographic?
Should we really act as if aging populations and declining fertility rates have had nothing to do with the economic circumstances that we now find ourselves in? Again, we might argue that it alone is the single most important aspect. As we constantly mumble and rant on this topic, we were very pleased to be referred to a piece of work from the G-10, published under the BIS, that very much aligns with our perceptions. Interestingly, this work was done in 1998.
Group of Ten – The macroeconomic and financial implications of ageing populations – Apr 1998
Just taking a few of the key points from their Executive Summary.
- “…demographic developments will have adverse effects on material living standards and will significantly widen budget deficits…”
- “…the burden of adjustment for governments and individuals increases the longer action is delayed.”
- “…reforms should encourage economic growth and the efficient use of resources.”
- “increase national savings and investment. Important in this regard will be further reduction of fiscal deficits and debt, including addressing the problems of funding public retirement and health benefits.
- “increase the supply and efficient utilisation of labour.
- “ensure the efficient allocation of savings both within and across borders.”
- “An immediate increase in the funding of private and public pensions would help to alleviate the potentially severe demographic pressures on existing pay-as-you-go and underfunded systems.”
Well said! Unfortunately, pretty much the exact opposite is what has taken place.
In the simple economic model, we write GDP = C + I + G. From the perspective of the common worker, you can think about it as dividing up his income: what he spends on his cost of living is Consumption, what he saves is Investment, and what he gets taxed is Government. Everything else, e.g. Government above what they collect in taxes, is credit creation, aka inflation. Makes it clear why the G-10 paper advocates for further reductions in fiscal deficits and debt. Fewer workers means fewer taxpayers, which means higher deficits. Higher cost of living means less post-consumption earnings available for savings and investment. Lower investment means lower productivity. Ever greater government support of increasing retired workers, while faced with fewer taxpayers, inevitably brings the issue of fiscal dominance into play. Deficit spending grows mechanically, eventually fueling more inflation as the government finances it, crowding out yet more of the available savings from seeking productive private sector investment opportunities. It is a very dangerous loop to get caught in and it sure seems like a good chunk of the world is in it, and probably has been for the last couple of decades or so.
Here is what we suggest to everybody. Whenever you are reading any sort of analysis about economies, markets, global imbalances, trade wars, fiscal policy, monetary policy, forecasts, projections, just insert in your head, at the end of every paragraph this small extension and then see if it adds additional meaning:
“And for every year going forward there will be fewer taxpayers.”
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