As Deep Thought revealed the classic sci-fi comedy novel The Hitchhiker’s Guide to the Galaxy, the ultimate answer to life, the universe and everything is 42.
But the fictional supercomputer dreamed up by British author Douglas Adams had an easy question compared to the real-life conundrum pondered by early 20th century polymath Frank Ramsey: how many people should you invite to a party?
Specifically, Ramsey sought to solve the riddle of how many guests would be required to guarantee that a certain number know each other, and a certain number do not.
For small gatherings the answer to the so-called ‘friends and strangers’ theorem is simple and exact: to guarantee your party has at least three acquaintances and three who are unknown to each other, for example, a guest list of six would suffice.
The ‘Ramsey Number’ solution, however, very quickly spirals out of control as the stranger-friend variable rises. Maths buffs can only confirm your invite list should number at least 43 and no more than 48 to ensure a minimum group of five friends and five strangers.
Beyond the five-and-five limit, however, the Ramsey problem becomes intractable. Indeed, another mathematical savant, Paul Erdős, later joked that if aliens landed on Earth demanding humanity solve the six-six Ramsey Number, we’d need to shoot the aliens.
In 2020 a pair of mathematicians significantly lowered the uncertainty factor for a special class of Ramsey numbers defined as ‘multicolour’.
Yet almost 100 years since the Cambridge University-based genius first posed the question, cocktail party-planners looking to guarantee at least five guests are friends and five are strangers still have to invite no more than 48 people and a minimum of 43.
Figure 1: Ramsey theory and the roots of unity
Yield curve invites trouble
Ramsey, however, was not principally concerned with improving the conversational quality of social gatherings. His theory offered a profound proof that large, seemingly chaotic systems must encompass some pockets of order.
The same is true of global financial markets, which can deliver reliable long-term returns despite the apparent random day-to-day disorder.
Nonetheless, investors of late have some reasonable concerns that chaos might hold the upper hand as central banks ‘move fast and break things’ while the surge in real yields tests the weakest links in the financial system.
Financial metrics might dominate the media chatter but the more important signal for investors always hinges on fundamental economic reality.
For investors today, the big question remains whether a US recession is looming or if a ‘soft landing’ remains feasible.
Investors of late have some reasonable concerns that chaos might hold the upper hand
And the global economy is flashing undeniable signs of rate-related stress such as rising delinquencies in US consumer loans, a spike in corporate bankruptcies across the world while ratings agencies warn of a coming surge in debt defaults.
Recession-istas point to the current state of the yield curve, which first inverted in mid-2022, as evidence an inevitable economic slowdown is close; on the other side of the coin, strong employment and consumer spending data continues to defy the doomsters.
History suggests, though, that something must give when the yield curve rights.
The yield curve can un-invert in one of two scenarios: under the ‘bull’ case, short rates drop to re-establish the logical relationship between time, risk and money; in the ‘bear’ reversion, long rates increase.
Logically, the ‘bull’ option offers a strong recession indicator, especially if central banks wait for employment data to crack before cutting rates.
Bear-based yield curve reversions tend to send more complicated, mixed messages to investors. Higher rates at the long end might reflect broad economic resilience; at the same time, an upwards spike in long-term rates could further tighten financial conditions, potentially pushing a fragile economy over the edge.
As the chart below tracking volatility in the US 30-year treasury market illustrates, investors are increasingly angsty.
Figure 2: The MOVE Index vs. USD Swaption 1Y30Y (showing 30 -year volatility)
Investors should note the shift in rates volatility action from the short- to the long-end of the market.
During the first 10 days of October, for instance, the key 10-year US Treasury rate oscillated between about 4.5% and 5%1 in rapid succession as investors repriced risk on the back of data points and intensifying geopolitical friction – the Gaza Strip war adding to ongoing conflicts in sub-Saharan Africa and Ukraine while US-China tensions wound tighter still.
Possibly, more volatile Treasury markets (which feature $25tn of outstanding contracts) portend a higher term premium with significant consequences for all financial assets.
Debt on the rocks and a volatility mixer
We need to put the current volatility into perspective, however.
As documented in a previous Fiorino, recent trends showing stress in corporate and consumer debt remain consistent with a period of ‘credit normalisation’ in the system after several years of deep, low-rate policy-induced hibernation.
Of course, investors and monetary authorities are closely watching potentially vulnerable sectors – commercial real estate and ‘shadow’ banking, for example – for evidence of contagion but compared to previous cycles the underlying macro-financial system sits on a much more even keel.
Rather than expecting an exact answer (42), we should be prepared for a range of outcomes based on a detailed analysis of the facts at hand that, as Ramsey said, can make “several things clearer” (43 to 48, perhaps) but “cannot make anything clear”.
In life, as in maths, Ramsey, showcased the uncertainty principle. He died in 1930, aged just 26.
1 Bloomberg as at 11 October